An ambulance is traveling east at 60.7 m/s. Behind it there is a car traveling along the same direction at 32.3 m/s. The ambulance driver hears his siren at a frequency of 521 Hz.

At what frequency does the driver of the car hear the ambulance’s siren? The velocity of sound in air is 343 m/s. Answer in units of Hz

The sign on the numerator should be a positive not a negative because the car (receiver) is approaching the ambulance (emitter).

To find the frequency heard by the driver of the car, we can use the formula for the Doppler effect in sound waves:

f' = (v + vd) / (v + vs) * f

where:
f' is the observed frequency,
v is the velocity of sound in air,
vd is the velocity of the observer (car),
vs is the velocity of the source (ambulance),
and f is the actual frequency emitted by the source.

Given values:
v = 343 m/s (velocity of sound in air),
vd = 32.3 m/s (velocity of the car),
vs = 60.7 m/s (velocity of the ambulance),
f = 521 Hz (actual frequency emitted by the ambulance).

Now let's substitute the values into the formula:

f' = (343 + 32.3) / (343 + 60.7) * 521

Simplifying:

f' = (375.3) / (403.7) * 521

f' = 0.930 * 521

f' ≈ 484.53 Hz

Therefore, the driver of the car will hear the ambulance's siren at a frequency of approximately 484.53 Hz.

To find the frequency of the siren as heard by the car driver, we need to take into account the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, sound) as perceived by an observer moving relative to the source of the wave.

The formula for the Doppler effect in sound is given by:

f' = f * (v + vd) / (v + vs)

Where:
f' is the observed frequency
f is the source frequency
v is the speed of sound in air
vd is the relative velocity between the observer and the source (ambulance velocity in this case)
vs is the velocity of the source (ambulance velocity in this case)

We are given:
f = 521 Hz
v = 343 m/s
vd = 32.3 m/s (relative velocity between car and ambulance)
vs = 60.7 m/s (velocity of the ambulance)

Substituting the given values into the formula:

f' = 521 * (343 + 32.3) / (343 + 60.7)

Calculating this expression will give us the frequency observed by the car driver.

Fr = (Vs-Vc)/(Vs+Va)*Fa

Fc = (343-32.3)/(343+60.7)*521 = 401 Hz=
Freq. heard by car driver.