Question

Why does the Doppler effect occur?

Answer 1

The Doppler effect occurs because the distance between the source and the observer changes while the sound is going from source to observer.

Explanation:

There are various situations that cause a Doppler effect. I will
discuss one of them.

Consider a stationary weather siren (sounding a 1 kHz alarm) and 2 observers. There is someone on a park bench and someone driving in a convertible toward the siren. We will consider the 1 second period starting when the convertible passes the man on the bench. At the end of that second, the convertible will be 26.8 m closer to the siren than the man on the bench.

In 1 second, the ears of the person on the bench detects 1000 cycles of sound. The ears of the woman in the convertible detect those same 1000 cycles, but also those that have not yet reached the observer on the bench but are within 26.8 m.

The wavelength of a 1 kHz sound, when the speed of sound is 330 m/s, would be

`lambda = (330 m/s)/(1000 Hz) = 0.33 m`

So in the 1 second that she traveled those extra 26.8 m, she will encounter an additional

`26.8 m * ((1 "cycle")/(0.33 m)) = 81 "cycles"`

And because of those extra 81 cycles received in that 1 second period, she perceives a tone of 1081 Hz.

I hope this helps,
Steve