eu1c2 by adel khamis

Unit one -68- Chapter Two

Choose the correct answer from those between brackets and write it in your answer paper

Evaluation book:

1. The tension of a string is measured in [kg/m – Newton – m/s – meter](1)

2. The second overtone of a vibrating string is produced when it vibrates in the

form of [one segment – two segments – three segments – four segments](2)

3. When the string vibrates as one segment, its length equals to [2 - - /2 – 3 λ2 ](3)

4. The velocity of propagation of the transverse wave through a vibrating string

is determined from [v= T

√m - v=√T

m - v=√ T

m - v=√ m

T .m ](4)

5. The standing waves are produced due to the superposition of two wave

motions having:(5)

a) The same frequency, amplitude and propagate in the same direction.

b) The same amplitude and propagate in the same direction.

c) The same frequency, amplitude and propagate in the opposite

direction.

d) The same amplitude and propagate in opposite direction.

6. a) A stretched string vibrates as shown in three segments to produce its tone

[fundamental – first harmonic – second

harmonic – third harmonic](6)

b) Using the same figure, the wavelength of the standing wave is [60 cm –

120 cm – 180 cm – 240 cm](7)

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c) Using the given information on the previous figure, the frequency of the

tone produced by the string (the velocity of the transverse wave in the

string 180 m/s) is [600 Hz – 450 Hz – 300 Hz – 150 Hz](8)

d) Using the information given on the previous figure, the frequency of the

fundamental tone of the string is [50 Hz – 100 Hz – 150 Hz – 200 Hz](9)

7. (Egypt 2001) When a string of length (L) vibrates and is divided into (n)

segments, then the wave length of its tone () equals [n/(2L) , L/n, n/L, (2L)/n]

(10)

8. A stretched string vibrates in the form of 5 segments, it emits its ……..

harmonic tone [four – second – third – five](11)

9. A person is standing in a large open field at a distance of 170 m from a vertical

wall, A gun X is sited at a point 34 m from the wall along, the line

perpendicular to the wall and passing through the observer “O” the gun is

fired:

Assuming that the speed of sound in air is 340 m/s what will the observer

hear(12)

a) Two reports only, separated by an interval of 0.2 S

b) Two reports only, separated by an interval of 0.4 S

c) One report only, immediately the gun is fired.

d) One report immediately the gun is fired, followed by a second report

0.25 S later.

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e) It is not possible to say what is heard from the information given.

10. Two stringed instruments are playing notes of the same pitch, which of the

following must be the same for the two notes(13)

a) amplitude

b) frequency

c) length of vibrating string

d) quality

e) tension of the vibrating string

11. When the pitch of a note is raised the(14)

a) Frequency is decreased

b) Speed of the sound is increased

c) Speed of the sound remains the same while wavelength decreased

d) Wavelength remains the same

12. A boy stands at x in open space, between two tall building P and Q, at distance

50 m and 200 m he strikes a drum once

and hears two marked echoes, separated

by a time interval 1 second from these

figure the calculated speed of sound in

air is [150 m/s – 250 m/s – 300 m/s –

330 m/s 500 m/s](15)

Pervious exams:

13. (August 96) The wavelength of a standing wave is [the distance between two

successive nodes, the distance between two successive anti-nodes, twice the

distance between two successive nodes](16)

Exercises 2008/2009


14. (August 97) The string emits its second over tone when it vibrates in the form

of [three segments – four segments – five segments](17)

Each question one or more of the responses given is (are) correct. Decide which of the response is (are)

correct, then choose

Evaluation book:

1. The frequency of the fundamental tone produced by a string depends on:(18)

a) Its tension

b) Its length

c) Its mass per unit length

2. The frequency of the string produced first over tone equals:(19)

a) Twice the frequency of its fundamental tone.

b) Three times the frequency of its fundamental tone

c) Five times the frequency of its fundamental tone.

3. The wavelength of the standing wave is:(20)

a) The distance between two successive nodes.

b) The distance between two successive antinodes.

c) Twice the distance between two successive nodes.

4. The ratio between the frequencies of the fundamental tone and that of the over

tones emitted from a vibrating string is:(21)

a) 1: 3: 5

b) 1: 2: 3

c) ¼: ½: ¾

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5. If the string vibrates in the form of two segments:(22)

a) If emits its first harmonic tone

b) If represents the length of a complete standing wave

c) If emits the fundamental tone.

Structured questions

Evaluation book:

1. The given graph represents the relation between

the frequency of the fundamental one of a

stretched string “” and reciprocal its length “1/L”

a) The slope = …………………..(23)

b) The wavelength which emits the string

= ………………(24)

c) The velocity of the wave propagates through the string = slope x

……….(25)

2. A vibrating string emits a tone related to the relation ν= 5

2 L √ Tm where v is

the frequency. L is the length of the string, T is the tension and m is the mass

per unit length.

a) This string emits its ……………….. tone.(26)

b) The wavelength of the propagated wave in the string = ………………(27)

3. If the tension increased 9 times its value and the length of string is increased 3

times, its value then: the frequency of the emitted tone ………… the original

value.(28)

Exercises 2008/2009


Previous Exams:

4. (Egypt 2004) When a string vibrates emitting its fundamental tone according

to the relation V=150

L so:

a) The velocity of the transverse wave propagating in the string = ………….

If the length of the string is 50 cm and its mass is 5 gm.

b) The frequency of the fundamental tone emitted by it = ……………..

c) The tension acting on the string = …………

d) The frequency of the third overtone = ……………

Additional Questions:

5. When a string of length 150 cm, and mass 150 gm, vibrates according to the

relation ν ( in hertz )=150

L producing its first over tone, then

a) The frequency of the fundamental tone = ……………

b) The tension of the string = ………………

Essay questions

Evaluation book:

1. (Egypt 94) What are the factors affecting the frequency of fundamental tone of a

vibrating string, mention the relation between each factor and the frequency, and

then write the mathematical relation of these factors with the frequency.(29)

2. Explain Meld’s experiment for the demonstration of standing waves in strings.(30)

3. Write down the relation between the frequency of the fundamental tone and their

overtones in a string.(31)

Previous Exams:

4. (Egypt 99) Mention the necessary condition to obtain a standing wave.(32)

Exercises 2008/2009


5. (Egypt 2000) Mention two factors only on which the frequency of the fundamental

tone of a vibrating string depends(33)

6. (August 2000, August 2001) What is the difference between each pair of the

following: The constructive and destructive interference in sound from the point

of view of [the intensity of sound produced and the path difference](34)

7. What happens with mention the reason for each of the following when:

a) (August 2001) Put a balloon filled with helium gas (lighter than air) between

your ear and a source of sound.(35)

b) (Egypt 2002) Increasing the tension on a stretched string to 4 times its value

(with respect to the velocity of propagation of the transverse waves in it)(36)

Give reasons

Evaluation book:

1. The vibrating string produces a tone, whose pitch increases with the tension.(37)

2. As the radius of the stretched string with constant tension decreases the pitch

of the tone increases.(38)

3. The frequency of the fundamental tone is the lowest frequency produced by

the string.(39)

4. We can hear a person talking behind a thick wall.(40)

5. A person under water surface does not hear clearly sound produced from air.

6. The tone produced from a guitar is different than that produced from flute

although they have the same frequency.

Previous exams:

7. (August 97) When the sound transfers from the air to the water, the angle of

refraction is greater than the angle of incidence.

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Additional questions:

8. Astronauts use wireless instruments for their communication on moon’s

surface.

9. A clear sound is heard at the side of the balloon contains CO2 if a sound source

is placed at the other side.

10. Sound refracts away from the normal to the surface as it transfers from air to

water.

Which of the following statements are right and which are wrong? Rewrite the incorrect statements in

a correct form

Previous exams:

1. (Egypt 93) The frequency of the fundamental tone of a vibrating string is

directly proportional to the density of its material.

What is meant by

Previous exams:

1. (Egypt 2002, Egypt 95) The wave length of a standing wave in a stretched string =

10 cm.

Define each of the following physical quantities and write the unit used to measure each of them if

available

Previous exams:

1. (Egypt 90) Standing waves.

Additional question:

2. Interference.

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3. Diffraction.

4. Anti-node.

5. Node.

6. Wavelength of standing wave.

Complete the following statements

Previous exams:

1. (Egypt 96) A vibrating string emits a tone related to the relation ν= 3

2 L √ Tm

where is the frequency, L is the length of the string, T is the tension and m is

the mass per unit length. Complete the following:

This string emits its ………….. tone.

The wavelength of the propagated wave in the string = …………….

If the tension is increased 4 times its value and the length of string is

decreased to the half, then: the frequency of the emitted tone becomes

…………… its original value.


2. Constructive interference between two waves occurs when the path difference

= …………..(41)

3. The standing waves are produced by …………….. of the incident wave and

the reflected wave, …….. is formed at the middle of the string while ……….

is formed at the ends.

4. The refraction of the sound wave will be clear if the difference in

…………….. between the two media is ….. but if this difference is … so most

of the sound energy ……

Exercises 2008/2009


5. The frequency of the stretched string is …. Proportional to its length and

directly to ….. of tension also it is inversely proportional to the square root

of…..

6. The anti node is the position which the amplitude is ……………. while the

node is the position at which the amplitude …..

7. The vibrating string produces its …..tone when it oscillates as one part

forming …..at the middle and …..at its ends.

Problems

Evaluation book:

1. A string 100 cm long produces its fundamental tone of frequency 420 Hz. Find

the length of the string, which produces its fundamental tone of frequency 600

Hz.

[70 cm]

2. A string of length 1m and the mass per unit length of its wire is 0.001 Kg/m

stretched by a tension of 90N. Find

a. The frequency of the fundamental tone produced.

b. The velocity of wave propagating through the string.

c. The frequency of the fourth harmonic.

[150 Hz, 300 m/s, 600 Hz]

3. A stretched string, calculate the velocity of propagation of the transverse wave

in this string known that the tension is 81 N and the mass per unit length is

0.01 kg. If the string is 0.45 m long, calculate the frequency of its fundamental

tone. What is the frequency of its third harmonic?

[90 m/s, 100 Hz, 300 Hz]

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4. A stretched string (T = 128 N, m = 0.02 kg/m) is vibrating in two segments to

produce its first overtone. What is the frequency of this tone if the length of

the string is 40 cm? And what is the frequency of the tone following it?

[200 Hz, 300 Hz]

5. The following table shows the relation between the frequency of the

fundamental tone of a stretched string and the reciprocal of its length when it

vibrates, the tension is kept constant:

1/L “m-1”10A54321

“Hz”50030025

0

B1489846

Draw a graphical relation between the reciprocal of the length on the x-axis

and the fundamental frequency on the y-axis. From the graph find:

a) The values of both A, and B.

b) The velocity of the transverse wave propagating in the string.

c) If the mass per unit length of the string wire is 0.01 kg/m find tension

action on the string.

6. In Meld’s experiment the length of the thread is 2.5 meter, if the wave length

is 0.5 meter, how many nodes and antinodes are formed.

7. A string of mass 2 g and length 1 m is fixed at one end and attached at the

other end to an oscillator of variable frequency. The string is under a tension

of 51 N. find the three lowest oscillator frequencies for which standing waves

will be formed.

Exercises 2008/2009


Previous exams:

8. (Azhar 93) A transverse wave propagates in a string of length 2 meters and

mass 0.02 kg in the shape of two parts, tensioned by force of 104 N, calculate

the speed of wave propagation of the wave in the string, and if the wave length

in the air 65 cm, calculate the speed of sound in air.

[1000 m/s, 325 m/s]

9. (Egypt 90) What is occurred in the frequency of a string when its length is

reduced to half and its tension force is reduced to the quarter.

[Remains constant]

10. (Egypt 95) An elastic string 2 meter long producing its fundamental tone of

frequency 400 Hz if the wave length of the produced wave in air is 80 cm.

calculate:

a. The velocity of sound wave in air.

b. The velocity of wave in the string.

[320 m/s, 1600 m/s]

11. (August 96) A string of length 1 m is stretched by a force of 4 kg wt. the mass

per unit length is 1 x 10-3 kg/m. what is the frequency of its fundamental tone

and its first overtone (g=10 m/s2)

[100 Hz, 200 Hz]

12. (Egypt 98) The following table shows the relation between the inverse of the

length of a uniform string and the frequency of its fundamental tone when it

vibrates. The tension is kept constant.

(1/L) m-11X23456

() Hz150210300450600Y900

Exercises 2008/2009


Draw a graphical relation between the reciprocal of the length on the x-axis,

and the fundamental frequency on the y-axis. From the graph find:

a. The frequency (y).

b. The length of the string that emits its fundamental tone with frequency

(210) Hz.

c. The velocity of the transverse wave propagating in the string.

d. If the mass per unit length of the string wire is 0.01 kg/m, find the tension

acting on the string.

[750, 1.4. 300, 900]

13. (Egypt 2006) A string from steel of length 1 meter vibrates in the form of

segments, it produces a frequency of 150 Hz, if the mass per unit length of the

string is 0.01 Kgm-1 the string is stretched by tension force 10 kg wt, what are

the number of segments in which the string is divided during its vibration,

given that g = 10 m/s2, calculate the velocity of the propagation and draw the

formation of produced tone.

[3, 100m/s]


14. A gun is fired; a person heard the sound of the bullet after 20 seconds from

seeing the fire. If the distance between the person and the gun is 6800 meters

calculate the sound velocity.

[340 m/s]

15. Find the velocity of a transverse wave propagates in a stretched string such

that tension is 10 kg weight; the mass per unit length is 0.02 kg/m. given that

the acceleration due to gravity is 9.8 m/s2.

[70 m/sec]

Exercises 2008/2009


16. Find the frequency of the third harmonic tone of a string stretched by tension

10 kg weight and the mass per unit length is 0.02 kg/m and the acceleration

due to gravity is 9.8 m/s2. Given that the length is 0.5 m.

[210 Hz]

17. A string of length 0.5 meter is stretched by a tension of 28.9 Newton. The

mass per unit length of the string equals 0.001 kg/meter. If the velocity of

sound in air is 340 meter / sec, calculate:

a) The frequency of the fundamental tone produced by the string.

b) The wavelength in air.

[170 Hz, 2 m]

18. A string 1 meter long and the mass of its wire is 0.0001 kg stretched by a

tension of 81 N. Find:

a) The frequency of the fundamental tone it produces.

b) The velocity of the wave propagating through the string.

c) The frequency of the third overtone.

[450 Hz, 900 m/s, 1800 Hz]

19. The following table gives the relation between frequency of fundamental tone

of vibrating string and its length:

L (m)0.10.20.250.40.50.60.8X

V(Hz)500250200125100y62.550

a. Plot a graph relation between L and v and deduce the relation between

them.

b. Find the velocity of transverse wave in string.

c. Find the value of x and y.

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20. A person stands up between two mountains and he is nearer to one of them

than the other mountain, he shoots a project, he heard two sounds: the first one

after 1.5 sec, and the second after 3 sec. Calculate: the distance between the

two mountain, given that the speed of sound in air is 320 m/s

[450 Hz, 900 m/s, 1800 Hz]

21. A ship is moving towards a mountain on seashore with regular velocity, when

it was (1 km) far from the mountain the ship makes a whistle, the echo was

heard after (5 sec), if the velocity of wound in air (340 m/s) calculate the

velocity of the ship.

[60 m/s]

22. A stretched string (60 cm) long vibrates at frequency of (100 Hz), at what

frequency would it vibrate if its length was reduced to (15 cm) but the tension

was unaltered.

[400 Hz]

23. A string of length (1.5 m) vibrates in the form of (6 segments), its mass =

(0.15 kg) tensioned by a force of 10 N, find the frequency of sound that the

string emits.

[20 Hz]

24. Two strings (A), (B) are from the same material and equal in length, knowing

that the diameter of (A) is half that of (B) and is stretched by a tension force

(20 N) calculate the tension force of (B) to produce the same fundamental tone

of (A)

[80 N]

25. A stretched string of length (L) produce fundamental tone of frequency (120

Hz), Calculate the frequency of this string when:

Exercises 2008/2009


a) The length decreases to its half value.

b) The tension increases to four times its original value.

[240 Hz, 240 Hz]

26. A string is stretched by a force of 100 N, its length is 2 m, its mass is 0.02 kg,

(g = 10 m/sec) Calculate:

a) The speed of propagation of the wave in it.

b) The frequency of the fundamental tone.

[100 m/s, 25 Hz]

27. A string is stretched on a sonometer, its frequency (500 Hz) when its tension

was 36 N, calculate the frequency of the string when the tension becomes (25

N).

[416.67 Hz]

28. String of length equal (80 cm) and its unit length has mass equals 0.4 gm, it is

stretched by a tension equals 49 N, calculate the frequency of the string tone,

if it vibrates at the shape of four parts.

[875 Hz]

29. Two strings have a length 80 cm and 100 cm respectively and radii (2 mm, 3

mm) respectively and the frequency of the second string is 160 Hz, calculate

the frequency of the first string given that the tensions are equal.

[300 Hz]

30. Two strings have the same material, the length of the first string is double the

length of the second, the radius of the second string is double the radius of the

first, compare between the frequency of both strings when the tension force

are equal.

Exercises 2008/2009


[equal]

31. A string has a length (50 cm), and its radius (0.5 mm), it is stretched by a force

of 12.1 kg.wt, its density equals 7700 kg/m3. Calculate the frequency of the

fundamental tone of the string.

[140 Hz]

32. Length of a string (54 cm) and its mass (10.8 grams), it is stretched over a

guitar by a force (10 kg. wt) calculate the point of string in which a musician

press by his finger on to produce the second over tone with frequency 210 Hz.

[4 cm]

33. A stretched string emits (500 Hz), and when its length is double it emits (750

Hz). Calculate the ratio between the two tensions.

[1: 9]

34. A string of length 150 cm, and mass 1.5 gram, and tensioned by force of 90 N,

calculate the frequency of fundamental tone, the speed of waves in the string,

the frequency of the second over tone.

[100 Hz, 300 m/s, 200 Hz]

35. The length of a string is 2 meter, produces a fundamental tone its frequency

400 Hz, and the length of the produced wave 80 cm, calculate :

a) The speed of sound in the air

b) The speed of wave propagation in the string

[320, 1600 m/s]

36. The length of a string is one meter and its mass (40 gm), stretched with a force

of 196 N, calculate the frequency of the fundamental tone given that

Exercises 2008/2009


gravitational acceleration 9.8 m/s2 then deduce how to increase the value of

frequency to 70 Hz, through:

a) Change the length only.

b) Change the tension only.

[35.5 cm, 784 N]

37. A string of mass 2.5 kg is under tension of 200 N, the length of the stretched

string is 20 m, if a transverse vibration begins at one end of the string, how

long does the vibration take to reach the other end.

[0.5 s]

38. A steel wire has a length of 12 m and mass of 2.1 kg, what should be the

tension in the wire so that the speed of a transverse wave on the wire equals

343 m/s

[2.06x104 N]

39. In meld's experiment used a vibrator of fixed frequency, when a load of

volume (V) and density 2700 kg/m3 was hanged at the end of the thread, the

thread divided into 6 segments, when another load of the same volume and of

different material the number of segments becomes 4 segments, calculate the

density of the other load.

[6075 kg/m3]

40. A wire stretched between two rigid supports vibrates in its fundamental tone

with frequency of 45 Hz, the mass of the wire is 3.5 x 10-2 kg, and its linear

density is 4x10-2 Kg/m, what is the speed of its transverse waves.

[78.75 m/s]

Exercises 2008/2009


41. The speed of a wave on string is 160 m/s when the tension force in the string is

100 N, to increase the speed to 200 m/s to what value must the tension must

increase.

[156.25 N]

42. If the tension force acting on a string stretched on a sonometer is changed

from 6.4 N to 8.1 N, knowing that it produce its fundamental tone in each

case, find the ratio between the two frequencies keeping its length constant.

[8: 9]

Exercises 2008/2009


Model Answers

Exercises 2008/2009

1 () Newton.

2 () Three segments

3 () /2

4 () v=√ T

m

5 () C

6 () Third harmonic

7 () 120 cm

8 () 150 Hz

9 () 50 Hz

10 () (2L)/n

11 () five

12 () a

13 () b

14 () c

15 () 300 m/s

16 () twice the distance between two successive nodes

17 () three segments

18 () a, b, c

19 () a

20 () c

21 () b, c

22 () b

23 () 1/2 velocity

24 () 2 L

25 () 2

26 () Fifth harmonic tone (fourth over tone)

27 () 2L/5

28 () Equal to

29 () Length of the string: υ∝ 1

L

Tension force: υ∝√F t

Mass per unit length: υ∝ 1

√m

υ= n2L √ Ft

m

30() Melde’s experiment:

1. The apparatus is consists of a vibrating source, connected to a soft string whose length

ranges from 2 to 3 meters.

2. The other end of the string passes over a smooth pulley and is connected at its free end to

appropriate weights.

3. When the source vibrates, a wave train is produced in the string, which reflects upon

reaching the pulley.

4. The reflected and incident waves are combined to form standing waves.

31() 1: 2: 3

32() Two waves in phase but opposite in direction.

33() Length of the string, tension force and mass per unit length of the string.

34()

Item Constructive Distractive

Intensity of sound High Low

Path difference m (m+1/2)

35() Fade of sound due to diffraction of sound when it travel from high density (low velocity) to less

density (high velocity).

36() Velocity double where velocity is directly proportional to the square root of tension force.

37() Because the pitch (frequency) is directly proportional to the square root of tension force.

38() Mass per unit length is directly proportional to the reduce of the string, then decrease the reduce

will decrease the mass per unit length. The frequency is inversely proportional to square root of

mass per unit length, then increase the mass per unit length leads to decrease the frequency.

39() Because it has the smallest number of segments and frequency is directly proportional to the

number of segments.

40() Duce to diffraction beside sharp edge.

41 () The path difference between two waves = m

eu1c2 by adel khamis

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