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# Doppler Effect

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1. Q) You are standing at the side of the road. An ambulance approaches you with its siren on. As it approaches, you hear a frequency of 460Hz. As it moves away, 410Hz.

If the hospital is 3km away, estimate the time taken for the ambulance to reach the hospital, assuming it keeps a constant velocity,
2. question asks for an estimate so IMO you can cut some corners

c=330 m/s (speed of sound)

ambulances typically travel much slower than the speed of sound (IME)
so
split the difference of the frequencies to get a frequency f perceived by the ambulance driver = f0 435Hz

use an approximate formula
Δf=(Δv/c)f0

to get the speed of the ambulance
Note
Δf is the difference between the frequency the stationary observer hears and f[sub]0 (i.e. +ve if the observer hears an increased frequency)
Δv is the speed at which the source is approaching or receding from the observer (i.e. +ve if the source is getting closer to the observer)

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Updated: October 6, 2016
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