# Doppler Effect

## The change in frequency of sound due to relative motion between source and listener

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 ^{o}C* 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)*

* v _{s} - velocity of the source relative to the medium (m/s)*