Doppler Effect Calculator: Wave Frequency Shift

The Doppler effect describes how the frequency of a wave changes when the source or observer moves relative to the medium. This is why a siren sounds higher-pitched as an ambulance approaches and lower-pitched as it recedes. Understanding the Doppler effect is essential in acoustics, radar, astronomy, and medical ultrasound.

The Formula

For sound waves (source moving, observer stationary):

Observed Frequency = Source Frequency × (Speed of Sound) / (Speed of Sound ± Source Velocity)

Use the minus sign if the source approaches, plus if it recedes.

For light waves (relativistic Doppler):

Observed Frequency = Source Frequency × √((1 - β) / (1 + β))

Where β = velocity / speed of light.

Worked Example

An ambulance siren emits at 1,000 Hz. Sound travels at 343 m/s in air. The ambulance approaches at 30 m/s.

Observed Frequency = 1,000 × 343 / (343 - 30)
                   = 1,000 × 343 / 313
                   = 1,000 × 1.096
                   = 1,096 Hz

The approaching siren sounds about 9.6% higher. After passing and receding at 30 m/s:

Observed Frequency = 1,000 × 343 / (343 + 30)
                   = 1,000 × 343 / 373
                   = 920 Hz

The decrease from 1,096 Hz to 920 Hz is dramatic — about 176 Hz shift.

Applications

Radar and Speed Guns: Emit radio waves, measure frequency shift in reflected waves to calculate vehicle speed.

Astronomy: Stars moving toward Earth show blue shift (higher frequency). Stars moving away show red shift (lower frequency). This revealed that the universe is expanding.

Ultrasound Imaging: Doppler ultrasound measures blood flow by detecting frequency shift of reflected waves from moving red blood cells.

Key Insight

The Doppler effect depends only on relative motion. A stationary observer and approaching source produce the same effect as a stationary source and approaching observer (though the math differs slightly).

Tips

For non-relativistic speeds (much slower than light), use the sound formula. For light or very high speeds, use the relativistic formula. The effect is more pronounced for high-frequency waves and high velocities.

Use our Doppler Effect Calculator to find observed frequency for any source and observer velocity.