Longitudinal Waves

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. Mechanical waves are known as compression waves as they develop compression and refraction while traveling through any medium.

One of the main types of the wave is transverse wave where the displacement of the medium is at right angles to the direction of propagation. There are some transverse waves that are mechanical which means that these waves need a medium to travel through. These transverse mechanical waves are known as t-waves. Longitudinal waves also include sound waves and seismic P-waves. A wave along with the length of a spring is a good visualization where the distance between the coils increases or decreases.

Longitudinal Wave Formula

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

Where,

• y = displacement of the point on the traveling sound wave
• X = distance the point traveled from the wave’s source
• T = time elapsed
• y0= amplitude of the oscillations
• c = speed of the wave
• ω = 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

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.

Pressure Waves

A harmonic pressure wave oscillation will be,

 y(x,t)=y0cos(kx-ωt+φ)

Where,

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

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Longitudinal Wave Questions

Q1) 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.

Q2) List a few differences 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

Q3) 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.

Q4) Waves that travel parallel to the direction of vibration are known as _____.

Q5) 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.

Q6) The longitudnal wave formula is given by the equation _____.

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

Q7) What is a pressure wave?

A pressure wave is a wave in which the propagated disturbance is a variation of pressure in a material medium.

Q8) List the characteristics of sound.