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# Wave Motion

Last updated date: 08th Sep 2024
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## Introduction to Wave Motion

There cannot be a better introduction of wave motion than comprehending it with the help of an example. At some point in time, we all have viewed the ripples formation during the time a small pebble (stone) has dropped inside a pond. The creation of disturbances by this stone within the water leads to producing ripples that get outwards towards the pond's shore.

When you start examining the motion of the leaf that is floating somewhere near to this disturbance for a shorter duration through a stable day, you will notice that this leaf starts moving upward and downward about its genuine position. But, it is interesting to notice here that it does not go towards the disturbance source. This shows water wave disturbance goes from a single place to another (here the water does not flow with it). The particles of water go upward and downward in the mean positions.

The transfer of energy and momentum from a point in a medium to another point in the medium without the actual transfer of matter between the points is defined as wave motion. In other words, it can be described as the propagation of disturbances through a medium that originates due to repeated vibrations of the particles about their mean positions. The disturbance is produced by the waves as the function of the time and this function is called the wave function. It may be the displacement of particles in the case of string and maybe a variation of pressure or density in the case of sound waves.

Example - Electromagnetic Waves

### Classification of Wave Motion

Wave motion has been classified on the various basis:

On the basis of mode of propagation:

1. Mechanical Waves- The waves that require a medium to travel are called mechanical waves. These are further classified as:

1. Transverse Wave- For a transverse wave, the particle vibrates perpendicular to the direction of propagation.

2. Longitudinal Wave- For longitudinal waves, the particle vibrates in the direction of propagation.

3. Standing Waves- The waves that do not transfer energy and momentum from one point to another.

4. Progressive Wave- The wave that transfers energy and momentum.

2. Non - Mechanical Waves- The waves that do not require a medium are called non-mechanical waves.

On the basis of the number of dimensions:

1. 1-D - The waves that propagate energy in only one direction.

2. 2-D - The waves that propagate energy In two directions.

3. 3-D - The waves that propagate energy in three directions.

On the basis of the transfer of energy:

1. Standing waves.

2. Progressive waves.

### Periodic and Non - Periodic Wave

Periodic Waves- If the pattern of a wave is repeated after one wavelength or a single time 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 time period and does not have the same pattern throughout the propagation then the waves are called periodic waves.

### Characteristics of Wave Motion

• The velocity of a particle is maximum at the mean position and zero at the extreme position.

• Velocity through which wave travel is different from the velocity through which particles vibrate.

• Disturbances that originate due to repeated vibrations of the particles about their mean positions travel through the medium.

• There is a phase difference between the particles of the medium because each particle is subjected to disturbance a little later than its preceding particle.

• Without any actual transfer of the particles of the medium, energy and momentum are transferred from one point to another.

### Important Terminologies

• Amplitude (A)- The amplitude of a wave is the maximum displacement of any particle in the medium from its equilibrium position.

• Wavelength (λ)- Wavelength is defined as the distance between two consecutive crests or troughs.

• Period (T)- The period of a wave is the time taken by the wave to complete one cycle.

• Wave Velocity (V)- It is defined as the velocity by which a wave travels in a medium. The velocity of a wave is defined as the product of its wavelength and frequency.

• Path Difference (Δx)- It is the distance between two positions of particles measured along the direction of propagation of the wave through the medium.

• Frequency (f)- The number of vibrations made per second by any particles of the medium is called the frequency of the wave. The frequency of a wave is a characteristic or unique property of the source and hence it only changes when the source changes irrespective of the medium through which the wave travels.

• Phase Difference Δ(φ)- It represents the different states of vibration of a particle at two different instants of time or any pair of particles at the same instant of time.

• Phase or Phase Angle (φ)- The state of vibration of the particle of a medium with respect to its mean position is called phase.

• Period (T)- The period of a wave is the time taken by any particle of the medium to complete one cycle of wave motion.

### Important Relations

v = λ/T = fλ

ω = 2π/T = 2πf = circular frequency/angular frequency

ω =angular frequency

t = time

k = angular wavenumber

x = position of the particle

Φ = phase difference

Velocity of wave (v) = fλ

Velocity of oscillation or transverse velocity or particle velocity = dy/dt.

### Phase Difference and Path Difference

Let's consider a wave propagating in the x-direction.

Consider two points A & B in the medium through which the wave travels.

Let the path difference between two points be  \[(x_{2} - x_{1})\] =Δx.

We know, the phase difference corresponding to λ is 2π.

Therefore, the phase difference corresponding to Δx is 2πΔx/λ.

Δϕ = 2πΔx/λ

Also, path difference corresponding to a time difference (T) is (λ), therefore, a path difference (Δx) corresponds to a time difference of (Δx/λ)T.

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## FAQs on Wave Motion

1. What is a standing wave?

The wave that is confined to a particular space and does not allow the transfer of energy is called a standing wave. This has a single frequency model for the vibration of the physical system of the body where amplitudes go varying from one place to another. The next thing about the standing wave is that it remains zero constantly at the fixed points. And, it goes maxima at the other points. Thus, this is how standing waves can be defined in simple words.

2. How does the sound we produce travel in the air?

The sound energy that we create is transferred from one point to another in the form of waves. The sound waves consisting of compression and refraction carry the sound energy we produce. So, the answer for this will be a sound sensation. Sound waves go towards the outer ear and they travel via a narrow passageway which is known as the ear canal. This goes towards the eardrum. The eardrum makes vibration via the coming waves sound and these vibrations are sent to three small bones within the middle ear.

3. Classify waves on the basis of duration.

On the basis of duration, waves can be classified into two categories; wave pulse (are called short duration wave) and wave train (are called long-duration wave). In total, the waves are classified into three primary categories named surface waves, transverse waves, and longitudinal waves. The surface waves float on the surface, and the transverse goes in the opposite direction and the next one remains perpendicular towards the direction. So, these are the basic duration waves and categories of the primary waves.

4. What are mechanical waves?

Mechanical waves are those produced due to the vibration of material particles and require a medium to propagate. eg, sound waves, vibrating string, etc. Mechanical waves are produced due to disturbance in the medium and this disturbance propagates through the medium without the motion of material particles of the medium. In other words, the waves that require a medium to travel or propagate are called mechanical waves.

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