"Doppler Effect: Applying a 35 m/s Car

[dietcokegal]

Homework Statement

A car moving at 35 m/s approaches a stationary whistle that emits a 220 Hz sound. The speed of sound is 343 m/s. What is the speed of sound relative to the driver of the car?

Homework Equations

fo = fs [1 +/- vo/v] / [1 +/- vs/v]

The Attempt at a Solution

Dont know how to do this problem at all. I am not understanding what the question is even asking for. I solved for the frequency that the observer in the car is hearing -- 242 Hz. Not sure how to figure out the question being asked.

 

[aeroengineer]

Well, the speed of something relative to something else would be that something minus the value of the something else.

So it looks like all you need to do is subtract the speed of sound from the speed of the car (but remember that they are on a collision course, so you would really by adding the two velocities).

Eh, that's an oddly phrased question.

 

[nlightner]

The Doppler Effect is a phenomenon where the observed frequency of a sound or light wave changes depending on the relative motion between the source and the observer. In this scenario, the car is moving at a constant speed of 35 m/s and is approaching a stationary whistle that emits a sound wave with a frequency of 220 Hz. The speed of sound is given as 343 m/s.

To find the speed of sound relative to the driver of the car, we can use the Doppler equation: fo = fs [1 +/- vo/v] / [1 +/- vs/v]

Where:
fo = observed frequency (Hz)
fs = source frequency (Hz)
vo = observer's velocity (m/s)
vs = source's velocity (m/s)
v = speed of sound (m/s)

In this case, the observer's velocity (vo) is the same as the car's velocity (35 m/s), and the source's velocity (vs) is 0 since the whistle is stationary. Plugging in the given values, we get:

fo = 220 Hz [1 + (35 m/s) / (343 m/s)] / [1 + 0 / (343 m/s)]
= 242 Hz

This means that the driver of the car will hear the sound with a frequency of 242 Hz. This is higher than the original frequency of 220 Hz because the car is moving towards the source, causing the sound waves to be compressed and resulting in a higher frequency.

In conclusion, the speed of sound relative to the driver of the car is still 343 m/s, as it is the same for all observers in a given medium. However, the observed frequency of the sound wave is affected by the relative motion between the car and the source.