# Longitudinal Waves

Mechanical waves are classified as longitudinal waves and transverse waves. Longitudinal waves occur in the large solids and also in engineering fluids. Longitudinal waves include sound waves, seismic P-waves, and ultrasound waves. These waves are known as compression waves as they develop compression and refraction while traveling through any medium. When the particles are together, the pressure is high and the region is known as compression and when the particles are apart, the pressure is low and the region is known as rarefaction.

These other mechanical waves are known the transverse and are defined as the wave where the displacement of the medium is at right angles to the direction of propagation and are known as t-waves. These waves need a medium to travel through. A wave along with the length of a spring is a good visualization where the distance between the coils increases or decreases.

## What Is A Longitudinal Wave?

Longitudinal waves are the waves where the displacement of the medium is in the same direction, or in opposite direction, and direction of the travel of the wave. The distance between the centers of two consecutive regions of compression or the rarefaction is defined by wavelength, λ. When the compression and rarefaction regions are of two waves coincide with each other, it is known as constructive interference and if the regions of compression and rarefaction do not coincide, it is known as destructive interference.

## Sound Waves

A sound wave is an example of a longitudinal wave and is produced by the vibrating motion of the particles that travel through a conductive medium. The example of sound waves in a longitudinal direction is tuning fork.

In Sound waves, the amplitude of the wave is the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium and temperature through which it propagates.

### Longitudinal Wave Formula

 $y(x,t)=y_{0}cos[\omega (t-\frac{x}{c})]$

Where,

• y is the displacement of the point on the traveling sound wave
• x is the distance the point traveled from the wave’s source
• t is the time elapsed
• yis the amplitude of the oscillations
• c is the speed of the wave
• ω is the angular frequency of the wave

Quantity x/c = time ( wave takes to travel the distance x).

Frequency (f) of the wave is given by the formula,
f=ω2π

## Pressure Waves

The pressure wave is defined as the propagation of disturbance in a medium as the pressure varies.

A harmonic pressure wave oscillation will be,

 y(x,t)=y0cos(kx-ωt+φ)

Where,

• y0 is the amplitude of displacement
• k is the wavenumber
• x is the distance along the axis of propagation
• ω is the angular frequency
• t is the time
• φ is the phase difference

### Difference Between Longitudinal And Transverse Wave

 Longitudinal Wave Transverse Wave A wave that moves in the direction of its propagation A wave that moves in the direction perpendicular to its propagation A sound wave is an example of a longitudinal wave Water waves are an example of a transverse wave It is made of refractions and compressions It is made of troughs and crests This wave can be produced in any medium such as gas, liquid or solid This wave can be produced in solid and liquid’s surface

## Longitudinal Wave Questions

Q1) Which of the following is not a longitudinal wave?

1. Infrasonic wave
2. Seismic wave
3. Ultrasonic wave
4. Infrared wave

Infrared wave is not a longitudinal wave.

Q2) Which of the following is not a transverse wave?

2. Light waves
3. Water waves
4. Sound waves

A sound wave is a longitudinal wave.

Q3) The longitudinal wave formula is given by the equation _____.

Answer: $y(x,t)=y_0\cos[\omega(t-\frac{x}{c})]$

Q4) List the characteristics of sound.

Answer: The characteristics of the sound are as follows:

• Loudness
• Pitch
• Quality

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#### Practise This Question

The threshold wavelength for a metal with work function W0 is λ0. What is the threshold wavelength for a metal whose work function is W02?