Waves: What happens when you drop a tiny pebble in a pond of still water? The surface of water gets disturbed. The disturbance does not remain confined to one place but propagates outward along a circle. Suppose multiple pebbles are dropped one after the other in the pond. In that case, we will see circles rapidly moving outward from the point where pebbles hit the water surface, thereby disturbing it. It gives a feeling as if the water is moving outward from the point of disturbance.

Waves transport energy and the pattern of disturbance has information that propagates from one point to another. Most of the communication systems are essentially dependent on the transmission of signals through waves. For example, speech means producing sound waves in the air and hearing these sound waves fall under the category of detection. Often, communication involves different kinds of waves. Although, not all waves require a medium for their propagation. For example, light waves can travel through a vacuum.

Waves: Definition

A wave is a form of disturbance that travels through a material medium due to the repeated motion of the particles of the medium about their mean positions without any actual transportation of matter. Simply put, a wave can be thought of as a periodic oscillation that travels through space-time, accompanied by a transfer of energy.

Wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium —that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations of the particles of the medium around almost fixed locations. A wave spreads across the region without any clear-cut boundaries. Hence, it can not be said to be localized at a particular place.

Characteristics of a Wave

The features of waves are as follows:

(i) The particles of the medium traversed by a wave execute relatively small vibrations about their mean positions. Still, the particles are not permanently displaced in the direction of propagation of the wave.

(ii) Each successive particle of the medium executes a motion quite similar to its predecessors along/perpendicular to the line of travel of the wave.

(iii) During wave motion, only transfer of energy occurs but not that of a portion of the medium.

(iv) Two properties for the propagation of a wave in a medium are

1. Elasticity

2. Inertia

Types of Waves

Based on the medium through which waves  travel, propagation of energy along with a wave motion, dimensions in which a wave is travelling, and the direction of vibration of the particles of a wave, the waves can be classified as:

Classification of Wave Based on Medium

a. Mechanical (Elastic) Waves: Mechanical waves can be produced or propagated only in a material medium. Newton’s laws of motion govern these waves. These waves require a medium for propagation; they cannot propagate through a vacuum. They involve oscillations of constituent particles and depend on the elastic properties of the medium. These are the most familiar waves, such as waves on a string, water waves, sound waves, and seismic waves.

b. Electromagnetic Waves: These are the waves that require no material medium for their production and propagation, i.e., they can pass through a vacuum and any other material medium. All electromagnetic waves have the same speed in a vacuum, \(c\), whose value is: \(c = 299,792,458\;{\rm{m}}/{\rm{s}}\). Common examples of electromagnetic waves are visible light, ultra-violet light, radio waves, and microwaves.

Classification of Wave Based on the Propagation of Energy

a. Stationary waves or standing waves: These are the waves that possess vertical oscillating movement but do not undergo forward motion in a horizontal direction. It results from the superposition of two identical waves of the same amplitude and frequency, propagating in the opposite direction. Stationary wave generates vibration pattern within the medium. Thus, energy is confined within it. It never appears to get travelled as the nearby points of the wave are of similar phase, and so the energy is not transferred from one point to another

b. Progressive waves: These waves are the ones that allow the propagation of energy through the medium as the wave continuously travels in one direction where the amplitude is kept constant. The molecules in the progressive wave transfer their oscillating energy in the forward direction. It leads to the propagation of energy from one point to another through the medium.

Classification of Wave Based on the Dimension

a. Waves in one-dimension: These waves travel along a line, i.e., along with one-dimensional space. These waves are only a function of one space variable. A wave on a string is an example of a one-dimensional wave

b. Waves in two-dimension: The two-dimensional wave travels along any two dimensions; it can have either \(x\) and \(y\) or \(y\) and \(z\) or \(z\) and \(x\) components. Waves can also travel on a surface that is a two-dimensional space, such as the surface of water or in a layer of clouds

c. Waves in three-dimension: The three-dimensional waves have the \(x\) component, \(y\) component, and \(z\) component. Many significant waves propagate in a three-dimensional space. These include sound waves, radio waves, light, and other electromagnetic waves. 

Classification of Wave Based on Vibration of Particles of Wave

a. Transverse Wave: In transverse waves, the particles of the medium vibrate at right angles to the direction in which the wave propagates. Waves on strings, surface water waves, and electromagnetic waves are transverse waves. In electromagnetic waves (which include light waves), the disturbance that travels is not a result of vibrations of particles; it is due to the oscillation of electric and magnetic fields at right angles to the direction in which the wave travels.

b. Longitudinal wave: In these types of waves, particles of the medium vibrate to and fro about their mean position along the direction of energy propagation. These are also called pressure waves. Sound waves are longitudinal mechanical waves.

Further, we have:

a. Matter waves: They are associated with constituents of matter: electrons, protons, neutrons, atoms, and molecules. They arise in the quantum mechanical description of nature. Though conceptually more abstract than mechanical or electromagnetic waves, they have already found applications in several devices essential to modern technology; matter waves associated with electrons are employed in electron microscopes.

b. Gravitational waves: These waves propagate through the gravitational field that is present throughout space. Similar to electromagnetic waves, gravitational waves can propagate through matter or space. Gravitational waves are a consequence of Einstein’s theory of general relativity and should not be confused with gravity waves, which is a name for the kind of waves found in deep water (a.k.a. ocean waves). Gravitational waves were predicted to exist in \(1916\) (or \(1918\)) but were not confirmed with direct observation until \(2015\).

Terms Related to Waves

1. Wavelength
The distance travelled by the disturbance during one vibration by a medium particle is called the wavelength \((\lambda )\). In a transverse wave, the wavelength may also be defined as the distance between two successive crests or troughs. In a longitudinal wave, the wavelength \((\lambda )\) is equal to the distance from the centre of one compression (or refraction) to another.

2. Amplitude
The amplitude of a wave is the maximum displacement of the particles of the medium from their mean position.

3. Frequency
The number of vibrations made by a particle in one second is called frequency. It is represented by \(v\). Its unit is hertz \(({\rm{Hz}}),\nu = \frac{1}{T}\).

4. Time-Period
The time taken by a particle to complete one vibration is called the time period.
\(T = \frac{1}{v}\), it is expressed in seconds.

5. Wave Velocity
Wave velocity is the time rate of propagation of wave motion in the given medium. It is different from particle velocity. Wave velocity depends upon the nature of the medium.

\({\rm{ Wave velocity }}(v) = {\rm{ frequency }}(v) \times {\rm{ wavelength }}(\lambda )\)

Applications of Waves

A variety of waves surrounds us. Sound is a type of wave that moves through matter and then vibrates our eardrums so we can hear. Light is a special kind of wave that is made up of photons. We even use waves (microwaves) for cooking our food fast. Radio waves are used in communication technology.

In X-Ray imaging: In nature, a wave is an essential kind of motion. Wave behaviours such as diffraction, refraction, and reflection make them useful in the medical industry for non-intrusive imaging, producing minimal damage to objects.

MRI scans: Resonance is a wave property used in MRI scans to find tumours. Resonance is a kind of oscillation, which presents maximum vibrating amplitude at a particular frequency. MRI stands for magnetic resonance imaging. It is a technology that transmits radio waves and uses a magnetic field to create images of organs and tissues inside the body.

Ultrasound: Ultrasounds are used for both medical applications and industrial applications to produce images using harmless sound waves

To study seismic activity: In the petroleum industry, detecting where oil is can be a challenge. Because of the particular properties of waves, they can be identified and used for specific purposes, such as using the speed of waves through Earth to determine the interior composition

As a cleanser: The higher the frequency is, the stronger the penetration ability of a wave will be. Vibrating sound waves can be used to clean industrial objects such as jewellery or medical cleaning of teeth.

Information Transmission: Movie images are reflected off movie screens. When polarized wave images are used, movies can be transmitted in 3D. Radio waves are reflected from satellites for GPS.

Telecommunication: Space agencies send space shuttles to outer space and communicate with astronauts through electromagnetic waves, which travel hundreds of thousands of miles in space.

Waves Formula

The motion of a transverse sinusoidal wave through a medium is in the form of crests and troughs. The crests represent particles position having maximum displacement, while troughs represent particles position having minimum displacement. The distance between two consecutive crests or the distance between two consecutive troughs is known as the wavelength. The wavelength of a given wave can be measured using the speed and frequency of the wave as follows:

\({\rm{ Wavelength }} = {\rm{ speed }} \times {\rm{ frequency }}\)
\(\lambda = v \times f\)

Where,
\(\lambda \) is the wavelength of the wave.
\(v\) is the velocity of the wave.
\(f\) is the frequency of the wave.

PRACTICE QUESTIONS ON WAVES

FAQs on Wave

Let’s look at some commonly asked questions about wave:

Q.1. What are the three types of waves?
Ans: Three types of waves are Mechanical, Electromagnetic, and Matter waves.

Q.2. What is a Wave?
Ans: In physics, a wave is a disturbance that travels through space and matter, transferring energy from one place to another.

Q.3. Why can transverse waves not occur in fluids?
Ans: Fluids have no shape of their own – they yield no shearing stress. This is why transverse waves are possible in solids and strings (under tension) but not in fluids.

Q.4. Explosions on other planets are not heard on Earth. Why?
Ans: Due to the absence of a material medium over a long distance between Earth and planets and in the absence of a material medium for propagation, sound waves cannot travel. Hence the explosions on other planets cannot be heard on Earth.

Q.5. Why sound wave is a longitudinal wave?
Ans: A sound wave is called a longitudinal wave because compressions and rarefactions in the air produce it. When the sound wave travels through the air, its particles vibrate parallel to the direction of propagation. The waves in which particles of the medium move in a direction parallel to the direction of the wave are called longitudinal waves.

Q.6. What is the amplitude of a wave?
Ans: The wave amplitude can be defined as the maximum displacement of the constituent medium particles from their mean positions.

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