An ambulance siren sounds higher as it approaches and lower as it leaves. Enter the source frequency, the speeds of source and observer and their direction to get the frequency actually heard.
Enter the source frequency.
Enter the source and observer speeds and choose the direction.
Read the observed frequency.
Approaching: f′ = f (v + v₀) ÷ (v − vₛ)
Receding: f′ = f (v − v₀) ÷ (v + vₛ)
When an ambulance races past, its siren sounds higher as it approaches and lower as it moves away. This change in heard pitch is the Doppler effect. The calculator takes the source frequency, the speeds of the source and the observer, whether they are closing in or moving apart, and the speed of sound, and returns the frequency the observer actually hears and the size of the shift.
The Doppler effect is part of Class 11 waves and sound and a regular JEE and NEET question. It is also practical physics: traffic police speed guns, weather radar used by the India Meteorological Department to track storms, ultrasound scans of blood flow and astronomers measuring how fast stars move all rely on it. This calculator handles the sound version, with both source and observer allowed to move along the line joining them.
1. Write the source frequency f in Hz and the speed of sound v, usually 343 m/s in air at 20 °C.
2. Write the source speed vₛ and the observer speed v₀ along the line joining them, in m/s.
3. If they are moving towards each other, use f′ = f × (v + v₀) ÷ (v − vₛ).
4. If they are moving apart, use f′ = f × (v − v₀) ÷ (v + vₛ).
5. Find the shift as f′ − f. Positive means a higher pitch, negative a lower one.
6. If only one of them moves, set the other speed to zero.
A source emits one crest every period T = 1/f. If it moves towards you at vₛ, by the time it sends the next crest it has moved vₛT closer, so crests arrive closer together. The wavelength in front of it becomes (v − vₛ) ÷ f instead of v ÷ f. You hear f′ = v ÷ λ′ = f × v ÷ (v − vₛ). Behind the source the crests spread out, giving a lower frequency. The medium carries the waves at v, whatever the source is doing.
If the source is still but you move towards it at v₀, the wavelength in the air is unchanged, but you run into crests faster, at a relative speed of v + v₀. So you count f × (v + v₀) ÷ v crests per second. Combining both effects gives the general formula. The two cases are not symmetric: a source approaching at 100 m/s raises the pitch more than an observer approaching at 100 m/s, because for sound the medium, the air, is the reference frame.
As vₛ approaches the speed of sound, the denominator v − vₛ approaches zero and the crests pile up into a shock wave. That is the sonic boom from a supersonic jet, and the calculator reports the formula as undefined there. For light there is no medium, so the relativistic Doppler formula depends only on the relative speed. Stars moving away show red shift and those approaching show blue shift. Radar guns use the shift of reflected microwaves, which is doubled because the moving car both receives and re-emits the wave.
An ambulance with a 700 Hz siren has just passed Pooja, who is standing at a bus stop, and is driving away from her at 25 m/s on a 20 °C day.
Doppler formula: f′ = f (v − v₀) ÷ (v + vₛ) = 700 × (343 − 0) ÷ (343 + 25) = 652.446 Hz
Shift: 652.446 − 700 = -47.554 Hz
Answer: Observed frequency 652.446 Hz; Frequency shift -47.554 Hz
Getting the signs backwards, so an approaching source gives a lower pitch.
Using speeds in km/h while the speed of sound is in m/s.
Using the full speed of a source that moves at an angle to the line of sight, instead of its component along that line.
Treating the formulas for moving source and moving observer as interchangeable.
Thinking the source's actual frequency changes; only the heard frequency changes.
Class 11, JEE and NEET problems on the Doppler effect.
Explaining why sirens and train horns change pitch as they pass.
Understanding police speed radar and weather radar principles.
Doppler ultrasound for measuring blood flow speed, as an educational example.
Sports speed guns for cricket and tennis balls.
Does light show a Doppler effect?
Yes. It is used to measure the speed of stars (red and blue shift) and in radar speed guns.
What speed of sound should I use?
343 m/s in air at 20 °C, unless the problem gives another value.