# Wave Motion | Definition, Discovery, Classifications, Uses

## Definition of Wave Motion

Wave motion is the transfer of energy and momentum from one point of the medium to another medium without the actual transport of matter between two points.

## Discovery of Wave Motion

In the 18th Century, French mathematician and scientist Jean Le Rond d’Alembert derived the wave equation. A thorough and general mathematical description of waves, which laid the foundation for generations of scientists to study and describe wave phenomena.

## Classification of Wave Motion

Wave motion has been classified on various bases:

### 1. Based on mode of Propagation

There are six types of waves based on the mode of propagation:

• Mechanical Waves – The waves that require a medium to travel are called mechanical waves. These are further classified as:
• Transverse Wave – For a transverse wave, the particle vibrates perpendicular to the direction of propagation.
• Longitudinal Wave – For longitudinal waves, the particle vibrates in the direction of propagation.
• Standing Waves – The waves that do not transfer energy and momentum from one point to another.
• Progressive Wave – The wave that transfers energy and momentum.
• Non – Mechanical Waves – The waves that do not require a medium are called non-mechanical waves.

### 2. Based on the Number of Dimensions

There are three types of waves based on the number of dimensions:

• 1-D – The waves that propagate energy in only one direction.
• 2-D – The waves that propagate energy In two directions.
• 3-D – The waves that propagate energy in three directions.

### 3. Based on the Transfer of Energy

There are two types of waves based on the transfer of energy:

• Standing Waves: Standing wave, also called a stationary wave, is the combination of two waves moving in opposite directions, each having the same amplitude and frequency. The phenomenon is the result of interference; when waves are superimposed, their energies are either added together or canceled out.
• Progressive Waves: A wave that generally travels continuously in a medium of the same direction without changing its amplitude is known as a traveling wave or a progressive wave.

### 4. Periodic and Non – Periodic Wave

• Periodic Waves – If the pattern of a wave is repeated after one wavelength or a single period and has the same pattern throughout the propagation. Then the waves are called periodic waves.
• Non – Periodic Waves – If the pattern of a wave is not repeated after one wavelength or a single period and does not have the same pattern throughout the propagation. Then the waves are called periodic waves.

## 5. Terminologies in Progressive Wave Motion

There are different types of terminologies used in wave motion:

• Amplitude (A): The amplitude of a wave is the maximum displacement of any particle of the medium from its equilibrium position.
• Period (T): The period (T) of a wave is the time taken by any particle of the medium to complete one vibration during a period (T).
• Wavelength (λ): Wavelength (λ) is equal to the distance between two consecutive particles of the medium which are in the same state of vibration. However, It is equal to the distance traveled by the wave by its time period (T).
• Frequency (f): It is the number of vibrations made per second by any medium particles (f = 1/T). Since the frequency of a wave is a characteristic property of the source that produces the wave motion. The frequency of a wave does not change when a wave travels from one medium to another medium.
• Phase or Phase Angle (Φ): It represents the state of vibration of the particle of a medium with respect to its mean position.
• Phase Difference Δ(Φ): It represents the different 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): The wave’s distance traveled in one second (v = λ/T). It 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. The wave velocity changes when the medium is in motion i.e., speed of sound through air changes when the wind is blowing.

## Uses of Waves

There are different uses of waves in different fields:

1. Medical use of waves: The great thing about waves is that they help doctors work out what’s going on inside our bodies and help treat diseases. A type of wave called Gamma rays can kill cancer cells. A machine called a ‘gamma knife’ converges hundreds of gamma rays onto a tumor with remarkable accuracy.

2. Radio waves are used for communication such as television and radio. Radio waves are transmitted easily through the air. However, they do not cause damage if absorbed by the human body, and they can be reflected to change their direction. These properties make them ideal for communications.

3. Electromagnetic waves have a vast range of practical everyday applications that includes such diverse uses as communication by cell phone and radio broadcasting, WiFi, cooking, vision, medical imaging, and treating cancer.

4. A factory may use X-rays to test for stress fractures in welding joints on an assembly line, or a scientist may use MRI imaging to analyze new treatments for muscles and joints. Also precise imaging is based on very high-frequency waves that make a very clear image of small objects.

## Characteristics of Wave Motion

These are some characteristics of wave motion:

1. In wave motion, the disturbance travels through the medium due to repeated periodic oscillations of the medium particles about their mean position (or) Equilibrium position.

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

3. There is a regular phase difference between the particles of the medium because each particle receives disturbance a little later than its preceding particle.

4. The velocity with which wave travels is different from the velocity of the particles with which they vibrate about their mean (or) equilibrium position.

5. For a given medium, the velocity of the wave motion remains constant, while the particle velocity changes continuously during its vibration about its equilibrium position.

6. The particle’s velocity is maximum at the mean position and zeroes at the extreme position.