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.

(Image Will be Uploaded Soon)

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.

(Image Will be Uploaded Soon)

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.

Why is Vedantu a Great Help to Prepare for the IIT JEE Examination?

All the aspirants want to remain fully prepared and dream of cracking the IIT JEE examination. For them, Vedantu coaching works as a perfect guide with perfect study material. We know that perfect practice leads the students to perfection. So, we make our students practice and learn every single day. 

The second thing is that we encourage them to sketch out a routine timetable for you. And, here considering the importance of the examination, our emphasis always remains on following this timetable without a miss. The reason is that each second counts to crack such a crucial test. 

Knowing the importance of possessing quality study material, we devote ample time to set the course according to the latest pattern of examination and the subject matter experts of Vedantu also draft crucial questions for a good revision.

Vedantu teachers know the fact that each student has some weak areas that have to be polished. So, we guide the students to not only focus on those areas but also help them fill up all those gaps that are coming their way in preparation for such a crucial examination. 

The tutors of Vedantu encourage students to attempt more and more mock as well as practice test papers. This is true that previous year papers prove to be a real help if the students resolve them honestly. 

All the students are advised to prepare revision notes for their study as self-made notes are a boon to have when it is time to prove the hard work of the entire year. And, notes in your own language are going to remain in your mind for longer.

Along with the everyday study, Vedantu also asks the students to take care of their health. They encourage the students to maintain a nutritious regimen and also have sufficient rest. It is also a wise move to indulge in a few mind relaxation techniques so that you can cope with the challenges with a charged-up mind.