Doppler Effect Calculator: Shifted Frequency for a Moving Source or Listener, Beat Frequency and Speed of Sound
Find the pitch of a passing siren or any moving sound source.
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How this calculator works
Enter the frequency, the air temperature, the speed of the source and of the listener, and whether each is moving toward or away.
The calculator finds the speed of sound at that temperature, the frequency heard f prime = f (c plus or minus vo) over (c minus or plus vs), the change in frequency and the wavelength heard.
The beat case gives the beat frequency of two close notes.
Formulas used
- c = 331.3\sqrt{1 + T/273.15}
- f' = f\,\frac{c \pm v_o}{c \mp v_s}
- f_b = |f_1 - f_2|
Worked example
With the default numbers in the calculator above:
- Speed of sound at this temperature: 343.21 m/s
- Frequency heard: 482.14 Hz
- Change in frequency: 42.14 Hz (9.58 percent)
- Wavelength heard: 0.71 m (the wavelength of the source is 0.78 m)
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Beat frequency of two notes.
- Speed of sound at this temperature: 343.21 m/s
- Beat frequency: 4.00 Hz (about 240.00 beats a minute)
- Average frequency heard, which rises and falls in loudness at the beat frequency: 442.00 Hz
- Wavelength of the first note: 0.78 m
Common questions
Why does the pitch of a siren drop as it passes?
While it approaches, the waves are squeezed together and the pitch is higher. After it passes, they are stretched and the pitch is lower.
Does the Doppler effect work for light?
Yes, but the formula is different, because light does not need a medium and the relativistic effects matter.
What are beats?
The rise and fall in loudness when two notes of almost the same frequency are heard together. The beat rate is the difference between them.
What if the source is faster than sound?
Then a shock wave (a sonic boom) forms and the formula no longer works.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any university physics text (waves and the Doppler effect); Kinsler et al, Fundamentals of Acoustics.
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