Chapter 2.5, Problem 100PE

The Doppler effect is a change in the observed frequency of a wave (such m a sound wave or light wave) when the source of the wave and observer are in motion relative to each other. The Doppler effect explains why an observer hears a change in pitch of an ambulance siren as the ambulance passes by the observer. The frequency $F\left(v\right)$ of a sound relative to an observer is given by $F\left(v\right)=f_a\left(\frac{s_0}{s_0-v}\right),$ where $f_a$ is the actual frequency of the sound at the source. $s_0$ is the speed of sound in air (772.4 mph). and v is the speed at which the source of sound is moving toward the observer. Use this relationship for Exercises 99-100.

Suppose the frequency of sound emitted by a police car siren is 600 Hz.

a. Write F as a function of v if the police car is moving toward an observer.

b. Suppose that the frequency of the siren as heard by an observer is 664 Hz. Determine the velocity of the police car. Round to the nearest tenth of a mph.

c. Although a police car cannot travel dose to the speed of sound. interpret the meaning of the vertical asymptote