How to use it
- Type the Frequency of the source, for example 700 Hz for a siren.
- Type the Speed of the source and the Speed of the listener: a positive value for a move toward the other, a negative value for a move away.
- Check the Speed of sound in the air. The default 340 m/s is the sea-level value on a standard day.
- Read Frequency heard and Change in frequency, then open How it is worked out for the formula with the numbers.
The formula
When a source of sound and a listener move through the air, the frequency the listener hears differs from the frequency the source emits. OpenStax gives the result for a moving source and a moving observer as f_o = f_s((v ± v_o)/(v ∓ v_s)), with the top sign for approach. Here f_s is the source frequency, f_o the frequency observed by the listener, v the speed of sound, v_o the speed of the listener and v_s the speed of the source.
f_o = f_s × (v + v_o) ÷ (v − v_s)
f_s = frequency of the source, Hz
v = speed of sound in the air, m/s
v_o = speed of the listener, positive toward the source
v_s = speed of the source, positive toward the listener- A source that moves toward the listener raises the frequency heard, because the denominator v − v_s becomes smaller.
- A listener that moves toward the source raises it too, through the numerator v + v_o.
- The source must be slower than the speed of sound, so that v − v_s is above zero.
What the calculator does not cover
- Wind, which carries the sound and changes its speed over the ground.
- A source or a listener that moves at the speed of sound or faster, where this formula does not apply.
- Light and radio. The same idea applies to them, but the formula is different, and this calculator is for sound in air.
Worked example: a siren at 700 Hz coming toward a listener
A siren emits 700 Hz and moves at 25 m/s toward a listener who stands still, in air where sound travels at 340 m/s. The listener hears f_o = 700 × 340 ÷ (340 − 25) = 755.56 Hz, which is 55.56 Hz higher than the siren's frequency.
| Quantity | Value |
|---|---|
| Frequency heard | 755.6 Hz |
| Change in frequency | +55.56 Hz |
Frequently asked questions
Why does a siren sound higher as it comes toward me?
As the source moves toward you, each wave is sent out from a point closer to the last one, so the waves reach you more often. The formula shows this as a smaller denominator v − v_s, which makes the frequency heard larger.
Which units can I type?
The speed boxes accept metres per second or km/h and convert them, so 90 km/h is the same as 25 m/s. Type the frequency in hertz, with k, M or G for thousands, millions or billions.
What is the speed of sound in air?
At sea level on a standard day it is about 340 m/s. NASA Glenn gives it as about 761 mph for that case. It rises as the air gets warmer, so use the value for the air you are in when you know it.
Does the Doppler effect work for light?
The same idea applies to light and radio, but the formula is different, because light does not need air to travel. This calculator works only for sound in air.
What happens if the source moves faster than sound?
The formula stops applying when the source moves at the speed of sound or faster, so the calculator shows a message instead of a frequency. Use a source speed below the speed of sound.
Why is the change negative when the source moves away?
When the source moves away, the denominator v − v_s becomes larger, so the frequency heard is lower than the frequency emitted. A negative change means the sound you hear is lower in pitch.
Sources
- OpenStax University Physics Volume 1, section 17.7: The Doppler Effect (equation 17.20)
- NASA Glenn: speed of sound, about 761 mph at sea level on a standard day
Figures and text last checked on Thursday, November 12, 2026.