Chapter-17

Waves-II

Chapter-17 Waves-II Topics to be studied:

Speed of sound waves

Relation between displacement and pressure amplitude

Interference of sound waves

Sound intensity and sound level

Beats

The Doppler effect

Longitudinal Waves: Particles displacement parallel to wave direction-Sound Waves

Wavefronts: Surfaces over which the oscillations have the same value. For point source such surfaces are represented by cirucles

Rays : lines representing the direction of sound wave.

Rays are to wavefronts

Ch 17-2 Sound Waves

Speed of Sound: speed of mechanical Wave v= (elastic property/inertial property)

A sound wave passes through medium, it undergoes compression and expansion due to pressure variation, then elastic property is due to change in volume or bulk modulus B=-p/(V/V) then

Speed of sound v = B/ where is density

Ch 17-3 Speed of Sound

Particle displacement s(x,t)=sm cos(kx-t)

where sm is displacement amplitude

Pressure variation given by

p= pmsin(kx-t)

where pm is pressure amplitude

Ch 17-4 Traveling Sound Wave

Ch 17-4 Traveling Sound Wave

Sound waves undergo interference if phase difference between two waves from s1 and s2 have phase difference =kx-t; k= 2/

=2- 1= kL2-t-kL1+ t =k(L2-L1) =k(L2-L1) = (2/ )L

-path difference L =L2-L1 is multiple of wavelength

Fully Constructive Interference for L =n (n=0,1,2,3,….) Fully Destructive Interference forL =m/2 (m=1,3,5,7…)

Ch 17-5 Interference

Ch 17-6 Intensity and Sound Level

Intensity I of sound is average rate of energy transferred by the wave through or onto the surface. If P is power and A is surface area (A=4R2 for a sphere) then

I=P/A=P/4R2 I=(v2s2

m)/2 Displacement Amplitude sm I

Ch 17-6 Intensity and Sound Level

The Decibel Scale Large variation in sound displacement amplitude: Loudest amplitude:10-5 m; Faintest amplitude: 10-

11 m Sound intensity variation expressed in logarithms. Instead of sound intensity I, sound level given in

decibels (dB) by: = (10dB) log (I/I0), where I0 is standard

reference intensity I0 =10-12 W/m2 The 2- 1= (10dB) log (I2/I1)

Pipes resonates if An open end is an antinodes

and A closed end is a node For pipe open at both end:L=/2, 2/2, 3/2,….. = mm/2 (m=1,2,3,4,…)

fm=v/m=mv/2L (m=1,2,3,4,…) For pipe close at one end:L=/4, 3/4, 5/4,….. = nn/4 ( n=1,3,5,7,…)

fn=v/n=nv/4L (n=1,3,5,7,…)

Ch 17-7 Sources of Musical Sound

Ch 17-9 The Doppler Effect

The Doppler Effect : Change in observed frequency f’ with respect to source frequency f due to motion of source (vS) or detector (vD) or both:

f’=f(vvD)/(vvS)

When the detector or source are moving towards each other, the sign of speed must results in an increase in observed frequency f’.

When the detector or source are moving away from each other, the sign of speed must result in a decrease in observed frequency f’.

Ch 17-9 The Doppler Effect

Det. Moving in opposite direction-Source Stationary

Distance traveled by wavefront in t sec is vt and Distance traveled by detector in t sec in opposite direction is -vDt

Distance traveled by wavefront with respect to detector= vt-(-vDt)= vt+vDt

Number of wavelength intercepted by Detector= (vt+vDt)/

Observed frequency f’= Number of wavelength intercepted /t

f’= (1/t)(vt+vDt)/=(v+vD)/= f(v+vD)/v For detector moving in same

direction f’= (1/t)(vt-vDt)/=(v-vD)/= f(v-vD)/v

Source. Moving Det. Stationary Source move towards detector

with speed vS. During time T, the wavefront move a distance vT while the source move a distance vST. At the end of T, second sound Wavefront is emitted. The physical seperation between the two wavefront is ’=vT- vST

The observed frequency f’= v/’=

f’= v/(vT- vST)=(v/T)(1/(v-vs)) f’= fv/(v-vs) Source moving from detector f’= fv/(v+vs)

f’= fv/(vvs)

Ch 17-9 The Doppler Effect

Ch 17-9 The Doppler Effect