# Longitudinal Waves and Doppler Effect

## Longitudinal Waves

The waves for which the displacement of the medium is along the direction of wave propagation is called a longitudinal wave. The displacement of the medium is parallel to the direction of wave propagation. Few examples of longitudinal waves are sound waves, seismic waves, and ultrasound waves. The longitudinal waves show compression and rarefaction. The region where the medium is compressed is called the compression and the region where the medium is spread out is called the rarefaction.

## Characteristics of Longitudinal Waves

Characteristics like the wavelength, frequency, amplitude and period can be defined for **longitudinal waves** just like transverse waves. However, instead of crests and troughs, longitudinal waves have compressions and rarefactions.

### Wavelength

The distance between two consecutive compressions or rarefactions is called wavelength.

### Frequency

The number of wavelengths in a second is called the frequency.

### Period

The time taken by the longitudinal wave to move one wavelength is called the period

### Amplitude

Amplitude is the maximum displacement of the particle from the rest point. In a longitudinal wave, it is the distance from the equilibrium position to the compression or the rarefaction.

## Sound Waves

The sound wave is an example of a longitudinal wave. Thus, sound waves consist of alternate compressions and rarefactions. These are regions of high pressure and low pressure. The sound wave propagation depends on various factors like the type, composition and temperature of the medium.

## Doppler Effect

When there is the motion of the source with respect to the observer, the Doppler effect can be observed. The change in the pitch of the siren from the ambulance crossing the person, the change in the pitch of the whistle from the train as it crosses the observer are the common examples considered to explain the phenomenon of the **Doppler effect**. This phenomenon explains the change in the frequency of the sound waves or the light waves when the source is moving with respect to the observer.

## Doppler Effect Formula

The apparent change in the frequency due to the relative motion between the source and the observer is given by the following formula

Here,

f’ is the observed frequency

f is the actual frequency

v is the velocity of the sound waves

v_{0} is the velocity of the observer

v_{s} is the velocity of the source

The given equation changes when there is a change in the velocities of the source or the observer.

### (i) Source Moving Towards Observer

When the source moves towards the observer, the velocity of the observer is zero. Therefore, v_{0 }= 0. The above equation becomes

### (ii) Source Moving Away from the Observer

The velocity of the observer is zero, v_{0} = 0. Since the source is moving away the above equation becomes

### (iii) Observer moving towards the stationary source

Since the source is stationary, v_{s} = 0. The observer moves towards the source, so the above equation can be written as

(iv) Observer moving away from the stationary source

Since the source is stationary, v_{s} = 0. The observer moves away from the source, so the above equation can be written as

## Application of Doppler Effect

The Doppler effect is widely used in astronomy. The Doppler effect helped in the discovery of the expansion of the universe by Edwin Hubble. Doppler effect is used in radars, medical imaging and blood flow management, audio, satellite communication etc.