7.3 Doppler effect for sound waves
- Syllabus
- 9702–2028–2029
- Topic
- 7.3
- Level
- AS
Learning objectives
7.3.1When a source of sound waves moves relative to a stationary observer, the• understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency (understanding of the Doppler effect for a stationary source and a moving observer is not required)7.3.2The expression fο = f sv / (v ± vs) for the observed frequency when a source• use the expression fο = f sv / (v ± vs) for the observed frequency when a source of sound waves moves relative to a stationary observer
A moving sound source changes the frequency received by a stationary observer
For a sound source moving relative to the medium and a stationary observer, the Doppler effect is the difference between observed frequency and the source's emitted frequency caused by the source motion.
| Source motion | Wavefront spacing / wavelength reaching observer | Observed frequency |
|---|---|---|
| towards observer | smaller | higher than source frequency |
| away from observer | larger | lower than source frequency |
The moving source emits successive wavefronts from different positions. In the same medium, sound speed remains v, so the changed wavelength gives a changed arrival frequency through v = fλ. The source itself can continue emitting at one steady frequency.
Greater speed towards the observer gives a greater upward shift; greater speed away gives a greater downward shift. A siren therefore sounds higher before passing and lower after passing a stationary listener.
This syllabus model covers a moving source and stationary observer. Understanding the separate case of a stationary source with a moving observer is not required here, and source motion does not change sound speed in the medium.
Choose the Doppler denominator from the source motion
fo=fsv/(v±vs)
f_o is observed frequency, f_s is source frequency, v is sound speed in the medium and v_s is source speed relative to the medium. The observer is stationary.
| Source motion | Denominator | Required check |
|---|---|---|
| towards observer | v − v_s | f_o > f_s |
| away from observer | v + v_s | f_o < f_s |
A horn emits 440 Hz while moving towards a stationary observer at 30.0 m s⁻¹; sound speed is 340 m s⁻¹. f_o = 440 × 340/(340 − 30.0) = 483 Hz (3 s.f.). The answer is above 440 Hz, as approach requires.
First predict higher or lower frequency. Then select the sign, substitute speeds in the same units, solve, and compare f_o with f_s. The same equation can be rearranged to find v_s; retain the physical sign and direction.
The minus sign does not mean a negative speed: it makes the denominator smaller for approach. The model requires v_s < v and does not use an observer speed term.