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)=s m cos(kx-  t) where s m is displacement amplitude  Pressure variation given by  p=  p m sin(kx-  t) where  p m is pressure amplitude Ch 17-4 Traveling Sound Wave

 Sound waves undergo interference if phase difference between two waves from s 1 and s 2 have phase difference  =kx-  t; k= 2  /   =  2 -  1 = kL 2 -  t-kL 1 +  t =k(L 2 -L 1 )   =k(L 2 -L 1 ) = (2  / )  L  -path difference  L =L 2 -L 1 is multiple of wavelength  Fully Constructive Interference for  L =n (n=0,1,2,3,….)  Fully Destructive Interference for  L =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=4  R 2 for a sphere) then  I=P/A=P/4  R 2  I=(  v  2 s 2 m )/2  Displacement Amplitude s m   I

Ch 17-6 Intensity and Sound Level  The Decibel Scale  Large variation in sound displacement amplitude:  Loudest amplitude:10 -5 m; Faintest amplitude: m  Sound intensity variation expressed in logarithms.  Instead of sound intensity I, sound level  given in decibels (dB) by:   = (10dB) log (I/I 0 ), where I 0 is standard reference intensity I 0 = W/m 2  The  2 -  1 = (10dB) log (I 2 /I 1 )

 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,….. = m m /2 (m=1,2,3,4,…) f m =v/ m =mv/2L (m=1,2,3,4,…)  For pipe close at one end: L= /4, 3 /4, 5 /4,….. = n n /4 ( n=1,3,5,7,…) f n =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 (v S ) or detector (v D ) or both: f’=f(v  v D )/(v  v S )  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 -v D t  Distance traveled by wavefront with respect to detector= vt-(-v D t)= vt+v D t  Number of wavelength intercepted by Detector= (vt+v D t)/  Observed frequency f’= Number of wavelength intercepted /t  f’= (1/t)(vt+v D t)/ =(v+v D )/ = f(v+v D )/v  For detector moving in same direction  f’= (1/t)(vt-v D t)/ =(v-v D )/ = f(v-v D )/v

 Source. Moving Det. Stationary  Source move towards detector with speed v S. During time T, the wavefront move a distance vT while the source move a distance v S T. At the end of T, second sound Wavefront is emitted. The physical seperation between the two wavefront is ’=vT- v S T  The observed frequency f’= v/ ’= f’= v/(vT- v S T)=(v/T)(1/(v-v s )) f’= fv/(v-v s )  Source moving from detector f’= fv/(v+v s ) f’= fv/(v  v s ) Ch 17-9 The Doppler Effect