Wave motion is the transfer of energy through a medium (such as air or water) in the form of a wave. It is caused by a disturbance in the medium, such as the vibration of a tuning fork or the movement of a stone thrown into a pond.

Wave motion is the transfer of energy and momentum from one point of the medium to another point of the medium without actual transport of matter between two points. There are three different types of wave motion:

The medium of propagation

The dimensions in which a wave propagates energy

The Energy Transfer

Table of Contents

Classification of Wave Motion

Mechanical Waves

Non-Mechanical Waves

Characteristics of Wave Motion

Terminologies in Progressive Wave Motion

Classification of Wave Motion

Medium of Propagation

Classification of Wave Motion Based on the Medium of Propagation:

Number of Dimensions a Wave Transfers Energy

Classification of Wave Motion Based on the Number of Dimensions a Wave Propagates Energy

Transfer of Energy

Standing Waves (or Stationary Waves)

Progressive Wave

Standing waves remain confined to a region without any transfer of energy or momentum, whereas progressive waves transfer energy and momentum between the particles of the medium.

Mechanical Waves (Elastic Waves)

Mechanical or elastic waves are types of waves which require a medium for their propagation. When these waves pass through a medium, the particles of the medium move periodically about a mean position.

For Example, waves on a string

A mechanical wave is produced when a disturbance occurs at a point in a medium.

The particle interacts with its neighboring particle, transferring its energy to the next particle due to the inertia of the medium.

Due to the elasticity of the medium, the disturbed particles return to their equilibrium position.

Properties of Mechanical Wave Propagation in Medium

The medium must possess inertia so that its particles can store kinetic energy, enabling them to possess energy of motion.

The medium must be elastic.

The minimum frictional force between the particles of the medium.

Non-Mechanical Waves

Non-mechanical waves, which do not require a medium for their propagation, can also propagate through a vacuum. These waves are transverse in nature and examples include electromagnetic waves and matter waves.

Transverse Wave Motion

The particles of the medium vibrate in a direction perpendicular to the direction of propagation of the wave. The region of maximum upward displacement is called the crest, the region of maximum downward displacement is called trough.

Transverse wave motion occurs only through a medium which has rigidity modulus or shape conservation. For example, string waves.

Longitudinal Wave Motion

The particles of the medium vibrate about their equilibrium position in a direction parallel to the direction of propagation of the wave, which is known as a longitudinal wave.

Longitudinal waves require a medium with elasticity of volume (or Bulk modulus) for its propagation. In this type of wave motion, the waves travel through a medium in the form of compression and rarefaction.

The region of high pressure is called compression and the region of low pressure is called rarefaction. For example, Sound waves in the tube.

Periodic Wave Motion

1. A periodic wave is produced if the disturbance is continuous and periodic in nature.

2. A periodic wave that varies in a sinusoidal pattern is referred to as a sinusoidal periodic wave.

3. When a sinusoidal periodic wave passes through the medium, the particles of the medium execute Simple Harmonic Motion (SHM).

Characteristics of Wave Motion

1. Wave motion is a disturbance that transfers energy from one location to another
2. Wave motion is a periodic motion
3. Wave motion can be transverse or longitudinal
4. Wave motion is affected by the medium it travels through
5. Wave motion can be described by its amplitude, wavelength, and frequency

In wave motion, the disturbance travels through the medium as a result of the particles of the medium regularly oscillating about their mean position (or) Equilibrium position. Periodic oscillations are responsible for this motion.

Energy and momentum are transferred from one point to another without any physical transfer of the particles of the medium.

There is a regular phase difference between the particles of the medium because each particle experiences a disturbance slightly after its preceding particle.

The velocity of a wave is distinct from the velocity of the particles that vibrate around their mean (or) equilibrium position.

The velocity of the wave motion for a given medium remains constant, while the particle velocity of the medium continuously changes as it vibrates around its equilibrium position.

The velocity of the particle is highest at the mean position and is zero at the extreme positions.

#Terminologies in Progressive Wave Motion

Amplitude

Period

Wavelength

Frequency

Wave Velocity

Phase or Phase Angle (θ)

Phase Difference

Path Difference

Time Difference

Explanation:

Amplitude (A): The maximum displacement of any particle of the medium from its equilibrium position is known as the amplitude of a wave.

Period (T): The time taken for one vibration to complete during a period (T) is known as the period (T) of a wave.

Wavelength (λ): The distance between two consecutive particles of the medium that are in the same state of vibration is known as the wavelength (λ). This is also equal to the distance travelled by the wave over its time period (T).

Frequency (f): It is the number of vibrations made per second by any particles of the medium (f = 1/T). Since the frequency of a wave is a characteristic property of the source which produces the wave motion, thus, the frequency of a wave remains constant when a wave travels from one medium to another medium.

Phase or Phase Angle (Φ): It represents the amount of displacement of a particle of a medium from its mean position in terms of a reference point.

Phase Difference Δ(Φ): It represents the difference between the states of vibration of a particle at two different instants (or) any pair of particles at the same instant. ΔΦ = Φ2 – Φ1.

Wave Velocity (v): It is the distance travelled by the wave in one second (v = λ/T), which is determined by the mechanical properties of the medium through which the wave propagates. The velocity of wave motion is measured with respect to the medium, and can change when the medium is in motion (e.g. the speed of sound through air changes when the wind is blowing).

⇒ Check: Sound Waves

There are two velocities associated with a wave:

• Wave Velocity
• Particle Velocity (the speed with which the particles of the medium vibrate when the wave passes through the medium)

Path Difference (Δx) or (x): It indicates the distance between two points, measured along the direction of propagation of the wave through the medium.

Time Difference (ΔT): It indicates the amount of time it takes for a wave to travel from one point to another through a medium.

Path Difference and Phase Difference

Consider a progressive wave motion advancing in the positive direction of the x-axis.

Path Difference vs Phase Difference

Let A and B be two points in the medium through which the wave passes.

The path difference between A and B is x = x2 - x1

The phase difference (ΔO) between the states of vibration of A and B is the result of the change in the phase of vibration of A by the time the wave reaches B from A.

The path difference between two consecutive crests c1 and c2 is $\lambda$, the time difference is $T$, and the phase difference is $2\pi$.

A path difference (x) of 2πr/λ corresponds to a phase difference of 2π, thus, a path difference (x) corresponds to the phase difference 2πr/λ.

Δϕ = \frac{2πx}{λ} = \frac{2π}{λ} \text{ (path difference)}

The wave number or propagation constant of the wave motion is denoted by $k = \frac{2\pi}{\lambda}$.

A path difference (x) corresponds to a time difference of [\frac{x}{\lambda}T], where [\lambda] corresponds to a time difference (T).

The following table outlines the connections between path difference, phase difference, and time difference:

| Path Difference | Phase Difference | Time Difference |

| X | $\frac{2\pi X}{\lambda}$ | $\frac{XT}{\lambda}$ |

	$\lambda \times \left[\frac{\Delta \phi}{2\pi}\right]$	$\Delta \phi$

| $\lambda \times \left[\frac{\Delta T}{T}\right]$ | $2\pi \times \left[\frac{\Delta T}{T}\right]$ | $\Delta T$ |

You Could Also Be Interested In:

HC Verma Solutions

HC Verma Solutions Part 1

HC Verma Solutions Part 2

Important Questions on Waves and Simple Harmonic Motion

Young’s Double Slit Experiment

![Young’s Double Slit Experiment]()

Superposition of Waves

![Superposition of Waves]()

Power Transmitted by a Wave

![Power transmitted by a Wave]()

Important Questions on Waves and Rolling Motion

Frequently Asked Questions on Wave Motion

Wave motion is the transfer of energy through a medium without the transfer of matter.

Wave motion is the propagation of energy and momentum from one point to another without the actual transport of matter in an organized manner.

Examples of Wave Motion

1. Water Waves
2. Sound Waves
3. Light Waves
4. Seismic Waves

Electromagnetic Waves, Sound Waves, Waves on a String, Seismic Waves etc.

What is the amplitude of the wave?

The amplitude of a wave is the distance from the centre line (equilibrium position) to the top of the crest or the bottom point of the trough.

Can Waves Travel in a Vacuum?

Electromagnetic waves are transverse waves that do not need a medium in order to travel.

How do light waves behave?

Light waves are transverse in nature.

Characteristics of Wave Motion

1. Wave motion involves the transfer of energy without the transfer of matter.
2. Wave motion can be transverse or longitudinal.
3. Wave motion can be described by its wavelength, amplitude, and frequency.
4. Wave motion can be reflected, refracted, diffracted, and/or absorbed.
5. Wave motion can be described mathematically using equations.

Wave motion is a disturbance that travels through a medium.

When the wave travels through the medium, its particles execute simple harmonic motion about the mean position.

The particles of the medium will possess both kinetic and potential energy due to their vibration.

Particles of the medium transfer the energy to the neighbouring particles, but the displacement over one time period is zero.

A mechanical wave or elastic wave is a wave that is created when a disturbance in a medium causes particles in the medium to vibrate. These waves travel through the medium and carry energy from one point to another.

A mechanical wave is a periodic disturbance which requires a material medium in order for it to propagate.

What is the Wavelength of a Longitudinal Wave Motion?

The distance between two successive compressions or between two successive rarefactions is known as the wavelength of a longitudinal wave.— title: “Wave Motion” link: “/wave-motion” draft: false

Wave Motion is a type of motion in which an energy wave propagates through a medium or space, accompanied by a transfer of energy.

Wave motion is the transfer of energy and momentum from one point of the medium to another point of the medium without actual transport of matter between two points. There are three main types of wave motion:

The mode of propagation

The dimensions in which a wave propagates energy

The Energy Transfer

Table of Contents

Classification of Wave Motion

Mechanical Waves

Non-Mechanical Waves

Characteristics of Wave Motion

Terminologies in Progressive Wave Motion

Classification of Wave Motion

Medium of Propagation

Classification of Wave Motion Based on the Medium of Propagation

Number of Dimensions a Wave Transfers Energy

Classification of Wave Motion Based on the Number of Dimensions a Wave Propagates Energy

Transfer of Energy

Standing Waves (or Stationary Waves)

Progressive Wave

Standing waves remain confined to a region without any transfer of energy or momentum, whereas progressive waves transfer energy and momentum between the particles of the medium.

Mechanical Waves (Elastic Waves)