Longitudinal Waves

Longitudinal Waves are a type of mechanical wave in which the particle oscillates parallel to the direction of the wave. The displacement of the medium in a longitudinal wave is along the direction of wave propagation. Examples of longitudinal waves include sound waves, seismic P waves, ultrasound waves, etc.

In this article, we will learn about Longitudinal Waves, their definition, formula, and examples, along with a comparison with transverse waves.

What are Longitudinal Waves?

Longitudinal Waves are a type of mechanical wave in which the waves travel adjacent to the direction of the wave propagation. In this wave, each particle of matter vibrates in its normal position along the axis of propagation, causing alternative regions of compression and rarefaction in the medium. The distance between two compression or two rarefactions is known as wavelength.

When the region of compression and rarefaction coincide with each other, it is called constructive interference, and when they do not coincide, it is known as destructive interference. As these waves produce compression and rarefaction, they are also known as compression waves. The oscillation in longitudinal waves is such that the wave moves in a direction parallel to the direction of the vibration of the medium.

Longitudinal Waves Definition

Longitudinal waves are waves in which the vibration of the medium is parallel to the direction of the wave travels, and the displacement of the medium is in the same direction as the wave propagation.

Examples of Longitudinal Waves

Here are some examples of longitudinal waves in detail:

• Sound Waves: Sound waves are a common example of longitudinal waves. When a sound is produced, the particles in the surrounding medium (such as air) oscillate back and forth, creating a longitudinal wave.

• Seismic P-waves: Seismic P-waves are longitudinal waves that travel through the Earth’s crust. These waves are generated by the sudden release of energy, such as during an earthquake. The vibrations of the Earth’s crust create alternating regions of compression and rarefaction, which propagate as longitudinal waves.

• Ultrasound Waves: Ultrasound waves are longitudinal waves created by a transducer’s vibration and propagate through a medium, such as human tissue or a solid object. The particles in the medium oscillate back and forth, creating a longitudinal wave.

• Vibration of a Spring: When a coiled spring is compressed at one end and released, it experiences a wave of compression followed by a stretching. This vibration is an example of a longitudinal wave, as the particles in the spring oscillate back and forth about their equilibrium position.

Longitudinal Waves Formula

The following formula can describe longitudinal waves:

y(x, t)= A cos(2πx/λ – 2πft + ϕ)

Where:

• y is the displacement of the point on the travelling wave
• x is the distance from the point to the wave’s source
• t is the time elapsed
• A is the amplitude of the oscillations
• λ is the wavelength
• f is the frequency
• ϕ is the phase angle

In the case of longitudinal harmonic sound waves, the formula can be written as:

y(x, t) = y₀ cos (ω(t-x/c))

Where:

• y₀ is the amplitude of the oscillations
• ω is the angular frequency of the wave
• c is the speed of the wave

Longitudinal Waves Formulas

A table containing all the formulas related to the longitudinal wave is given below:

Description	Formula
Displacement	y(x, t) = A cos(kx – ωt + ϕ)
Velocity	v = λ/T
Frequency	f = v/λ
Wave Length	λ = vT
Period	T = 1/f
Angular frequency	ω = 2пf

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.

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

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

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.

Difference Between Longitudinal Waves and Transverse Waves

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

Property	Longitudinal Waves	Transverse Waves
Vibration	Parallel to the direction of the wave	Perpendicular to the direction of the wave
Energy Transfer	In the same direction as the wave motion	Perpendicular to the direction of the wave motion
Medium	Can move in solids, liquids, and gases	Can move in solids, liquids, and gases
Vacuum	Can move in a vacuum	Cannot move in a vacuum
Key Features	Compressions and rarefactions	Crests and troughs
Examples	Sound Waves, Ultrasonic Waves, etc.	Water Waves, Light Waves, etc.

Read More,

• Wave
• Types of Wave
• Difference between longitudinal and transverse wave

Longitudinal Waves: FAQs

What is Longitudinal Waves?

Longitudinal waves are a type of mechanical wave where the particles in the medium move parallel to the direction of wave propagation. Each particle vibrates along the axis of propagation, causing regions of compression and rarefaction.

What are Transversal Waves?

Transverse waves are another type of mechanical wave where particles move perpendicular to the direction of wave propagation. They exhibit crests and troughs in their oscillation.

What is Amplitude of Longitudinal Wave?

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

Sound Wave is Longitudinal Wave or Transverse Wave?

Sound wave is longitudinal wave because their oscillations are parallel to the direction of wave propagation.

What are Three Examples of Longitudinal Waves?

Sound Waves, Seismic P-waves, and Ultrasound Waves are three examples of Longitudinal Waves.

What is another Name of Longitudinal waves?

Longitudinal waves are also known as compression waves due to the alternate regions of compression and rarefaction they create in the medium.

Distinguish Between Transverse and Longitudinal Waves?

Transverse waves exhibit vibrations perpendicular to the direction of wave propagation, while longitudinal waves show vibrations parallel to the wave’s direction.

What are Compression and Rarefaction in Longitudinal Waves?

Compression and rarefaction represent areas of high and low particle density, respectively, contributing to the wave’s energy transfer and propagation.

Is Light Longitudinal or Transverse?

Light is a transverse wave. Unlike longitudinal waves, light’s vibrations occur perpendicular to its direction of propagation, involving electric and magnetic fields oriented at right angles to the wave’s path.

Is Water Wave Longitudinal or Transverse?

Water waves are mainly transverse, with particles moving up and down perpendicular to the wave direction. Some longitudinal aspects may exist, particularly in deeper layers.

What is Speed of Longitudinal Wave?

The speed of a longitudinal wave depends on the medium’s properties. The velocity is determined by factors like density and elastic properties, following the formula v = λ/T = ω/k , where v is velocity, λ is wavelength, T is period, ω is angular frequency, and k is wave vector.