Dr. Jie ZouPHY Chapter 17 Sound Waves (cont.)

Dr. Jie ZouPHY Outline Intensity of periodic sound waves The Doppler effect Shock wave

Dr. Jie ZouPHY Intensity of periodic sound waves Intensity I of a wave: The power per unit area, or the rate at which the energy being transported by the wave flows through a unit area A perpendicular to the direction of travel of the wave, or I = P/A. P: Rate of energy transfer or power. The amount of energy that passes by a given point during one period of oscillation can be shown to be E = (1/2)  A(  s max ) 2. Power P = E /T= (1/2)  Av(  s max ) 2. Intensity I = P/A = (1/2)  v(  s max ) 2. Using  P max =  v  s max, I = (  P max ) 2 /(2  v). The intensity of a periodic sound wave  (  P max ) 2.

Dr. Jie ZouPHY Example 17.3 The faintest sounds the human ear can detect at a frequency of 1000 Hz corresponds to an intensity of about 1.00 x W/m 2 - the so-called threshold of hearing. The loudest sounds the ear can tolerate at this frequency corresponds to an intensity of about 1.00 W/m 2 - threshold of pain. Find the pressure amplitude and displacement amplitude associated with these two limits.

Dr. Jie ZouPHY The Doppler effect Doppler effect (sound waves): The change in pitch (frequency) of the sound, due to the relative motion between a source of sound and the receiver. Stationary source, moving observer: Stationary observer, moving source: Both source and observer are in motion:

Dr. Jie ZouPHY Example 17.6 As an ambulance travels east down a highway at a speed of 33.5 m/s (75 mi/h), its siren emits sound at a frequency of 400 Hz. What frequency is heard by a person in a car traveling west at 24.6 m/s (55 mi/h) (a) as the car approaches the ambulance and (b) as the car moves away from the ambulance?

Dr. Jie ZouPHY Shock Waves When the speed v s of the source > the wave speed v. The envelope of the waves fronts is a cone whose apex half-angle  is given by: sin  = vt/v s t = v/v s. Mach number: The ratio v s /v is called the Mach number. Shock wave: The conical wave front produced when v s > v (supersonic speeds) si known as a shock wave.

Dr. Jie ZouPHY Homework Ch. 17, P. 537, Problems: #18, #37.