A car sounds its horn (502 Hz) as it approachs a pedestrian by the side of the road. The pedestrian has perfect pitch and determines that the sound from the horn has a frequency of 520 Hz. If the speed of sound that day was 340 m/s , how fast was the car travelling

f(observed) = 520 Hz, f(source) = 502 Hz, u = 340 m/s

At source approaching
f(observed) = [v/(v-u)] •f(source),
v =[f(obs)-f(sour)] •u/ f(obs) =
= (520-502) •340/520 = 18•340/520 =
=11.77 m/s.

To calculate the speed at which the car was traveling, we can use the Doppler effect equation. The formula for the apparent frequency observed by the pedestrian can be expressed as:

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

Where:
f' is the observed frequency by the pedestrian (520 Hz)
f is the actual frequency of the car horn (502 Hz)
v is the speed of sound (340 m/s)
vo is the velocity of the observer (pedestrian)
vs is the velocity of the source (car)

We need to solve for vs, which represents the velocity of the car.

Let's rearrange the equation to solve for vs:

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

Now, let's substitute the given values:

vs = (502 Hz - 520 Hz) * 340 m/s / (502 Hz + 520 Hz)

Simplifying this calculation:

vs = -18 Hz * 340 m/s / 1022 Hz

Finally, we can calculate the velocity of the car:

vs ≈ -5.98 m/s

Since we are considering the magnitude of the velocity, the car was traveling at approximately 5.98 m/s.