Review of Chapter 17 Dec. 7th 2004

The speed of sound It should not surprise you that the speed of sound is given by a similar expression to the one for a wave on a string, where B is the bulk modulus of the medium, as defined in chapter 12 (page 318), and r is the density or mass per unit volume.

Traveling sound waves Longitudinal displacement: Pressure variation: Pressure amplitude:

Sound wave intensity Intensity: In analogy to waves on a string: Sound waves radiate in all directions from a point source. Wavefronts are surfaces over which the phase (displacement or pressure) of the wave is constant. Intensity: PS is the power produced a the source. The wavefronts are spherical close to a point source. At large distances, the wavefronts are approximately planar. In analogy to waves on a string:

Interference - spatial The waves reaching P from S1 and S2 will have traveled different distances, i.e. they will not be in phase. However, if their phase difference is a multiple of 2p, the waves will interfere constructively. On the other hand, if their phase difference is an odd integer multiple of p, the waves will interfere destructively. Constructive interference Destructive interference

Interference - temporal (or beats) A maximum amplitude occurs whenever w't has the value +1 or -1. This happens twice in each time period of the cosine function. Therefore, the beat frequency is twice the frequency w', i.e. Link 2

Standing waves in air columns A harmonic series 2 3 4

Standing waves in air columns A different harmonic series 1 3 5 7

Doppler effect general Doppler formula We use S to denote the source, and D to denote the detector. We then assume that S and D move either directly towards each other or directly away from each other along a straight line, at speeds less than the sound velocity, then general Doppler formula v is the sound velocity, vS is the source velocity, and vD is the detector velocity; all velocities are measured relative to stationary observers. When the motion of the detector or source is towards the other, the sign on its speed must give an upward shift in frequency. When the motion of the detector or source is away from the other, the sign on its speed must give an downward shift in frequency.