The waves are of three types:

• Mechanical Waves- When the waves need a medium to transmit
• • Transverse waves
  • Longitudinal waves
• Electromagnetic waves- When the waves do not need a medium to transmit
• Matter waves- When the waves are involved with the moving particles of the matter

The transverse and the longitudinal waves belong to mechanical waves. These waves require a medium to transport. This is an important topic for Class 11 Waves. 

• Transverse Waves- When the particles propagate perpendicular to the direction of the wave, those waves are known as transverse waves. The waves consist of refractions and compressions. The particles transfer energy moving at right angles to the direction of the wave. The waves can act only in a single dimension. These waves cannot be polarised or aligned. The transverse waves can be produced in any medium (as it requires a medium to travel). The ripple on the surface of the water surface is an example of a transverse wave.
• Longitudinal Waves- When the particles of the waves propagate along the direction of the waves, those waves are known as longitudinal waves. These waves consist of troughs and crests. The waves can act in two dimensions. These waves can be polarised or aligned. This wave can only be produced on a solid or liquid surface. The seismic P-waves are an example of a longitudinal wave.

When a wave is travelling continuously in the same direction in a medium with no change in amplitude, then the wave is termed a progressive wave or travelling wave. 

Understanding the displacement relation in a progressive wave through equations.

= y(x, t) = a sin (kx - ωt + φ)

= y(x, t) = A sin (kx - ωt + φ) + B cos (kx - ωt + φ)

Considering a = \( \sqrt{A^{2}} \) + B² and φ= tan^-1 B/A

= y(x, t) = a sin (kx + ωt + φ)

(x, t) = displacement of a particle from position x.

t = the time taken for displacement from x.

a = amplitude

φ = initial phase change

k = The angular wave number

ω = Angular frequency

The characteristics of waves

• Amplitude- The maximum number of displacements of a particle in a wave from its equilibrium position is termed Amplitude.
• Phase- The quantity kx- ωt + φ that is represented as the argument of the sine function is termed as the phase of the particular wave.
• Wavelength- The wavelength is defined as the minimum distance between two points with the same phase and is denoted by λ.
• Angular wave number- This is defined as the spatial frequency of the particular wave. It can be mentioned as the number of waves existing over a specific distance, in line with frequency.
• Angular Frequency- The angular frequency is the angular displacement per unit time at the rate of change of phase of a waveform.

The speed of a travelling wave is a crucial topic for the Class 11 Physics Chapter 15 Notes. There are four different kinds of travelling waves.

• Transverse waves- When the motion of the particles is in right angles to the direction of the wave, the waves are known as transverse waves. The speed of the transverse wave on a stretched string is, \( v = \sqrt{T}/\mu (\mu \)is the linear mass density and T is the tension)
• Longitudinal waves- When the motion of the particles is in the direction of the wave, the waves are known as longitudinal waves. The speed of the longitudinal wave on a stretched string is, \( v = \sqrt{Y}/\rho (Y \) is Young’s modulus, ρ is the mass density)
• Pulse waves- The pulse waves are created when there is a sudden disturbance in the medium. The disturbance can be because of a chain reaction or an explosion.
• Continuous waves- When an electromagnetic wave has continuous amplitude and frequency, it is known as a continuous wave. It is a sine wave with an infinite duration.

 

The superposition of waves states that the resultant displacement of waves in a particular medium at any point of time is the vector sum of individual displacements produced by each and every at that point. There are two different kinds of superposition of waves.

• Constructive Interference- When two waves superimpose with each other, the total amplitude is the sum of the amplitudes of all the waves, producing maximum intensity of light.
• Destructive Interference- When two waves superimpose with each other, the total amplitude is the difference of the amplitudes of all the waves, producing minimum intensity of light.

The superposition of waves produces three different effects 

• When two waves travel at the same speed and frequencies in the same direction, they superpose to produce interference of waves.
• When two waves travel at the same speed and frequencies in the opposite direction, they superpose to produce stationary waves.
• When two waves travel at the same speed but varying frequencies in the same direction, they superpose to produce beats.

Until now, we have been discussing the waves travelling a medium with no obstruction. So, when a wave meets a rigid boundary, the wave gets transmitted back, which is termed as a reflection of waves. The common example of reflection of waves is Echo. The incident and the refracted waves obey Snell’s law, whereas the incident and reflected waves obey the laws of reflection. The laws of reflection states 

• The normal to the surface of reflection, the incident, and the reflected ray lie on the same plane of incidence.
• The incident angle between the incident and the normal is always equal to the reflected angle formed by the reflected ray and normal.
• The incident and the reflected ray are always on the opposite side of the normal.

The Class 11 Waves chapter has an interesting topic known as Beats. When two harmonic waves of close frequencies are heard at the same time, the two waves produce interference because of overlapping and produce an interference pattern known as Beats.

When two sound waves with different frequencies overlap, then their amplitudes get added and subtracted alternatively over a period of time. This causes the sound to be louder or softer. This is termed Beat frequency.

The Austrian Physicist Johann Christian Doppler proposed the Doppler effect in 1842 and was tested successfully by Buys Ballot in 1845. The Doppler effect is equally effective on sound and electromagnetic waves. 

The Doppler effect is the increase or decrease of the frequency of sound, light, or other waves as the distance between the source and observer increases or decreases. A common example is the horn of a vehicle increases as it approaches a person and decreases as it goes away from the person.

f’ = [(V±V₀)/(V±V_S)f

f’ = observed frequency

V = Velocity of sound waves

V₀ = Velocity of the observer

V_S = Velocity of source

The applications of the Doppler effect are

• Medical Imaging
• Radar
• Satellite communication
• Vibration Measurement
• Blood Flow measurement

• Explain in simple words the fundamental properties of waves?

A. The particles in the waves display small vibrations in their mean position with no displacement. Every successive particle follows the pattern set by its predecessor. During the motion, only energy transfer takes place in the particles.

• State some characteristics of waves?

A. The waves have five important characteristics. They are Wavelength(λ), Velocity(c), Amplitude(a), Frequency(v), and Wave number.

• What are the topics covered under Waves Class 11 NCERT physics?

A. The NCERT Physics Class 11 Waves chapter covers topics like types of waves, progressive waves, speed of a travelling wave, principle of superposition of waves, reflection of waves, Beats, and Doppler effect.