The Doppler effect (named after ChristianDoppler) is the change in the pitch (frequency) of the soundfrom a source 1s2 as heard by an observer 1o2 when oneor both are in motion. If we assume both the source and theobserver are moving in the same direction, the relationship is f′ = fa [ ( v - vo)/(v - vs) ]where f′ = perceived pitch by the observerfa = actual pitch of the sourcey = speed of sound in air (assume 772.4 mph2)yo = speed of the observerys = speed of the sourceSuppose that you are traveling down the road at 45 mphand you hear an ambulance (with siren) coming toward youfrom the rear. The actual pitch of the siren is 600 hertz (Hz).(a) Write a function f′(vs) that describes this scenario.(b) If f′ = 620 Hz, find the speed of the ambulance.(c) Use a graphing utility to graph the function.(d) Verify your answer from part (b).
The Doppler effect (named after Christian
Doppler) is the change in the pitch (frequency) of the sound
from a source 1s2 as heard by an observer 1o2 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′ = fa [ ( v - vo)/(v - vs) ]
where f′ = perceived pitch by the observer
fa = actual pitch of the source
y = speed of sound in air (assume 772.4 mph2)
yo = speed of the observer
ys = 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′(vs) that describes this scenario.
(b) If f′ = 620 Hz, find the speed of the ambulance.
(c) Use a graphing utility to graph the function.
(d) Verify your answer from part (b).
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