The Sound of Motion
The Doppler Effect is the change in frequency (or pitch) of a wave in relation to an observer who is moving relative to the wave source. It is most commonly experienced when a vehicle sounding a siren approaches, passes, and recedes from an observer.
Why Does the Pitch Change?
- Approaching: As the source moves toward you, it "catches up" to the sound waves it just emitted. This bunches the waves together, shortening the wavelength and increasing the frequency (making the pitch sound higher).
- Receding: As the source moves away, the waves are stretched out, lowering the frequency (making the pitch sound lower).
This calculator uses the standard convention where velocities are positive when moving toward each other and negative when moving away.
The Formula
Where:
f=
Observed Frequency (Hz)=
Source Frequency (Hz)v=
Speed of Sound in the medium=
Velocity of the Observer=
Velocity of the SourceExample Calculation
An ambulance siren emits a $1,000 , \text{Hz}$ tone. It is driving toward you (standing still, $v_o = 0$) at $30 , \text{m/s}$ (about $67 , \text{mph}$). The speed of sound is $343 , \text{m/s}$.
- Calculate Numerator: $343 + 0 = 343$.
- Calculate Denominator: $343 - 30 = 313$.
- Divide and Multiply: $(343 / 313) \times 1000 \approx 1,095.8 , \text{Hz}$.
You will hear the siren at a higher pitch of $1,096 , \text{Hz}$.