Doppler Effect (Receding)

f' = f\frac{v - v_o}{v + v_s}

Frequency decreases when source and observer recede.

Variables

Observed frequency

Lower frequency

In SI units: 1/s

Allowed values: greater than 0

Source frequency

Emitted frequency

In SI units: 1/s

Allowed values: greater than 0

Wave speed

Speed in medium

Allowed values: greater than 0

m/s

v_o

Observer velocity

Away from source

m/s

v_s

Source velocity

Away from observer

m/s

Derivation

Special case of general Doppler formula.

Your notes

0/5000

Check value

Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

f = 5 Hz (Source frequency)
v = 4 m/s (Wave speed)
v_o = 3 m/s (Observer velocity)
v_s = 2 m/s (Source velocity)

Result: f' = 0.83333333 Hz

Other waves formulas with the same quantities

Wave Equation (Wave Properties) shares Wave speed
Wave Speed on String (Wave Properties) shares Wave speed

Where this formula is listed

Waves formulas, under Doppler Effect, alongside Doppler Shift (Light).
In the waves list it comes after Doppler Effect (Approaching) and before Doppler Shift (Light).
Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Doppler Effect (Receding) formula?

Doppler Effect (Receding) is written f′ = f((v − v_o)/(v + v_s)). Frequency decreases when source and observer recede. It belongs to Waves, under Doppler Effect.

What are the units in f′ = f((v − v_o)/(v + v_s))?

In SI units, f′ is observed frequency, measured in 1/s; f is source frequency, measured in 1/s; v is wave speed, measured in m/s; v_o is observer velocity, measured in m/s; v_s is source velocity, measured in m/s.

How is the Doppler Effect (Receding) formula derived?

Special case of general Doppler formula. The result is f′ = f((v − v_o)/(v + v_s)).