The siren on an ambulance is emitting a sound whose frequency is 2250 hz. the speed of sound is 343 m/s. (a) if the ambulance is stationary and you (the "observer") are sitting in a parked car, what are the wavelength and the frequency of the sound you hear? (b) suppose that the ambulance is moving toward you at a speed of 26.6 m/s. determine the wavelength and the frequency of the sound you hear. (c) if the ambulance is moving toward you at a speed of 26.6 m/s and you are moving toward it at a speed of 11.0 m/s, find the wavelength and frequency of the sound you hear.

(a) 2250 Hz, 0.152 m

In this situation, both the ambulance and observer are stationary.

This means that there is no shift in frequency/wavelength due to the Doppler effect. So, the frequency heard by the observer is exactly identical to the frequency emitted by the ambulance:

f = 2250 Hz

While the wavelength is given by the formula:

where

v = 343 m/s is the speed of sound

f = 2250 Hz is the frequency of the sound

Substituting, we find

(b) 2439.2 Hz, 0.141 m

The Doppler effect formula for a moving source is

where

f' is the apparent frequency

f is the original frequency

v is the speed of sound

is the velocity of the source (the ambulance), which is positive if the source is moving away from the observer, negative otherwise

Here the ambulance is moving toward the observer, so

Substituting into the formula, we find the frequency heard by the observer:

while the wavelength seen by the observer will be:

(c) 2517.4 Hz, 0.136 m

In this situation, we must use the most general formula for the Doppler effect, which is

where

is the velocity of the observer, which is positive if the observer is moving toward the source, negative otherwise

is the velocity of the source (the ambulance), which is positive if the source is moving away from the observer, negative otherwise

In this situation,

Therefore, the frequency heard by the observer is

while the wavelength seen by the observer will be:

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