Doppler Effect Calculator

The Doppler effect describes the shift in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. The core equation implemented in this calculator is:

fobs = f0 × (v ± vr) / (v ± vs)

Where f_obs is the observed frequency, f₀ is the emitted source frequency, v is the wave propagation speed in the medium, v_r is the receiver's velocity, and v_s is the source's velocity. The signs in the numerator and denominator depend on the direction of movement: adding or subtracting velocities is determined by whether the objects are moving toward or away from each other.

Let us calculate the frequency heard by a stationary observer when an ambulance siren emits a sound. Imagine a source frequency (f₀) of 700 Hz, traveling through air at a speed of 343 m/s (v). The ambulance source is moving toward the observer at a velocity of 25 m/s (v_s = 25), while the receiver is stationary (v_r = 0).

1. Identify your values: f₀ = 700, v = 343, v_r = 0, v_s = 25.

2. Set up the equation for a moving source approaching a stationary receiver: f_obs = 700 × (343 + 0) / (343 - 25).

3. Simplify the terms: f_obs = 700 × (343 / 318).

4. Complete the division and multiplication: f_obs ≈ 700 × 1.0786 ≈ 755.02 Hz.

The observer hears a higher pitch of approximately 755 Hz as the ambulance approaches.

Always ensure your input units are consistent before performing calculations—typically using meters per second (m/s) for velocities and hertz (Hz) for frequencies. Pay close attention to directional signs: a common pitfall is reversing the signs for approaching versus receding objects, which flips the resulting frequency shift entirely. Finally, remember that the wave speed variable (v) changes depending on the medium, such as ~343 m/s for sound in dry air at room temperature versus ~1,500 m/s for sound traveling through seawater.