Sound - Doppler Effect

The change in frequency of sound due to relative motion between a source and a listener is called the Doppler Effect.

The observed sound frequency for a listener can be expressed as

f_r = f_s (c + v_r) / (c + v_s)                                 (1)

where

f_r = frequency observed by the receiver (1/s, Hz)

f_s = frequency emitted from the source (1/s, Hz)

c = speed of sound (m/s) 

v_r = velocity of the receiver relative to the medium - positive if the receiver is moving towards the source (m/s)

v_s = velocity of the source relative to the medium - positive if the source is moving away from the receiver (m/s)

Example - A Train passing a Bell

A train with speed 200 km/h (55.6 m/s) passes a bell with sound frequency 1000 Hz. With an air temperature of 20 ^oC the speed of sound is 343 m/s.

The frequency observed by a passenger in the train before passing the bell can be calculated as

f_r = (1000 Hz) ((343 m/s) + (55.6 m/s)) / ((343 m/s) + (0 m/s))  

  = 1162 Hz

The frequency observed by the passenger in the train after passing the bell can be calculated as

f_r = (1000 Hz) ((343 m/s) + (- 55.6 m/s)) / ((343 m/s) + (0 m/s))  

  = 838 Hz

Doppler Effect Calculator

Calculate the observed frequency with the calculator below:

f_s - frequency emitted from the source (Hz) - 

c - speed of sound (m/s)

v_r - velocity of the receiver relative to the medium (m/s) - m/s vs. km/h vs. mph

v_s - velocity of the source relative to the medium (m/s)

Download and print the Doppler Effect Chart

• Note Frequencies

Temperature ^oC
K
^oF

Length m
km
in
ft
yards
miles
naut miles

Area m²
km²
in²
ft²
miles²
acres

Volume m³
liters
in³
ft³
us gal

Weight kg_f
N
lbf

Velocity m/s
km/h
ft/min
ft/s
mph
knots

Pressure Pa
bar
mm H₂O
kg/cm²
psi
inches H₂O

Flow m³/s
m³/h
US gpm
cfm