PHY 2311

PHYSICS 231Lecture 35: interference & sound

Remco ZegersQuestion hours:Monday 9:15-10:15

Helproom

PHY 2312

exampleA pendulum with a length of 4 m and a swinging mass of 1 kg oscillates with an maximum angle of 10o. What is the gravitational force parallel to the string, perpendicular to the string, the total gravitational force and the centripetal force when the mass passes through theequilibrium position and when it reaches its maximum amplitude?

PHY 2313

describing a traveling wave

While the wave has traveled onewavelength, each point on the ropehas made one period of oscillation.

v=x/t=/T= f

: wavelengthdistance betweentwo maxima.

On a string: v=(F/)

PHY 2314

InterferenceTwo traveling waves pass through each other withoutaffecting each other. The resulting displacement is thesuperposition of the two individual waves.

example: two pulses on a string that meet

PHY 2315

Interference II

constructive interference destructive interference

PHY 2316

Interference III

constructive interferencewaves in phase

demo: interference

+

=

destructive interferencewaves ½ out of phase

+

=

PHY 2317

Interference IV

Two interfering waves canat times constructivelyinterfere and at times destructively interfere

If the two interferingwaves always have thesame vertical displacementat any point along thewaves, but are of oppositesign: standing waves

later more!!!

PHY 2318

Interference holds for any wave type

The pulses can be sine-waves, rectangular wavesor triangular waves

PHY 2319

Interference in spherical wavesmaximum of wave minimum of wave

positive constructive interferencenegative constructive interferencedestructive interferenceif r2-r1=n then constructive interference occursif r2-r1=(n+½) the destructive interference occurs

r1

r2

r1=r2

PHY 23110

Interference of water waves

PHY 23111

Example

0.7m

direction of walking person

two speakers separated by 0.7m producea sound with frequency 690 Hz (from the same sound system). A person starts walking from one of thespeakers perpendicular to the line connecting the speakers. After whatdistance does he reach the first maximum? And the first minimum?vsound=343 m/s

PHY 23112

Reflection of waves.

Frope on wall=-Fwall on rope

FIXED END: pulse inversion FREE END: no inversion

demo: rope onwall

PHY 23113

Connecting ropesIf a pulse travels froma light rope to a heavy rope(light< heavy) the boundary isnearly fixed. The pulse ispartially reflected (inverted) and partially transmitted.

before

after

If a pulse travels froma heavy rope to a light rope(light< heavy) the boundary isnearly free. The pulse ispartially reflected (not inverted) and partially transmitted.

before

after

Ain

AR AT

Ain

AR AT

|AR|<|Ain||AT|<|Ain| |AR|<|Ain|

|AT|>|Ain|

PHY 23114

Sound: longitudinal waves

PHY 23115

The speed of soundDepends on the how easy the material is compressed (elastic property) and how much the material resistsacceleration (inertial property)

v=(elastic property/inertial property)

v=(B/) B: bulk modulus : density

The velocity also depends ontemperature. In air:

v=331(T/273 K)

so v=343 m/s at room temperature

PHY 23116

Quick questionThe speed of sound in air is affected in changes in:(more than one possible)a) wavelengthb) frequencyc) temperatured) amplitudee) none of the above

PHY 23117

Intensity

Intensity: rate of energy flow through an area

Power (P) J/s A (m2)

I=P/A (J/m2s=W/m2)example: If you buy a speaker, it gives power output

in Watts. However, even if you put a powerful speaker in a large room, the intensity of the

sound can be small.

PHY 23118

IntensityFaintest sound wecan hear: I~1x10-12 W/m2

(1000 Hz)Loudest sound we canstand: I~1 W/m2

(1000 Hz)

Factor of 1012? Loudness works logarithmic…

PHY 23119

decibel level =10log(I/I0) I0=10-12 W/m2

y=log10x inverse of x=10y (y=ln(x) x=ey) log(ab) =log(a)+log(b)log(a/b) =log(a)-log(b)log(an) =nlog(a)

PHY 23120

decibels=10log(I/I0) I0=10-12 W/m2

An increase of 10 dB:intensity of the sound is multiplied by a factor of 10.

2-1=10 10=10log(I2/I0)-10log(I1/I0) 10=10log(I2/I1) 1=log(I2/I1) 10=I2/I1 I2=10I1

Next quiz!

PHY 23121

Frequency vs intensity

1000 Hz

PHY 23122

exampleA machine produces sound with a level of 80dB. Howmany machines can you add before exceeding 100dB?