The frequency you hear when a sound source, the listener or both are moving, for any speed of sound, checked against OpenStax University Physics Volume 1
How the Doppler Formula Works
A moving source crowds the sound waves ahead of it and stretches them behind, so a listener in front hears a higher frequency and one behind hears a lower one. A moving listener runs into wave crests faster or slower. OpenStax combines both in one formula, with speeds measured relative to the air (or other medium):
f₀ = fₛ × (v ± v₀) ÷ (v ∓ vₛ)
- Pick signs. Observer moving toward the source: + in the numerator; away: −. Source moving toward the observer: − in the denominator; away: +.
- Example 17.8, train approaching: 150 × 340 ÷ (340 − 35.0) = 150 × 1.115 = 167 Hz.
- Train receding: 150 × 340 ÷ (340 + 35.0) = 136 Hz.
- The engineer riding the train moves with the horn: 150 × (340 − 35.0) ÷ (340 − 35.0) = 150 Hz, no shift.
The shift up (17 Hz) is larger than the shift down (14 Hz): approaching and receding are not symmetric because the source speed sits in the denominator.
Worked Values
The rows after the textbook example use 343 m/s for the speed of sound and illustrative speeds. Change the speed of sound for other media or temperatures: OpenStax section 17.2 gives 331 m/s for air at 0°C, 343 m/s at 20°C and 1,480 m/s for fresh water, so the same motion gives a much smaller shift under water.
Common Mistakes
- Getting the signs backward. Check the answer: toward each other must raise the frequency.
- Treating source and observer motion as the same. 35 m/s of source motion and 35 m/s of observer motion give different shifts.
- Mixing units. Convert km/h or mph to m/s before using the formula (the calculator does it for you).
- Using the formula at or above the speed of sound. A source moving that fast creates a shock wave instead.
- Using it for light. The relativistic Doppler effect for light uses a different formula.
What This Calculator Does Not Cover
It assumes motion along the line between source and observer in still air. Wind, motion at an angle (use the speed component along the line) and light waves need adjustments the calculator does not make.
Frequently Asked Questions
What is the Doppler effect formula for sound?
f₀ = fₛ (v ± v₀) ÷ (v ∓ vₛ), with the top signs when the observer and source move toward each other and v the speed of sound.
Why does a siren sound higher as it approaches?
The moving source compresses the sound waves in front of it, so more crests reach you each second and the frequency rises.
What frequency does a 150 Hz train horn have at 35 m/s?
About 167 Hz approaching and 136 Hz receding with a 340 m/s speed of sound, per OpenStax University Physics Example 17.8.
Is the Doppler shift the same for a moving source and a moving observer?
No. At the same speed, a moving source gives a larger shift than a moving observer, because its speed is in the denominator.
Does the person riding with the source hear a change?
No. Source and listener move together, so the effects cancel and the frequency is unchanged.
What happens when the source reaches the speed of sound?
The waves pile up into a shock wave, a sonic boom, and the ordinary Doppler formula no longer applies.
How to Use This Calculator
- Enter the source frequency — the pitch the source actually emits, in Hz.
- Set the speed of sound — 340 m/s as in OpenStax, about 343 m/s in room-temperature air, or a value for another medium.
- Enter the source and observer speeds and directions — toward or away from each other, in m/s, km/h or mph.
- Read the heard frequency — with the shift, the percent change and the wavelength.
📚 Sources & References- [1] OpenStax. University Physics Volume 1, 17.7 The Doppler Effect (2016; accessed October 2026). openstax.org
- [2] OpenStax. University Physics Volume 1, 17.2 Speed of Sound (2016; accessed October 2026). openstax.org
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