Table of Content

• What are Longitudinal Waves?
• Examples of Longitudinal Waves
• Longitudinal Waves Formula
• Longitudinal Waves Formulas
• Formation of Longitudinal waves
• Longitudinal Wave of Sound
• Longitudinal Waves of Pressure
• Parts of Longitudinal Wave
• Longitudinal Wave Diagram
• Longitudinal Waves Characteristics
• Particle Vibration
• Difference Between Longitudinal Waves and Transverse Waves

Formation of Longitudinal waves

Longitudinal waves are formed when a disturbance or vibration occurs in a medium, causing the medium particles to oscillate back and forth in the same direction as the wave’s propagation.

This disturbance can be caused by a variety of sources, such as a vibrating object or a sudden pressure change. As the particles of the medium oscillate, they create regions of compression and rarefaction, which propagate through the medium as a longitudinal wave.

Check: Electromagnetic Waves

Longitudinal Wave of Sound

Sound waves are longitudinal waves, which means that the vibrations of the particles in the medium are parallel to the direction the wave travels. In other words, the particles of the medium vibrate back and forth in the same direction as the wave movement. As the sound wave travels through the medium, it creates compressions and rarefactions, which are areas of high and low pressure, respectively.

When an electrical signal is sent to a speaker, it causes a coil of wire within the speaker to vibrate rapidly. This vibration, in turn, moves a cone-shaped diaphragm back and forth, pushing and pulling on the surrounding air particles. This creates sound waves that travel through the air, allowing us to hear the sound produced by the speaker.

Read More,

• Propagation of Sound Wave
• Frequency and Wavelength of Sound Wave

Longitudinal Waves of Pressure

Longitudinal waves of pressure, also known as pressure waves, describe a type of mechanical wave where particles within the medium oscillate in the same direction as the wave’s propagation.

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

Parts of Longitudinal Wave

The following properties characterize longitudinal waves:

Compression: Longitudinal waves have regions of high pressure called compressions, where particles are close to each other.

Rarefaction: Rarefactions are the regions of low pressure, where particles are spread further apart.
Note: In longitudinal waves, the particles in areas of compression are closer together than on average, while in areas of rarefaction, the particles are further apart than on average.

Wavelength: The wavelength of a longitudinal wave is the distance between two consecutive compressions or rarefactions.

Amplitude: It is the maximum displacement of a point on the wave from its rest position.

Period: The period is the time taken by the wave to complete one wavelength.

Frequency: Frequency of longitudinal wave is the number of wavelengths per second.

Longitudinal Wave Diagram

Longitudinal Wave Diagram explaining compression, rarefaction and wavelength is given below:

longitudinal wave

Check: Refraction of Sound – Definition, Echo, Examples, and FAQs

Longitudinal Waves Characteristics

The characteristics of longitudinal waves are:

Medium

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction the wave travels, and the displacement of the medium is in the same direction as the wave’s propagation. These waves can be observed in various media, such as solids, liquids, and gases.

Velocity

The velocity of longitudinal waves depends on the properties of the medium, such as its density and elastic properties, rather than the source of the wave. For example, the speed of sound in a medium is primarily determined by the medium’s properties, not the intensity of the sound produced.

In the context of longitudinal waves, the forward velocity of a longitudinal wave is given by the formula:

v= λ/T = ω/k

Where:

• v is the velocity of the wave
• λ is the wavelength of the wave
• T is the period of the wave
• ω is the angular frequency of the wave
• k is the wave vector

Some key points about the velocity of longitudinal waves include:

• The velocity of longitudinal waves is directly proportional to the wavelength and inversely proportional to the period.
• The velocity of longitudinal waves is also directly proportional to the angular frequency and inversely proportional to the wave vector.
• The velocity of longitudinal waves is independent of the amplitude of the wave.

Particle Vibration

In longitudinal waves, the particles of the medium vibrate parallel to the direction the wave travels, and their displacement is in the same direction as the wave’s propagation. Some critical aspects of particle vibration in longitudinal waves include:

• As the wave travels, the particles create regions of compression (where the particles are squashed together) and rarefaction (where the particles move apart). These regions alternate along the wave’s path.
• The particles of the medium do not move with the wave; they simply oscillate back and forth about their individual equilibrium positions.
• When the wave passes, the particles return to their equilibrium position.

Check: Introduction to Waves – Definition, Types, Properties

Difference Between Longitudinal Waves and Transverse Waves

The basic difference between Longitudinal and Transverse wave is given below: