Doppler effect is the phenomenon of the apparent change in the frequency of sound due to the relative motion between the source of sound and the observer.

Key words:

apparent change in frequency

relative motion

source and observer

**Cases**

**Both source and observer at rest**

S = source

O = observer

SO = the distance traveled by n number of waves in one second = v

We know ,

s = v x t

s = displacement, v = velocity, t = time

when t = 1 sec

s = v [ Note: displacement = velocity when t = 1 s]

n = number of waves per second

**Source moves towards the stationary observer**

SS’ = distance moved by the source in one second = Vs

distance occupied by n waves emitted by the source = V – Vs

The apparent wavelength of the sound

The apparent frequency

Since n’ > n, the pitch of the sound appears to increase.

**Source moves away from the stationary observer
**

Since the source moves away from the stationary observer, the velocity of source, Vs becomes -Vs.

The apparent frequency

Since n’ < n, the pitch of the sound appears to decrease.

**Source is at rest and observer in motion
**

S, O = positions of source and observer

n = number of waves produced by the source in one second.

Wavelength is given by,

A = a point of consideration

OA contains n number of waves which cross the ear of the observer in one second.

When the first wave is at the point A, the nth wave will be at O, where the observer is situated.

**Observer moves towards stationary source
**

Vo = velocity of observer

Distance traveled by the observer in one second = OO’ = Vo

The apparent frequency of sound

Since n’ > n, the pitch of the sound appears to increase.

**Observer moves away from the stationary source**

When n’ < n, the pitch of sound decreases.

**The source and the observer move along the same direction**

The apparent frequency

**Influence of wind velocity**

W = velocity of wind blowing in the direction of propagation of sound.

**Applications of Doppler effect**

- To measure the speed of an automobile
- electromagnetic wave emitter is fixed in police jeep.
- moving source – the wave reflected by a moving vehicle
- there is a shift in frequency of the reflected wave
- speedy vehicles are trapped.

- Tracking a satellite
- Radio waves are emitted by a satellite.
- Frequency of emitted radio waves decreases as the satellite passes away from the Earth
- The frequency is received by the Earth station.

- RADAR
- Radio Detection And Ranging
- Sending high frequency radio waves towards aircraft.
- Reflected waves are detected by the receiver of the radar station.
- The difference in speed is used in determining the speed of the aircraft.

- SONAR
- Sound Navigation And Ranging
- Sound waves are generated from a ship.
- transmitted towards the approaching submarine
- the frequency of reflected waves is measured.
- the speed of submarine is calculated.