A fire engine is driving directly away from a solid wall at 25 m/s on a hot 30.0

Question

A fire engine is driving directly away from a solid wall at 25 m/s on a hot 30.0o C day while its siren emits a steady 480. Hz sound. The speed of sound on this day is 349 m/s.

Compute the frequency heard by a stationary listener standing near the wall.

Compute the wavelength of the waves as they approach the stationary listener.

A firefighter on the back of the fire engine hears the sound waves after they are reflected from the wall. What is the frequency of this reflected wave as heard by this firefighter?

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Explanation / Answer

The general equation accounting for any motion given by Doppler Effect is:

f/= f (v +/- vO) / (v -/+ vs)

Where,
v = 349 m/s
vO = 0
vs = 25 m/s
f = 480 Hz

Substituing Values -

f/ = 480 *(349) / (349 + 25 )
f/ = 447.9 Hz
Frequency heard by a stationary listener standing near the wall, f/ = 447.9 Hz

Velocity = Frequency * Wavelength
Wavelength = 349 / 447.9 m
Wavelength = 0.779 m

f/ = f (v +/- vO) / (v -/+ vs )
Now,
Vo = 0 m/s
Vs = 50 m/s
f = 480 Hz

f/= 480 * (349 / 349 + 50)
f/= 419.8 Hz

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