When a sound source is moving, a stationary observer will hear a frequency that differs from that which is produced by the source. The doppler effect will be noticed as a marked drop in pitch when a vehicle passes at high speed. An interesting fact is that doppler for any straight line movement always sweeps down in pitch!

If one approaches a sound source by moving toward it with a velocity, v, the frequency of the sound heard is F=Fo(c+v)/c, where Fo is the emitted sound frequency, c is the speed of sound in still air and v is the speed of the observer or the moving source. if one moves away from a sound source, the sign of v is reversed.

But for an approaching sound source, the frequency of the sound heard is F=Fo*c/(c-v). For a receding source the sign of the velocity, v, term is reversed.

The speed of sound in air is approximately 340 m/s (see 2.11).

Example 1: A sound source, S, emits 1000 waves per second (1 kHz) and is moving directly towards an observer, O, at a speed of 100 metres per second (equivalent to approximately 225 miles per hour).

After 1 second the wave front, which is travelling at the speed of sound, will have travelled 340 metres from the original source position. Also after that second the sound source will have moved 100 metres towards the observer.

```  0 m                                            340 m
S |     |     |     |     |     |     |     |     |          O

100 m                           340 m
S |   |   |   |   |   |   |   |   |          O
```

Therefore the same number of waves will occupy a space of 340-100 = 240 metres and the wavelength will be 240/1000 = 0.24 metres. To the observer the frequency heard will be the speed of sound divided by its wavelength = 340/0.24 = 1416.7 Hz.

Example 2: An observer moving at 100 metres per second directly approaches a stationary sound source, S, which is emitting 1000 waves per second (1 kHz). In this example there is no change in wavelength. In one second, the observer will hear the number of waves emitted per second plus the number of waves which s/he has passed in the time (1000+100/0.34) = 1294.1 Hz.

Note the interesting result – a stationary observer with moving source will not hear the same frequency as a would a moving observer with a stationary source.

Interesting corollaries are that if one is confined to movement velocities equal to or less than the speed of sound, on approaching a sound source, one will observe frequencies up to only twice the radiating frequency, but if one is stationary and approached by a sound source, there is no upper frequency limit.

Thought teaser: Apply these principles to light, aether, red shift and quasars. What would cause a “blue shift”?