Chapter 4.3, Problem 58AYU

Doppler Effect The Doppler effect (named after Christian Doppler) is the change in the pitch (frequency) of the sound from a source (s) as heard by an observer (o) when one or both are in motion. If we assume both the source and the observer are moving in the same direction, the relationship is $f\text{'}=f_a\left(\frac{v-v_o}{v-v_s}\right)$

where $f\text{'}=$ perceived pitch by the observer

$f_a=$ actual pitch of the source

$f_a=$ actual pitch of the source

$v_o=$ speed of the observer

$v_s=$ speed of the source

Suppose that you are traveling down the road at 45 mph and you hear an ambulance (with siren) coming toward you from the rear. The actual pitch of the siren is 600 hertz (Hz).

(a) Write a function $f\text{'}\left(v_s\right)$ that describes this scenario.

(b) If $f\text{'}=620$ Hz, find the speed of the ambulance.

(c) Use a graphing utility to graph the function.

(d) Verify your answer from part (b).

Source: www.kettering.edu/~drussell/