Wave Motion

Wave motion may be defined as the means of energy transferred by oscillations or vibrations in any medium. There are two basic types of waves: mechanical waves, which need a medium for their propagation, and electromagnetic waves, for example, light waves in a vacuum. Properties of waves include wavelength, frequency, amplitude, and speed. Principles like reflection, refraction, diffraction, and interference govern it.

In this article, we will cover the concept of Wave Motion. This concept falls under the broader category of Properties of Solids and Liquids which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more.

Wave Motion

Wave motion is defined as a form of disturbance transferred from one point to another involving transfer of energy but no transfer of matter.

Ex. A sound wave, a water wave, a wave on a string.

The simplest types of wave motion are vibrations of elastic media, such as air, crystalline solids, or stretched strings. If, for example, when the string of the guitar is plucked and let say a piece of paper is placed on it then the piece of paper will oscillate perpendicular to the direction of wave motion (energy or disturbance transfer). Particles in wave motion do not travel, they only oscillate about their position. A wave is a form of energy or momentum that travels due to disturbances produced.

Classification of Wave Motion

Waves can classified based on 3 different characteristics.

(a). Based On Medium

On the basis of medium waves can be classified into two categories.

1. Mechanical waves: The waves which require a medium for their propagation are called mechanical waves.

Ex: Waves on string and spring, waves on the water surface, sound waves, and seismic waves.

2. Non-mechanical waves: The waves which do not require a medium for their propagation are called non-mechanical or electromagnetic waves.

Ex: Light, heat (Infrared), radio waves, gamma rays, X-rays etc.

(b). On the basis of vibration of the particles :

On the basis of the vibration of the particles, waves can be classified into two categories.

1. Transverse waves: Particles of the medium execute simple harmonic motion about their mean position in a direction perpendicular to the direction of propagation of wave motion.

Ex. Movement of a string of a sitar or violin.

2. Longitudinal waves: If the particles of a medium vibrate in the direction of wave motion the wave is called longitudinal.

Ex. Sound waves travel through the air, Vibration of the air column in organ pipes.

(c). On the basis of energy propagation :

On the basis of energy, propagation waves can be classified into two categories.

1. Progressive waves: Progressive wave is formed due to continuous vibration of the particles of the medium. Progressive waves travel with a certain velocity. Progressive wave transports energy.

2. Stationary waves: A stationary wave is formed by the superposition of two identical progressive waves travelling in the opposite direction. Stationary wave doesn't travel in any direction. There is no flow of energy in stationary waves.

Ex. wave on a guitar string

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Solved Examples Based On Wave Motion

Example 1: Out of the following, which is not an example of the wave?

1) Sound wave

2) Ripples on the surface of the water

3) Wave on a string

4) None of the above

Solution:

Wave motion: Wave is a disturbance from the equilibrium position which travels through a medium without the actual transfer of particles/matter. It also propagates energy and momentum from one place to another.

Ex. A sound wave ripples on the surface of the water and waves on a string.

All of the above is an example of wave motion.

Example 2: A wave motion has the function . The graph in the figure in the following shows how the displacement y at a fixed point varies with time t. Which one of the labelled points shows a displacement equal to that at the position

1) P

2) Q

3) R

4) S

Solution:

At $\mathrm{t}=0$ and $\mathrm{x}=\pi / 2 \mathrm{k}$

Displacement,

$
y=a_0 \sin \left(-k \times \frac{\pi}{2 x}\right)
$
$
y=-a_0 \sin \left(\frac{\pi}{2}\right)=-a_0
$

The point of maximum displacement in the negative direction is a

Example 3: The speed of the wave in a certain medium is 960 m/s. If 3600 waves pass over a certain point of the medium in 1 minute, the wavelength is (in m)

1) 16

2)4

3)8

4)2

Solution:

Given:

Speed of wave $v=960 \mathrm{~m} / \mathrm{s}$
3600 wave passes in 1 minute.
frequency,

$
n=\frac{3600}{60}=60 \mathrm{~Hz}
$
Wavelength, $\lambda=\frac{v}{n}=\frac{960}{60}=16 \mathrm{~m}$

Example 4: Which of the following statements is correct?

1) Particles in wave motion do not travel, they only oscillate about their position

2)With the propagation of the wave, the particle moves along with the wave.

3)Some particles move but some particles oscillate in the same place

4)The particle moves some distance up to when the energy of the particle and wave is the same and then the particle stops

Solution:

The simplest types of wave motion are vibrations of elastic media, such as air, crystalline solids, or stretched strings. If, for example, when the string of the guitar is plucked and let say a piece of paper is placed on it then the piece of paper will oscillate perpendicular to the direction of wave motion (energy or disturbance transfer).

Particles of the medium in wave motion do not travel, they only oscillate about their mean position.

So we can say that the particles in a wave only oscillate about their position, they do not move at the speed of the wave, nor do they need to move in the same direction in all kinds of waves.

Summary

Wave motion is the transfer of energy from one medium to another without a permanent shift in the particles in those media. This occurs in everyday examples, which include travelling sound through the air, ripples on the water, and string vibrations. Characterization of waves involves wavelength—distance between two similar points on a wave, frequency—how often it goes through, and amplitude—the height of the wave. Wave motion helps us to understand how many technologies work—from devices used in communication to medical imaging tools. It explains much of natural phenomena and the development of solution-oriented innovations.