sound_syno and exercise1

8/18/2019 Sound_syno and Exercise1

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SYNOPSIS

1. EQUATION OF PLANE PROGRESSIVEWAVE :

i) y = f(vt – x) represents a progressive wavemoving along positive - x direction.

ii) y = f(vt + x) represents a progressive wavemoving along negative - x direction.

iii) If a travelling wave is a sine or cosine function

of (at – bx) or (at + bx) then the wave is called

harmonic (or) plane progressive wave.

iv) The equation for a simple harmonic plane pr ogressive wave pr opaga ting along the positive direction of x - axis is

Y

O A y(x,0)

X

y A sin t kx , y A sink vt x

t xy Asin2

T

y displacement of the particle located at position 'x' at time 't'.

x Particle position at time 't'

k Propogation constant 2k v) The equation for a plane progressive wave

propagating along the negative direction of x-

axis is y Asin t kx

Note: Analytically any function of space and

time which satisfies the equation

2 2

2 2 2

y 1 y

x v t

must represent a wave.

2. PARTICLE VELOCITY :

i) particledy

v Acos t kxdt

ii) 2 2particlev A y

iii) It will be maximum when y = 0 , maxv A

It will be minimum when y = A, vmin

= 0

3. WAVE VELOCITY (V) :

i) The distance travelled by the wave in one

second is called wave velocity .

ii) Wave velocity V f T k

iii) The wave velocity depends on the nature of the

medium, it does not depend on the nature of the source.

iv) When a given wave passes from one mediumto another, its frequency does not change,velocity and wavelength changes.

In this case

1 1

2 2

V

VNote : During one complete time period (T),

the displacement of the particle is zero while

the wave travells a distance .

4. SLOPE OF THE WAVE :Slope of the wave will be

dy

kAcos t kxdx

particlev

slope of the wave k

v particle = – wave velocity x slope of the wave

5. PHASE :

i) In the plane progressive wave equation

t kx denotes phase.

ii) Phase change with time:The phase change at a given point in time

interval t is2

tT

iii) Phase change with position:

The phase change at a given time for a change

in position x is

2

x

iv) A path difference of' '

corresponds to a phase

difference of 2 radian and a time difference of T..6. MECHANICAL WAVES IN DIFFERENT

MEDIA :

i) In st r ings mechanical waves are alwaystransverse.

ii) In gases and liquids mechanical waves arealways longitudinal. This is because fluidscannot sustain shear.


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iii) In solids mechanical waves can be either transverse or longitudinal depending on themode of excitation.

iv) The speeds of the two waves in the same solid are different(longitudinal waves travels faster than transverse waves).

v) In the case of vibrating tuning fork the wavesin the prongs are transverse.

7. INTENSITY OF A WAVE :

i) The wave intensity is defined as the averageamount of energy flowing in a medium per unittime normal to unit area of cross section.

2 2 2 2 21

a v , 2 f a v2

a amplitude, f frequencyv wave velocity ,

density of the mediumii) In case of a point source of power 'p', at a

distance 'r' from the source, the intensity is given

by 2 2p 1

4 r r

iii) The energy associated with unit volume of the

medium is defined as energy density.

Energy density = 2 2 2energy Intensity 2 f a

volume velocity

8. REFLECTION AND REFRACTION OF

WAVES :

i) Reflection from rigid end : When a wave isreflected from a rigid end there is a phasechange of radians

F

FIn this case if the incident wave is represented

by i iy A sin t kx then the reflected

wave is represented by

r r y A sin t kx (or)

r r y A sin t kx 2) Reflection from free end : When a wave is

reflected from a free end, then there is no changeof phase

In this case if the incident wave is represented by i iy A sin t kx then reflected wave

is r r y A sin t kx

Note : In case of reflection of longitudinal pressure wave there occurs no phase changeon reflection from a rigid boundaries and thereoccurs phase change of radians on reflectionfrom free or open end.

9. STATIONARY WAVES :

i) When two coherent waves of equal ampl i tude

t ravel l i ng through a medi umi n opposi tedi recti ons superpose, the resul tant effect i s awave, whi ch does not travel ei ther way wi thti me, these waves are cal l ed stati onary wavesor standing waves.

10. STATIONARY WAVES PRODUCED ON

REFLECTION FROM THE FREE END :

yi = A sin (wt – kx) y

r = A sin (wt + kx)

y = yi + y

r y 2A Cos kx Sinwt

Amplitude of stationary wave is 2A Cos kx

For amplitude to be maximum

Cos kx 1 , kx n (or)n

x2

(where n = 0,1,2, ...........)

So Antinodes are obtained at

x = 0,2 3 4

, , ,2 2 2 2

..........

For the amplitude to be zero

Cos (kx) =0, kx 2n 1 /2 (or)

x=(2n +1)

4

(Where n =0, 1, 2, 3 . . .. .. .. .)

So nodes are obtained at

x=3 5 7

, , ,4 4 4 4

..............

11. STATIONARY WAVE PRODUCED ON

REFLECTION FROM FIXED END :

yi =A si n (wt – kx) y

r =– A si n (wt +kx)

y =yi +y

r y =– 2A si n kx cos wt


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Ampl i tude of stati onary wave i s – 2A si n (kx)

For the ampl i tude to be maxi mum(Anti nodes)

Si n (kx) =1, kx= 2n 12

x =(2n +1)

4

(where n =0, 1, 2, 3 . . .. .. . .)

Anti nodes are obtained at

x=3 5 7

, , ,4 4 4 4

...............

For the ampl i tude to be zero

Sin (kx) =0, kx =n, x =n

2

(Where n =0, 1, 2, 3 ...........)

Nodes are formed at

x =0,2 3 4

, , ,

2 2 2 2

...........

Note : At free end always anti node i s f ormed.

At f i xed end always node i s f ormed.

STRINGS

12. TRANSVERSE WAVE ALONG

STRETCHED STRING:

i) When a string stretched between two ends is plucked at right angles to it and relea sed,atransverse wave travels along the length of string.

ii) Velocity of transverse wave along stretched string: TV

(T is tension in the string and

is linear density or mass per unit length)

2m ass A d Ad r dlength

Where r is radius of the string, d is the densityof the material of the wire.

V = 2T T

Ad r d

iii) V depends upon tension and linear density, itdoes not depend upon frequency of wave

iv) When the tension in the string arise due to aload of mass M

MgV

[ T = Mg]

v) If the load in the above case is completelyimmersed in liquid then

b

dMg 1

dV

b

dT Mg 1

d

Where d is the density of liquid

bd is the density of material of the load.

iv) When tension in the string arises due to elasticstrain

YAe YAe

V T

YAe Ye

m dWhere m is mass of the string.

vii) When tension in the string arises due to thermalstress. ( by contraction)

F = YA V =YA YA Y

Ad d

viii) A uniform rope of length 'L' and mass 'm' hangs

vertically from a rigid support. A block of mass

'M' is attached to the free end of rope.

A transverse pulse of wavelength B is

produced at the lower end of the rope, the

wavelength of the pulse when it reaches the top

of the ropeT then

T T

B B

V M m M m

V M M

ix) A uniform rope of mass 'm' and length ' '

hangs from a ceiling then

a) The speed of transverse wave in the rope at

a point which is at a distance x from the lower

end is gx

b) The time taken by a transverse wave to travel

the full length of the rope is

2 t g

13. FORMATION OF A STATIONARY WAVE

ON A STRETCHED STRING :When a stretched string is plucked, a transversewave travels along its length, it gets reflected atother end, the superposition of incident and reflected waves form stationary wave.

i) Fundamental mode or first harmonic:The string vibrates in fundamental mode whenthe string is plucked at mid point

The string vibrates in one loop


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A N N

AN one N one

2

2

and

, n =V

,

1 Tn

2

where n is fundamental frequency

ii) Harmonics : The frequencies which are integralmultiples of the fundamental frequency arecalled Harmonics

Ex. n, 2n, 3n, 4n

iii) Overtones : All possible higher frequenciesother than fundamental are called overtones

iv) All harmonics are overtones except first But, allovertones need not be harmonics

v) All overtones may not be integral multiples of

fundamental frequencyvi) Second harmonic or first overtone:–

a) The string vibrates in 2nd harmonic when itis plucked at l/4.

b) The string vibrates in 2 loops

AN two N three

N N N

A A

1 l ,

1

2 Tn

2 , n

1

= 2n

Where n1 is the frequency of second harmonic

or first over tone.

vii) If the string is plucked at length2P

l then the

String vibrates in 'P' loops and we have P th

harmonic (or) (P-1)th overtone.

Pth harmonic (P 1)th overtone

P Tn n

2

2

P

No.ofLoops

No.of antinodes

No.ofnodes

Harmonics Overtone

1 1 2 1

2 2 3 2 1

n n (n+1) n (n-1)

-

viii) When string is plucked at midpoint, odd harmonics are present and even harmonics areabsent

ix) When string is touched at midpoint, evenharmonics are present and odd harmonics areabsent

Note :When the string is subjected to a stretchingforce producing an elongation then

1 T 1 T 1 T

n2 Ad 2 Ad 2 mass of the string x

In this case1

n

x) Laws of vibrating strings:

a) First Law (Law of length)

n1

, 1 1 2 2n n (T,, are constants)

b) Second Law (Law of tension)

n T ,1 1

2 2

n Tn T

( , are constants)

c) Third Law (Law of linear density)

1n

( , T are constants)

14) Sonometer experiment :

Verification of laws of transverse vibrations of

string.

a) Sonometer Box has holes. The purpose of holes

is to dissipate the energy of air inside box into

the surroundings so that resonance does notoccur inside the box.

b) Tuning fork is not brought in contact with string.

c) Vibrations of tuning fork are communicated to

string through platform and bridges.

d) Resonating length of string can be determined

by paper rider method.

e) First law is verified directly,1

n

(law of length)

f) Second law is verified by showing

T l = constant.

(same tuning fork, same wire) (n, constant).

g) Third law is verified by showing

l = constant, (n, T are kept const).

15) Uses of sonometer:

a) To determine velocity of transverse wave alonga stretched string.


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b) To determine unknown frequency of tuningfork.

c) To determine frequency in A.C. circuits.

d) To verify laws of transverse vibrations instretched strings.

16. SOUND (INTRODUCTION) :

i) The mechanical wave energy which can beheard by human ear is known as sound

ii) Sound is propagated in the form of longitudinalmechanical waves

iii) A material medium is necessary for the propagation of sound

iv) Medium must possess elasticity and inertia

Velocity of sound in air at S.T.P is 330 ms -1

(approximately)

v) velocity of sound depends on nature of themedium and temperature of the medium.

vi) Velocity of sound is maximum in solids,intermediate in liquids and minimum in gases.

vii) If a sound wave travelling from one medium toanother medium, its velocity & wave lengthchange, but its frequency remains constant.

17. AUDIBLE SOUND :

i) The limit of audiable frequencies are 20 Hz -- 20,000Hz

ii) Audible wave length range is 16.5 x 10-3m 16.5m.(at STP, in air velocity of sound is330 ms

-1

)

iii) Audible wave length range varies withtemperature of the medium (nature of themedium ).

18 . INFRASONICS : sound waves of frequenciesless than 20 Hz are known as infrasonics

Ex. The waves produced during earth quake and thunders are infrasonics.

Infrasonics can be perceived by elephants and snakes etc.

19. ULTRASONICS :

i) The sound waves of frquency greater than20,000Hz are known as ultrasonics

ii) ultrasonics are produced and perceived by bats.

iii) ultrasonics have applications in industrial and medical fields.

Note : In any given medium at a giventemperature velocity of audible sound,infrasonics and ultrasonics is the same

20. VELOCITY OF SOUND :

i) Velocityof sound is the characteristic of themedium in which waves propagate.

ii) Velocity of sound in a medium of elasticity E

and density ' ' is given by

E

V

iii) As solids are most elastic while gases leastelastic, velocity of sound is maximum in solidsand minimum in gases.

gassolid liquid V V V iv) In case of propagation of sound in solids (rods)

E = Y and

solid Y

V

While for liquids and gases E = B

fluid BV

(B is the bulk modulus)

21. NEWTON'S FORMULA :

i) He assumed that when sound propagatesthrough air, temperature remains constant (i.e.,the process is isothermal)

ii) B = isothermal elasticity = Pressure (P) then

PV

iii) at NTP for air by this formula v = 279m/s. Butthe experimental value of velocity of sound inair is 332 m/s.

22. LAPLACE CORRECTION :

i) Laplace modified Newton's formula. Heassumed that propagation of sound in air is anadiabatic process.

ii) In this case B = Adiabatic elasticity P

iii)P

V

iv) For air at NTP by this formula v = 331.3 m/swhich is in agreement with the experimentalvalue. (332 m/s).

23. IN CASE OF GASES :

P PV nRT RT V

mass mass M

RT V

M

;

3rms

RT V

M ;

1 2

3rms

V

V

/


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24. FACTORS AFFECTING VELOCITY OF

SOUND IN GASES :

i) Effect of temperature :

With rise in temperature velocity of sound in agas increases.

t C V T V V T

V T V t C

0

11 1 1

02 2 2 2

273

273

t

t

V t C t C V V

V

0 0

0

0

2731

273 546

as v0 = 332 m/s hence

00 0.61t V V t C

For 10C rise, speed of sound in air increases by0.61 m/s.

ii) Effect of pressure (at constant temperature) :

Pressure has no effect on velocity of sound in agas as long as temperature remains constant.

iii) Effect of humidity :

a) With increase in humidity, density of air decreases. So, with increase of humidityvelocity of sound increases.

b) Sound travels faster in humid air (rainyseason) then in dry air (summer) at thesame temperature because

moist air moist air dry air dry air V V

Note:Amplitude, frequency, phase, loudness, pitch. Quality etc., have practically no effecton velocity of sound.

25. FREE VIBRATIONS :

i) When a body is excited and left free to itself , it begins to vibrate and the vibration of the bodyare called free or natural vibration.

ii) The frequency of vibrations depends upon thedimensions of the body and the elastic constant

of the material of the bodyiii) Ex: Oscillations of simple pendulum in vacuum,

vibrations of prongs of a tuning fork in vacuum

26. FORCED VIBRATIONS :

i) Vibrations in a body under the influence of external periodic impulses

ii) Vibrations of factory floor when heavymachines are working

iii) The diaphragms of loud speakers when wespeak in front of it execute forced vibrations.

iv) Sympathetic vibrations : When a body vibratesunder the influence of external periodicimpulses whose frequency is equal to its naturalfrequency, those vibrations are called

sympathetic vibration.27. RESONANCE :

i) It is the phenomenon in which system makessympathetic vibrations with max amplitude(theoritically infinite amplitude)

ii) This does not violate the law of conservationof energy

iii) Ex: Soldiers are advised to go out of steps whilecrossing a bridge to avoid breakage of bridgedue to resonance

iv) Ex: A great singer can shatter a glass object by

his singing.

28. STANDING WAVE IN A ORGAN PIPE

(VIBRATIONS OF AIR COLUMNS) :

i) The mechanical waves in an organ pipe are

longitudinal stationary.

ii) In organ pipe, harmonics are formed with a

displacement node at closed end and with

displacement antinode at free end.

29. CLOSED ORGAN PIPE :

AN

l

NFundamental

AN

AN

N

N

l

First overtone

AN

N

AN

N

AN N

Second overtone

l

1

1

vl = ,n =

4 4 l

2

2

3 3vl = , n =

4 4 l

3

3

5 5vl = , n =

4 4 l

i) Fundamental frequency is

C

V f

4ii) In closed organ pipe, only odd harmonics are

present.

iii) Ratio of harmonics is 1 : 3 : 5 : .........

iv) First harmonic is fundamental, third harmonicwill be first overtone.

(pth overtone = ((2P+1)th harmonic)

v) The maximum possible wavelength is ' 4 '


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vi) In general N

4

2 1

where N = 1,2,3 ....

corresponding to order of mode of vibration.

vii) Frequency n =

N V 2 1

4 where N = 1, 2, 3

...... corresponding to order of mode of vibration.

viii) Position of node from closed end,

x = 0, , ,

3

2 2 .........

ix) Position of antinodes from closed end

x = , , 3 5

4 4 4 .........

30. OPEN ORGAN PIPE :

AN

N

ANFundamental

AN

N

AN N

ANFirst overtone

AN

NAN

N

AN

N

ANSecond over tone

11

v,n

2 2l 2 2

v,nl

l

3 3

3 3v,n

2 2l

l

i) Fundamental frequency is f 0 =

V

2ii) In open pipe, all (even and odd) harmonic are present, the ratio of harmonics is 1:2:3:4:.....

iii) First harmonic is fundamental, second harmonicwill be first overtone and so on (p th overtone =(p +1)th harmonic).

iv) The maximum possible wavelength is ' 2 '

v) Wa velength N

2

(N = 1,2,3 ......

corresponding to order of mode of vibration)

Frequency n =

NV 2

vi) Position of nodes from one end

, , x

3 5

4 4 4 ........

vii) Position of antinode from one end

x = 0, , ,

3

2 2 ..........

31. END CORRECTION :

i) Due to finite momentum of air molecules inorgan pipes reflection takes place not exactlyat free end but slightly above it.

ii) The distance of antinode from open end is called

end correction and e = 0.6r where 'r' is radius of pipe.

iii) For closed organ pipe effective length

L| = (L+e)

iv) For open organ pipe effective length

L| = (L+2e)

v) Hence with end correction fundamental

frequency of closed pipe f C = .

V

L r 4 0 6

Fundamental frequency of open pipe

.V

f L r

02 1 2

32. RESONANCE TUBE :

i) In a resonating air column experiment, if ,1 2

are the first and second resonating lengths then

e

14

, e

23

4

2 1

2

2 12

ii) Speed of sound in air at room temperature is

V n 2 12 Where n be the frequency of the tuning fork.

iii) e

2 13

2

33. TUNING FORK :

i) Tuning fork is a device which produces puretone

ii) Transverse vibrations are present in the prongs

iii) longitudinal vibrations are present in the shank iv) If small mass is added to one of the prongs,

frequency decreases due to increase in inertia.

v) If small mass is removed from the end of the prongs frequency increases due to decrease ininertia.

vi) When a tuning fork is heated, its frequencydecreases due to decrease in elasticity.


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BEATS

34. BEATS : When two sound waves of slightlydifferent frequencies travelling in same directionsuperimpose together, the resultant sound waxesand wanes at regular intervals of time. Thiswaxing and waning of sound is called beats.

i) The phenomenon involved in beats issuperposition of waves.

ii) Beat frequency = no. of maxima heard per second = no. of minima heard per second = no.of beats per second = n

1 ~ n

2n

1, n

2 are frequencies of parent sounds.

iii) As persistence of hearing is 0.1 sec, max no. of beats that can be heard per second is 10. (If thedifference in frequences greater than 10Hz, beats are formed but not heard)

iv) If n1 and n

2 are the frequencies of the two sound

waves combined to produce beats, the

combined wave has a frequency 1 22

n n

v) The amplitude of combined wave varies from0 to 2a if the amplitude of each wave is 'a'.

vi) The frequency with which the amplitude of

combined wave changes is1 2

2

n n

vii) Beat frequency = n1 ~ n

2.

viii) Beat period =1 2

1~n n

= Time interval between

two consecutive maxima (or) minima.

ix) Time interval between maxima and next minima

is 1 2

1

2 ~n n

x) For the formation of beats, the amplitudes of two waves need not be equal.(I

min 0)xi) If the amplitudes are equal,

amax

= a + a = 2a

I a2

Imax

= 4Io , I

o - intensity of single wave

Here, amin

= 0, Imin

= 0.xii) If amplitudes of waves are not equal,

amax

= a1+a

2 ; a

min = a

1 ~ a

2

xiii) Intensity ratio:–

22

1 21 2max2 2

min 1 2 1 2~ ~

I I a a I

I a a I I

xiv) Beats and parent sounds tra vel with samevelocity

xvi) Uses of Beats :

a) Can be used to determine unknownfrequency of a tunining fork

b) To tune a musical instrument to a givennotec) To detect poisonous gases in minesd) In radio reception of heterodyne receiver,

high frequency oscillations from atransmitter are combined with a slightlydifferent frequency produced in thereceiver so that the resultant frequency will be in the audio range.

e) Beats are used to produce special effectsin cinematography.

35. ECHOES :

i) When an observer produces a sound and receives its reflection from an obstacle, thereflected sound is called echo of the originalsound.

ii) The Phenomenon involved in echo is "reflectionof sound".

iii) Since wavelength of sound is large, large objectsalone can produce echo.

iv) The minimum distance between observer and

reflecting surface to hear an echo isV

20 (where

V is velocity of sound)v) If a sound wave is reflected from an obstacle

there will be no change in its velocity , wavelength & frequency , but its intensity decreases

vi) A man standing at distance 'd' from a big wall produces a sound and receives its echo after 't

1'

sec. He then walks through a distance 'x'towards the wall. He produces a sound and receives its echo after 't

2' sec then.

2d = vt1; 2(d-x)=vt

2;

1 2

2xV

t t

In the above case if he moves away from thewall then

2d = Vt1; 2(d+x) = Vt

2 ;

2 1

2xV

t t

vii) A car approaches a cliff with velocity V

c blows

a horn when it is at a distance 'd' from the cliff,the echo is heard after a time 't' then

V= c2d V t

t


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In the above case if the car is moving away from

the cliff then V= c2d V t

t

V = Velocity of sound viii) A person standing between two parallel cliffs

fires a bullet. He receives first echo after 't1' sec

and second echo after 't2' seconds after firingthen

V= 1

1

2d

t ,2

2

2dV

t distance between two cliffs

d = d 1+d

2 =

1 2V t t

2

ix) In the above case if he recives first echo after 't

1' sec and second echo 't

2' sec latter then

d = d 1 + d

2 =

V

2(2t

1+t

2)

x) A car is moving with velocity 'u' on a road

running parallel to a row of buildings. Thedistance between row of buildings and road is'd'. The driver sounds the horn, he receives theecho after a time 't' (V is the velocity of sound)

In this case 2 2

2dt

V u

xi) If the car runs midway between parallel rowsof buildings. If the distance between the parallelrows of buildings is 'd' then

t =2 2 –

d

v uxii) Uses of echo :

a) It can be used to determine the velocity of sound. b) To determine height of aeroplane and depthof ocean.

c) SONAR (sound navigation and ranging principles can be used for determining position

and speeds of submarines) : Echo techniquescan be applied together with the doppler effectin detecting the presence of submarines in theseas using ultrasonics.d) In SONAR – ultrasonics are used becauseordinary sounds are highly absorbed by water.e) Mega phone, ear trumpet, hydrophone,fathometer, stethoscope are based on principleof reflection of sound.

36. DOPPLER EFFECT :

i) The apparent change in the frequency of the

source of sound due to relative motion between

the observer and the source of sound is called

"Doppler effect."

ii)S OVS V0

If the source follows observer as shown in the

above figure then the apparent frequency n1 =

0

s

nv v

v v

iii) Sign conventions :a) Direction of velocity of sound is always

from source to observer irrespective of their

directions of motions.

b) v0 and vs are positive if they are in thedirection of sound.

c) v0 and vs are –ve if they are opposite to

the direction of sound.

iv) a) If wind blows in the direction of sound

wave, then in place of velocity of sound v,

we take 'v + w' . (w is the velocity of wind)

b) If wind blows in opposite direction of

sound wave, then in place of velocity of

sound v, we take 'v – w'.

v) Doppler effect is independent of distance between the source and observer.

37) Formulae for apparent frequency in different

cases

a) Source moving towards a s tationary

observerS

| Vn nV V

;

b) Source moving away from a stat ionary

observerS

| Vn nV V

c) Observer moving towards a stationary

source0| V Vn n

V

d) Observer moving away from a stationary

source0| V Vn n

V


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e) Source moving towards a receding

observer0

S

| V Vn nV V

f) Observer moving towards a receding

source 0S

| V Vn nV V

g) The relative velocity between source and the observer is always taken along the lineof sight of the source by the observer.

h) When observer is at rest, source is movingas shown in the below figure. Then

n| = – coss

v nv v

i) When observer is at rest and source movesas shown in the given figure. Then

nA =n;

– coss

v

v v

nB = n; nC = coss

vn

v v

j) A source is at origin and observer moves,with constant velocity V0 on the line x = k

nA=0 1co sv v nv

; nB = n ; nC=0 2 – cosv v nv

k) When source is at rest and observer moves

perpendicular to the line of sight or vice-

versa, there is no Doppler effect.

In both cases, shown above there is no Doppler

effect because one is moving at right anglesto the line of sight and the other is at rest.l) Observer is crossing a stationary source

a p p

V V n n

V

0;

recd

V V n n

V

0

0

0

app

recd

n V V

n V V

.

.

Drop in frequency heard by the observer

. .app recd n n n02v n

v

m) Source crossing a stationary observer :-

a p p

s

V n nV V

; recd

s

V nV V

n

.

.–

ap p s

recd s

n v v

n v v

Drop in frequency heard by the observer :

. .app recd n n =2

_ sv n

nv

n) If the observer is standing outside thecircular track,

nA=nmax= – s

vn

v v

; nB = n ; nC = nmin=s

vn

v v

Drop in frequency heard by the observer :

nmax –nmin 2 2

_ snv nr

v v

=

2 2nr

v

ƒ = frequency of rotation of circular platform

o) Source in circular motion and observer in SHM

nmax =0max

– s

v vn

v v


11/19

Maximum frequency is heard when thesource is at A and observer is at P movingtowards circular orbit on platform.

Minimum frequency is obtained whensource is at C and observer at P movesaway from circular orbit. On platform.

m ax

10v A w ; vs = rw

w1 = angular Velocity of SHM (platform)

w = angular Velocity of source in thecircular orbit

p) If source is moving towards a wall withspeed vs and the observer is standing

behind the source as shown in the figurethen

Vs Vs

image of source

wall

direct

s

vn n

v v

; – reflected s

vn n

v v

No. of beats = nd –nr 2

snv

v

q) If the source is moving towards wall and observer standing between source and wallas shown in the figure then

Vs Vs

image of

source

wall

– d

s

vn n

v v

; nr – s

vn

v v

n = No. of beats heard =difference in frequencies = 0

r) If both source and observer are movingtowards a wall with same speed u then

u

u

image of source

wall

observer

source

nd = n ; – r v u

n nv u

r d n n n 2

–

un

v u

ix) Motion of source produces greater change in

frequency than motion of observer even thoughthe relative velocities are same in both cases.

x) Doppler effect in sound is asymmetric.xi) Doppler effect in light is symmetric

xii) Doppler effect is not observed if a) V0 = V

s = 0 (both are at rest)

b) V0=V

s=0 and medium is alone in motion.

c) V0=V

s=u and V

0, V

s are in same direction

d) Vs is r to line of sight

xiii) Doppler effect is applicable only when,

V0


12/19

Now the plane act as a moving source , the

frequency of the wave from it is11 c vn n

c v

(c is velocity of microwave )

Change in frequency 2nv

n

cBy measuring n , the speed 'v' can be obtained.

Wave Equations & Basics :

1. Which of the following expressions represents

a simple harmonic progressive wave

1) y = A sin wt 2) y = A sin wt cos kx3) y = A sin (wt-kx) 4) y = A cos kx

2. The displacement y of a particle in a medium

can be expressed as y = 10–6 sin

100 204

t x m

where 't' is in second andx in metre. The speed of wave is(AIEEE 2004)

1) 2000 ms –12) 5 ms –13) 20 ms –1 4) 5 ms –1

3. The equation of a transverse wave travelling

on a rope is given by

y 10sin 0.01x 2.00 t where y and x arein cm and t in seconds. The maximum

transverse speed of a particle in the rope is

about

1) 62.8 cm/s 2) 75 cm/s 3) 100 cm/s 4) 121 cm/s

4. The angular frequency of a particle in a

progressive wave in an elastic medium is

100 rads-1 and it is moving with a velocity

of200ms-1. The phase difference between two

particles seperated by a distance of 20m is

1) 31.4 rad 2) rad 3)3

4rad 4) 36 rad

5. A progressive wave moves with a velocity of

36m/s in a medium with a frequency of 200Hz.

The phase difference between two particles

seperated by a distance of 1cm is

1) 40° 2) 20 rad 3)

9 rad 4) 0

9

6. The speed of a wave in a medium is 760 m/s.

If 3600 waves are passing through a point in

the medium in 2 minutes, then its wavelength is

1) 13.8 m 2) 25.3 m 3) 41.5 m 4) 57.2 m

7. A progressive wave of frequency 500 Hz is

travelling with a speed of 350 m/s. A

compressional maximum appears at a place

at a given instant. The minimum time interval

after which of refraction maximum occurs at

the same place is

1)1

s250

2)1

s500

3)1

s1000

4)1

s350

8. A wave of length 2m is superposed on its

reflected wave to form a stationary wave. A

node is located at x = 3m. The next node will

be located at x =

1) 3.25 m 2) 3.50 m 3) 3.75 m 4) 4m

9. The equation of a stationary wave is

y= x

0.8cos sin 200 t20

where x is in cm

and t is in seconds. The separation between

consecutive nodes is

1) 10 cm 2) 20 cm 3) 30 cm 4) 40 cm

Strings :

10. Length of a string tied to two rigid supports

is 40 cm. Maximum wavelength in cm of a

stationary wave produced on it is (AIEEE 2002)

1) 20 cm 2) 80 cm 3) 40 cm 4) 120 cm

11. The length of a sonometer wire AB is 100 cm,

where should the two bridges be placed from

A to divide the wire in 3 segments whose

fundamental frequencies are in the ratio of 1 : 2 : 6

1) 30 cm, 90 cm 2) 60cm, 90 cm

3) 40 cm, 80 cm 4) 20 cm, 30 cm

12. A 5.5 m long string has a mass of 0.035 kg. If

the tension in the string is 77 N, the speed of a

wave on the string is

1) 110 m/s 2) 165 m/s 3) 77 m/s 4) 102 m/s

13. The length of a sonometer wire tuned to a

frequency of 256 Hz is 0.6 m. Calculate the

frequency of the tuning fork with which the

vibrating wire will be in tune when the length

is made 0.4 m.

1) 78 Hz 2) 512 Hz 3) 384 Hz 4) 126 Hz

14. The fundamental frequency of a string stretched

with a weight of 4kg is 256 Hz. The weight

required to produce its octave is

1) 4 kg wt 2) 12 kg wt

3) 16 kg wt 4) 24 kg wt

15. Two strings A and B, made of the same

material, have equal lengths. The cross


13/19

sectional area of A is half that of B while the

tension on A is twice that on B. The ratio of

the velocities of transverse waves in A and B

is

1) 2:1 2) 1: 2 3) 2 : 1 4) 1 : 2

16. The density of the stretched string is changed

by 2% without change in tension and radius.

The change in transverse wave velocity.

1) 2% increase 2) 1% increase3) 1% increase or decrease4) 4% change

17. The tension in the string is changed by 2%

what is the change in the transverse wave

velocity

1) 1% 2) 2% 3) 3% 4) 4%

18. To increase the frequency by 20 % ,the tension

in the string vibrating on a sonometer has to

be increased by (2007 M)

1) 44 % 2) 33% 3) 22 % 4) 11%

19. When the tension in a string is increased by

44%. the frequency increased by 10Hz the

frequency of the string is

1) 100 Hz 2) 200 Hz 3) 150 Hz 4) 50 Hz

20. A wire whose linear density is 5 x 10-3 kg/m is

stretched between two points with a tension

450 N. The wire resonates at a frequency of

420 Hz. The next higher frequency at which

the same wire resonates is 490 Hz. What isthe length of the wire? (2007 M)

1) 1.2 m 2) 1.8 m 3) 2.1 m 4) 8.1 m

21. In order to double the frequency of the

fundamental note emitted by a stretched

string, the length is reduced 3/4 th of the

original length and the tension is changed. The

factor by which the tension is to be changed is

(2001 E)

1)8

32)

3

23)

9

84)

4

9

22. Two uniform strings 'A' and 'B' made of steelare made to vibrate under the same tension.

If the first overtone of 'A' is equal to the

second overtone of 'B' and if the radius of 'A'

is twice that of 'B' the ratio of the lengths of

the string is (2003 E)

1) 1:2 2) 1:3 3) 1:4 4) 1:5

23. Transverse waves are generated in two steel

wires A and B by attaching their free ends to

a vibrating source of frequency 500 Hz. The

diameter of A is half that of B and tension on

B is double that on A. What is the ratio of the

velocities of waves in wires A and B?

1) 1 : 2 2) 2 : 1 3) 1 : 2 4) 2 : 1

24. The third overtone produced by a vibrating

string 0.5m long is 1200Hz. The speed of

propagation of the wave in 1ms is

1) 400 2) 300 3) 600 4) 1200

25. A wave of frequency 100Hz is sent along a

string towards a fixed end. When this wave

travles back then after reflection, a node is

formed at a minimum distance of 10 cm from

the fixed end of the string. The speed of the

incident wave is

1) 40 m/s2) 20 m/s 3) 10 m/s 4) 5 m/s

Velocity of Sound :

26. The temperature at which the speed of sound

in air becomes double of its value at 00C is

[AIEEE 2002]

1) 273 K 2) 546 K 3) 1092 K 4) 0 K

27. The ratio of the speed of sound in nitrogen

gas to that in helium gas, at 300 K is [IIT 99]

1) 2 / 7 2) 1/ 7 3) 3 /5 4) 6 / 5

28. The speed of sound in air at 150C and 76 cm

of Hg is 340 m/s. The speed of sound in air at300C and 75 cm of Hg will be (in m/s)

1)303

340288

2)288

340303

3) 340 2 4)2 75

34076

29. The velocities of sound in an ideal gas at

temperature T1 and T

2 K are found to be V

1

and V2 respectively. If the r.m.s velocities of

the molecules of the same gas at the same

temperatures T1

and T2

are

1 and

2respectively then

1)

1

2 1

2

V

V 2)

2

2 1

1

V

V

3) 2

2 1

1

V

V 4) 12 1

2

V

V

30.1 and 2 are the velocities of sound at the

same temperature in two monoatomic gases


14/19

of densities1 and 2 respectively. If

1

2

1

4

then the ratio of velocities 1 and 2 is

1) 1 : 2 2) 4 : 1 3) 2 : 1 4) 1 : 4

Pipes :

31. An open organ pipe sounds a fundamental

note of frequency 330 Hz. If the speed in air

is 330 m/s then the length of the pipe is nearly

1) 0.25 m 2) 0.50 m3) 0.75 m 4) 2.00 m

32. A cylindrical tube, open at both ends, has a

fundamental frequency f 0 in air. The tube is

dipped vertically into water such that half of

its length is inside water. The fundamental

frequency of the air column now is

(RPET99, RPMT98, 2000 ; J & K CET 2000 ;KCET 2002, BHU 2002, BCECE 2003]

1) 3f 0 / 4 2) f

03) f

0 / 2 4) 2f

0

33. An organ pipe P1 , closed at one end and

vibrating in its first overtone, and another

pipe P2 open at both ends and vibrating in its

third overtone, are in resonance with a given

tuning fork . The ratio of the length of P1 to

that of P2 is

(EAMCET 97, MH CET 1999, AFMC 2001)

1)8

32)

3

83)

1

24)

1

3

34. An open pipe 30 cm long and a closed pipe 23

cm long, both of the same diameter, are each

sounding their first overtone are in unison.

The end correction of these pipes is

1) 0.5 cm 2) 0.3 cm

3) 1 cm 4) 1.2 cm

35. Two closed organ pipes of length 100 cm and

101 cm produces 16 beats in 20 sec when each

pipe is sounded in its fundamental mode

calculate the velocity of sound

1) 303 m/s 2) 332 m/s

3) 323.2 m/s 4) 300 m/s

36. If l1, l

2 and l

3are wave lengths of the waves

giving resonance with fundamental, first and

second over tones of closed organ pipe. The

ratio of wavelengths l1: l

2:l

3is ..........

1) 1 : 2 : 3 2) 1 :5

1:

3

1

3) 1 : 3 : 5 4) 5 : 3 : 1

37. An open organ pipe and closed pipe havesame length. The ratio of frequencies of their

nth over tone is ..........

1)1n2

1n

2)1n2

)1n(2

3)1n2

n

4)

n2

1n

38. Two pipes have each of length 2m. One is

closed at one end and the other is open at both

ends. The speed of sound in air is 340m/s the

frequency at which both can resonate is .....

1) 340 Hz 2) 510 Hz

3) 42.5 Hz 4) does not exist

39. The first overtone of an open pipe has

frequency n. The first ovetone of a closed pipe

of the same length will have frequency

1) n/2 2) 2n 3) 3n/4 4) 4n/3

40. If a resonance tube is sounded with a tuning

fork of frequency 256 Hz, resonance occurs

at 35 cm and 105 cm. The velocity of sound is

about

1) 360 m/s 2) 512 m/s3) 524 m/s 4) 400 m/s

41. Fundamental frequency of pipe is 100 Hz and

other two frequencies are 300 Hz and 500 Hz

then (RPMT 1998, 2003, CPMT 2001)

1) Pipe is open at both the ends2) pipe is closed at both the ends3) One end open and another end is closed 4) None of the above

Beats :

42. Two tuning forks when sounded togetherproduce 5 beats in 2 seconds. The time interval

between two sucessive maximum intensities of

sound is

1) 0.5 s 2) 0.2 s 3) 0.4 s 4) 0.3 s

43. Two progressive waves y1 = 4 sin 400 t and

y2 = 3 Sin 404 t moving in the same direction

superpose on each other producing beats.

Then the number of beats per second and the


15/19

ratio of maxium to minimum intensity of the

resultant waves are respectively

1) 2 and5

12) 4 and

49

1

3) 4 and 169

4) 2 and49

1

45. Two stretched wires of same length, diameter

and same material are in unison. The tension

in one is increased by 2% and 2 beats per

second are heard. What was the frequency of

the note produced when they were in unision

1) 100 Hz 2) 200 Hz 3) 300 Hz 4) 400 Hz

46. The frequency of a tuning fork A is 5% greater

than that of a standard fork K. The frequency

of another fork B is 3% less than that of K.

When A and B are vibrated simulataneously 4

beats per second are heard. Find the frequencies

of A and B.

1) 52.5 Hz, 48.5 Hz 2) 63.5 Hz, 79.5 Hz

3) 10.5 Hz, 101 Hz 4) 124 Hz, 120 Hz

47. 64 tuning forks are arranged such that each

fork produces 4 beats per second with next

one. If the frequency of the last fork is octave

of the first, the frequency of 16th fork is

1) 316 Hz 2) 322 Hz 3) 312 Hz 4) 308 Hz

48. A tuning fork produces 4 beats per sec with

one fork of frequency 288 cps. A little wax is

placed on the unknown fork and it produces 2

beats per second. The frequency of unknown

fork is (AIEEE 2002)

1) 286 cps 2) 292 cps 3) 294 cps 4) 288 cps

49. A tuning fork produces 7 beats/s with a tuning

fork of frequency 248Hz. Unknown fork is

now loaded and 7 beats/s are still heard. Thefrequency of unknown fork was

1) 241 Hz 2) 248 Hz

3) 255 Hz 4) 234 Hz

50. Tuning fork A of frequency 258 Hz gives 8

beats with a tuning fork B. When fork B is

filed nd again A and B are sounded the number

of beats heard remains same. The frequency

of B is

1) 250 Hz 2) 264 Hz

3) 258 Hz 4) 266 Hz51. Two tuning forks A and B vibrating

simultaneously produce 5 beats /s. Frequency

of B is 512 Hz. If one arm of A is filed, the

number of beats per second increases.

Frequency of A is

1) 502 Hz 2) 507 Hz

3) 517 Hz 4) 522 Hz

52. Tuning fork A of frequency 258 Hz gives 8

beats with a tuning fork B. When the tuning

fork A is filed and again A and B are sounded

the number of beats heard decreases. The

frequency of B is

1) 250 Hz 2) 266 Hz 3) 258 Hz 4) 242 Hz

53. Two tuning forks A and B vibrating simultaneously produce 5 beats /s. Frequency of B is 512 Hz. If

tuning fork B is now loaded with wax, when it vibrated with A the number of beats become 6 beats

per second. Frequency of A is

1) 502 Hz 2) 507 Hz 3) 517 Hz 4) 522 Hz

54. A tuning fork of frequency 340 Hz produces 5 beats per second with a sonometer wire. If the

tension is slightly increased the number of beats becomes 4. The frequency of sonometer wire is

1) 335 Hz 2) 345 Hz 3) 330 Hz 4) 350 Hz55. Two tuning forks x and y produce tones of frequencies 256 Hz and 262 Hz respectively. An unknown

tone sounded with x produces, beats. When it is sounded with y the number of beats produced is

doubled. The unknown frequency is

1) 254 Hz 2) 258 Hz 3) 264 Hz 4) 259 Hz

56. A source of frequency ‘X’ gives 5 beats/s when sounded with a source of frequency 200 Hz. The

second harmonic of source gives 10 beats/s when sounded with a source of frequency 420 Hz. The

value of ‘x’ is


16/19

1) 200 Hz 2) 210 Hz 3) 205 Hz 4) 195 Hz

Echoes :

57. The minimum distance between the man and the reflecting surface so that he can hear the echo is

(velocity of sound 340 ms-1)

1) 16.5 m 2) 17m 3) 18m 4) 16 m

58. A man standing at some distance from a cliff hears the echo of sound after 2s. He walks 495 m away

from the cliff. He produces a sound there and recieves the echo after 5s. What is the speed of

sound?

1) 330 m/s 2) 340 m/s

3) 390 m/s 4) 380 m/s

59. A person moving in a car with a velocity of 36 kmph towards a large wall blows a horn. If he hears

the echo after 3s, the distance of wall from him when he blows the horn

(velocity of sound 340 ms-1)

1) 340 m 2) 1050m 3) 700m 4) 525 m

60. The height of a cloud above the earth is 100 m. If an observer hears the sound of a thunder 0.3s

after the lightening is seen, what is the velocity of sound on that rainy day1) 300 m/s 2) 333.3 m/s3) 100 m/s 4) 666.6 m/s

61. A rifle is fired in a valley formed between two parallel mountains. The echo from one mountain is

heard after 1.5s and from the other is heard 3s later. What is the width of the valley? (velocity of

sound = 340 ms-1)

1) 1080 m2) 1060 m 3) 1040 m 4) 1020 m

62. A man standing between two parallel cliffs produces sound and heard the first echo after 4 secs and

next echo after 2 sec later v = 330 ms -1. when is the third echo heard

1) 4s 2) 5 s 3) 10s 4) 6 s

Doppler Effect :

63. A whistle producing sound waves of frequencies 9500 Hz and is approaching a stationary person

with speed ms–1. The velocity of sound in air is 300 ms–1. If the person can hear frequencies uptoa maximum of 10,000 Hz. The maximum value of upto which he can hear the whistle is(AIEEE 2006)

1) 30 ms –1 2) 15 2 ms –1

3) 15 2 ms –1 4) 15 ms –1

64. A source of sound is travelling towards a stationary observer. The frequency of sound heard by the

observer is 25% more that the actual frequency. If the speed of sound is v, that of the source is

1) v

52)

v

43)

v

34)

v

2

65. To an observer, the pitch of a stationary source of sound appears to be reduced by 20%. If thespeed of sound is 340m/s then speed and direction of the observer is

1) 86 m/s towards the source2) 68 m/s towards the source3) 86 m/s away from the source4) 68 m/s away from the source

66. An observer moves towards a stationary source of sound with a velocity one–fifth of velocity of

sound. The percentage increase in apparent frequency is (AIEEE 2005)


17/19

1) 5% 2) 20% 3) Zero 4) 0.5%

67. When both source and listner approach each

other with a velocity equal to half the velocity

of sound, the change in frequency of the sound

as detected by the listner is (frequency of

sound=n)

1) n 2) 2n 3) n2

4) 3n

68. An engine giving off whistle is moving towards

a stationary observer with 50m/s speed. What

will be the ratio of the frequencies of the

whistle heard when engine is approaching and

receding from the observer? (speed of sound

= 350 m/s)

1) 2 : 1 2) 4 : 5 3) 4 : 3 4) 3 : 4

69. A train running at 108 km/hr towards east

whistles at a frequency of 800 Hz. The

frequencies heard by a passenger sitting in thetrain and a person standing near the track

whom the train has just passed(Speed of Sound

=330 m/s)

1) 800 Hz, 733 Hz 2) 740 Hz, 800 Hz3) 800 Hz, 880 Hz 4) 800 Hz, 750 Hz

70. A source and a deterctor move away from

each other, each with a speed of 10 m/s with

respect to ground with no wind. If the detector

detects a frequency 1650 Hz of the sound

coming from the source, what is the original

frequency of the source? (speed of sound =

340 m/s)1) 750 Hz 2) 1750 Hz3) 2000 Hz 4) 1800 Hz

71. Two trains are moving towards each other at

speeds of 144 km/hr and 54 km/hr relative to

the ground. The first train sounds a whistle of

frequency 600 Hz. Find the frequency of the

whistle as heard by a passenger in the second

train before the trains meet. (v=340m/s)

1) 610 Hz 2) 510 Hz 3) 710 Hz 4) 170 Hz

72. A Car is travelling atv

10 ms–1 and sounds horn

of frequency 990 Hz. The apparent frequencyheard by a police chasing the car at

v

9 ms–1

where V is velocity of sound

1) 990 Hz 2) 900 Hz3) 1000 Hz 4) 0

73. A source is moving with a constant speed of

10 m/s on a circular track of 200 m. It emits a

sound of frequency 200 Hz. A listener stands

at the centre of the circular track. The

frequency recieved by the listener is (velocity

of sound = 340 m/s)

1) zero 2) 200 Hz 3) 190 Hz 4) 210 Hz

74. A car travels at a speed of 'a' towards a high

wall. The driver sounds a horn of frequency

'n'. If V is the velocity of sound in air,

frequency of reflected sound heard by the

driver is

1)V a

nV a

2)V a

nV a

3)V a

nV

4)

V an

V

75. The wave length of the sound produced by a

source is 0.8m. If the source moves towards

the stationary listner at 32 ms–1, what is theapparent wave length of sound if the velocity

of sound is 320 ms–1

1) 0.32 m 2) 0.4 m 3) 0.72 m 4) 0.80 m

76. A person going away from a factory on his

scooter at a speed of 36 km/hr listens to the

siren of the factory. If the frequency of siren

is 525 Hz and a wind is blowing along the

direction of scooter at 36km/hr the frequency,

heard by the person is (velocity of sound =

340 m/s)

1) 680 Hz 2) 510 Hz 3) 640 Hz 4) 600 Hz

Accoustics :

77. The absorption coefficient of a material is .

The ratio of maximum to minimum current

during its determination by stationary wave

method is

1) 8 2) 4 3) 2 4) 3

78. In a big hall of volume 30 x 20 x 10 m3, if the

reverberation time is 1.7 sec. The total sound

absorption in the hall is ---- Metric Sabine

1) 6000 2) 600 3) 3000 4) 300

79. The reverberation time of a hall of volume

200m3 is 1.7sec. The reverberation time if 20

persons having absorption 0.4 metric sabine

entered the hall, nearly is

1) 1.5S 2) 1.4S 3) 1.3S 4) 1.2S

80. The volume of a room is 600 m3. The wall area

of the room is 220 m2. The floor and ceiling

7 7


18/19

have area of 120 m2 each. The absorption

coefficients of walls, floor and ceiling are 0.03,

0.8 and 0.06 respectively. Calculate the

reverberation time

1) 0.93 s 2) 0.5 s 3) 0.2 s 4) 1.8 s

81. If due to the entry of audience into a hall theabsorption becomes 3/2 times of initial

absorption the final reverberation time, (if

initial reverberation time was T) wil be

1) T 2) 3/2 T 3) 0.67 T 4) 0.75 T

82. The correct graph repressenting the relation

between intensity and time when a sound of is

turned on in an enclosure and after some time

it is switched off

1) 2)

3) 4)

83. When a sound wave of wavelength ' ' is

propagating in a medium, the maximum

velocity of the particle is equal to the velocity.

The amplitude of waves is (2008-E)

1) 2) 2

3) 2

4) 4

84. A car is moving with a speed of72 kmph

towards a hill. Car blows horn at a distance

of 1800 m from the hill. If echo is heard after

10 seconds, the speed of sound (in m/sec) is

(2008-E)

1) 300 2) 320 3) 340 4) 360

85. The frequencies of three tunuing forks A, B

and C have a relation nA > n

B > n

C. When the

forks A and B are sounded together the

number of beats produced is n1. When A andC are sounded together the number of beats

produced is n2, then the number of beats

produced when B and C are sounded together

is (2008-M)

1) n1 + n

22)

1 2n n

2

3) n

2 – n

14) n

1 – n

2

86. Two strings of the same material and the same

area of cross – section are used in sonometer

experiment. One is loaded with 12kg and the

other with 3 kg. The fundamental frequency

of the first string is equal to the first overtone

of the second string. If the length of the second

string is 100 cm, then the length of the first string

is (2008-M)

1) 300 cm 2) 200 cm 3) 100 cm 4) 50 cm

87. The speed of sound in oxygen (O2) at a certain

temperature is 460 ms-1. The speed of sound

in helium (He) at the same temperature will

be (assumed both gases to be ideal)

(2008-AIEEE)

1) 1420 ms-1 2) 500 ms -1

3) 650 ms-1 4) 330 ms-1

88. A wave travelling along the x-axis is described

by the equation y(x,t) = 0.005 cos

( x t .If the wavelength and the timeperiod of the wave are 0.08 m and 2.0 s,

respectively, then and in appropriate

units are (2008-AIEEE)

1) 25.00 , 2)0.08 2.0

,

3)0.04 1.0

,

4) 12.50 ,2.0

89. While measuring the speed of sound by

performing a resonance column experiment,a student gets the first resonace condition at

a column length of 18 cm during

winter.Repeating the same experiment during

summer, she measures the column length to

be x cm for the second resonance. Then

(2008-AIEEE)

1) 18 > x 2) x > 54

3) 54 > x> 36 4) 36 > x > 18

90. Two sources A and B are sending notes of

frequency 680 Hz. A listener moves from A

to B with a constant velocity 'u'. If the speed

of sound in air is 340 ms–1, what must be the

value 'u' so that he hears 10 beats per second ?

(2009 -E)

1) 2.0 m-s –1 2) 2.5 m-s –1

3) 3.0 m-s –1 4) 3.5 m-s –1

91. Two identical piano wires have a fundamental

frequency of 600 c/s when kept under the same


19/19

tension. What fractional increases in the

tension of one wire will lead to the occurence

of 6 beats per second when both wires vibrate

simultaneously? (2009 -E)

1) 0.01 2) 0.02 3) 0.03 4) 0.04

92. A theatre of volume 100 x 40 x 10 m3 canaccommodate 1000 visitors. The

reverberation time of the theatre when empty

is 8.5 sec. If the theatre is now filled with 500

visitors, occupying the front - half seats, the

reverberation time changes to 6.2 seconds.

The average absorption coefficient of each

visitor is nearly (2009-M)

1) 0.6 2) 0.5 3) 0.45 4) 0.7

93. An observer is standing 500 mts away from a

vertical hill. Starting from a point between theobserver and the hill, a police van moves

towards the hill with uniform speed sounding

a siren of frequency of 100 Hz. If the

frequency of the sound heard by the observer

directly from the siren is 970 Hz, the frequency

of the sound heard by the observer after

reflection from the hill (Hz) is nearly (Velocity

of sound in air=330 m/s) (2009-M)

1) 1042 2) 1031 3) 1022 4) 1012

94. Three sound waves of equal amplitudes have

frequencies (v-1), v, (v+1). They superpose to

give beats. The number of beast produced per

second will be: (2009-AIEEE)

1) 3 2) 2 3) 1 4) 4

95. A motor cycle starts from rest and accelerates

along a straight path at 2 m/s2. At the atraight

point of the motor cycle there is a stationary

electric siren. How far has the motor cycle

gone when the driver hears the frequency of

the siren at 94% of its value when the motor

cycle was at rest? (Speed of sound = 330 ms-1

) (2009-AIEEE)

1) 98 m 2) 147 m 3) 196 m 4) 49m

ANSWERS

EXERCISE – II(A)

1) 3 2) 2 3) 1 4) 1 5) 3

6) 2 7) 3 8)4 9) 2 10) 2

11) 2 12) 1 13) 3 14) 3 15) 3

16) 3 17) 1 18) 1 19) 4 20) 3

21) 4 22) 2 23) 4 24) 2 25) 2

26) 3 27) 3 28) 1 29) 2 30) 3

31) 2 32) 2 33) 2 34) 3 35) 3

36) 2 37) 2 38) 4 39) 3 40) 1

41) 3 42) 3 43) 4 44) 1 45) 2

46) 1 47) 3 48) 2 49) 3 50) 1

51) 3 52) 2 53) 3 54) 1 55) 2

56) 3 57) 2 58) 1 59) 4 60) 2

61) 4 62) 3 63) 4 64) 1 65) 4

66) 2 67) 2 68) 3 69) 1 70) 2

71) 3 72) 3 73) 2 74) 1 75) 3

76) 2 77) 4 78) 2 79) 4 80) 1

81) 3 82) 4 83) 3 84) 2 85) 3

86) 3 87) 1 88) 1 89) 2 90) 2

91) 2 92) 1 93) 2 94) 2

sound_syno and exercise1

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