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Waves Class 11 Notes CBSE Physics Chapter 15 (Free PDF Download)

Last updated date: 03rd Dec 2023
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MVSAT Dec 2023

Revision Notes for CBSE Class 11 Physics Chapter 15 (Waves) - Free PDF Download

Waves and Vibrations are extremely very important phenomena in Physics. Oscillations are found everywhere in this nature in many different forms. From the large oscillations of sea waves to the jiggling of atoms, we can easily find vibration’s examples in almost every system which is physical. A wave can be thought of as oscillation in physics or a disturbance that travels through time and space accompanied by an energy transfer. Transfer of energy by wave motion from one point to another is often without permanent displacement of the particles of the medium that can be said as with no or little associated mass transport. They instead consist of oscillating or vibrations around almost fixed locations.

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Waves Class 11 Notes Physics - Basic Subjective Questions

Section – A (1 Mark Questions)

1. Why can the transverse waves not be produced in air?

Ans. For air, the modulus of rigidity is zero or it does not possess property of possession. Therefore, transverse Waves cannot be produced.

2.  Why are all stringed instruments provided with hollow boxes?

Ans. The stringed instruments are provided with a hollow box called sound box. When the strings are set into vibration, forced vibrations are produced in the sound box. Since sound box has a large area, it sets a large volume of air into vibration. This produces a loud sound of the same frequency of that of the string.

3.  Can beats be produced in two light sources of nearly equal frequencies?

Ans. No, because the emission of light is a random and rapid phenomenon and instead of beats, we get uniform intensity.

4. A stationary boat is rocked by waves whose crests are 100m apart velocity is 25m/s. Find the time after which the boat bounces up every time.

Ans. $v=n\lambda$

$v=\dfrac{\lambda }{T}\Rightarrow T=\dfrac{\lambda }{v}$


5. A long string having mass density as 0.01kg/m is subjected to a tension of 64N. Then find the speed of the transverse wave on the string.

Ans. $v=\sqrt{\dfrac{T}{\mu }}=\sqrt{\dfrac{60}{0\cdot 01}}$


Section – B (2 Marks Questions)

6. Three harmonic waves of same frequency (f) and intensity $I_{0}$ having initial phase angles $0,\dfrac{\pi }{4},\dfrac{\pi }{4}$ rad respectively. When they are superimposed, find the resultant intensity.

Ans. Amplitude can be added using vector addition


Since $1\varpropto A^{2}$ ,Where I is intensity 

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Therefore, $I_{res}=\left ( \sqrt{2}+1 \right )^{2}I_{0}=5\cdot 8I_{0}(Approx)$

7. Guitar strings X and Y striking the note ‘Ga’ are a little out of tune and give beats at 6 Hz. When the string X is slightly loosened and the beat frequency becomes 3 Hz. Given that the original frequency of X is 324 Hz, find the frequency of Y.

Ans. Given,

Frequency of X, $f_{x}=324Hz$

Frequency of Y = fy

Beat’s frequency, n = 6 Hz


$n=\left | f_{x}\pm f_{y} \right |$

$6=324\pm f_{y}$

$\Rightarrow f_{y}=330\;Hz$ or $318\;Hz$

As frequency drops with a decrease in tension in the string, thus $f_{y}$ cannot be 330 Hz

$\Rightarrow f_{y}=318\;Hz$

8. A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium.

(a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation?

(b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produces by the whistle equal to 1/20 or 0.05 Hz?


(a) The speed of propagation is definite; it is equal to the speed of the sound in air. The wavelength and frequency will not be definite.

(b) The frequency of the note produced by a whistle is not 1/20 = 0.05 Hz. However, 0.05 Hz is the frequency of repetition of the short pip of the whistle.

9. A transverse wave passes through a string with the equation y = 10 sin $\pi$ (0.02 x - 2.00t) where x is in meter and t in second. Then find the maximum velocity of the particle in wave motion.

Ans. $y=10sin\pi \left ( 0\cdot 02x-2\cdot 00t \right )$

In order to derive maximum velocity,

$\dfrac{dy}{dt}=-20\pi cos\pi \left ( 0\cdot 02x-2\cdot 00t \right )$

$v=-20\pi cos\pi \left ( 0\cdot 02x-2\cdot 00t \right )$



10. Two tuning forks P and Q when set vibrating, given 4 beats/s. If a prong of the fork P is filed, the beats are reduced to 2 beats/s. What is frequency of P, if that of Q is 250 Hz ?

Ans. If fork P is filed then frequency increases, increased frequency is given by




Therefore, initial frequency of P is lower than 252Hz and at that time 4 beats are heard




PDF Summary - Class 11 Physics  Oscillations Notes (Chapter 15)

The last point to be highlighted is the emphasis of an important misconception of waves. Waves transfer energy but do not transfer mass. To see this an easy way is to take an example of a floating ball a few yards out to sea. As the propagation i.e., travelling of waves towards the shore the ball which was in the example will not come towards the shore. 

Eventually, it may come to shore due to a few other factors like winds, tides, or current, but the waves themselves will not carry the ball with them. A mass only moved by the wave which is perpendicular to the direction of propagation and in this case up and down as illustrated in the figure which is given below:

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Depending on the direction of the oscillation of the wave, A wave can be transverse or longitudinal. When a disturbance is caused due to oscillations perpendicular to the propagation the transverse waves occur at the same time. When the oscillations are parallel to the direction of propagation then the waves which are longitudinal occur. While both longitudinal and transverse can be mechanical waves as all electromagnetic waves are transverse waves. An example of longitudinal waves is Sound.


The famous scientist and physicist d'Alembert's formulated the formula of F or shape involves the argument that is denoted as x − vt. In this argument, we can say Constant values which correspond to constant values of F, and if x increases then the rate that vt increases here the constant of values occur. That can be said as the wave-shaped like the F function which will move in the positive direction of x at velocity v and G will propagate at the same speed in the negative direction of x.

In another case of a periodic function F with period denoted as λ, that is  F(x + λ − vt) = F(x − vt) in this the periodicity of F in space has a meaning that a snapshot of the wave which at a given time denoted as t finds the wave varying periodically in space with period λ is denoted as the wavelength of the wave. In a similar manner this periodicity of F implies a periodicity in time t as well that is F(x − v(t + T)) = F(x − vt) 

and then vT = λ, so we can observe the wave at a fixed location that is x that finds the wave undulating periodically in time with period T = λ/v.

Phase Velocity and Group Velocity

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If we consider a red square then the red square moves with the phase velocity, while the green circles which we take as another mark propagates with the group velocity.

There are two velocities that are associated with waves that are the group and the phase velocity.

Velocity which is of the same phase is defined as the rate at which the phase of the wave propagates that to in space at any phase which is given by the wave for example the crest that appears to travel at the phase velocity. The phase velocity is denoted as wavelength λ that is lambda and time period as T.

Group velocity that is the second part is the property of waves that have a defined envelope measuring propagation through space that is of phase velocity and of the overall shape of the waves' amplitude and envelope or modulation of the wave.

Types and Features of Waves

There are two kinds of Waves that are transverse and the longitudinal waves. Transverse waves are like those which are on the water, with the surface going down and up, and longitudinal waves are like those similar to sound waves. The transverse wave high point is called the crest whereas the low point is called the trough. For waves that are longitudinal, the refractions and compressions are analogous to the through and crests and transverse waves. 

The distance between successive troughs and crests or is called the wavelength. The height of a wave is defined as the amplitude. How many troughs and crests pass a specific point during a unit of time is known as the frequency. The wave velocity can be expressed as the wavelength which multiplied by the frequency.

Waves can travel far distances even though the oscillation at one point is small. For example, a thunderclap can be heard kilometers away from where it is actually present yet the sound carried manifests itself at any point only as a minute refraction of air and compressions.

Waves display several basic phenomena like In reflection phenomenon a wave encounters an obstacle and it is reflected back. In the phenomenon of refraction, a wave bends when it enters a medium through it has a different speed. In the phenomenon of diffraction, the waves bend when they pass around small obstacles and spread out when they go through small openings that are present. 

FAQs on Waves Class 11 Notes CBSE Physics Chapter 15 (Free PDF Download)

Q1. What are the Wave Oscillations?

Ans: A wave is said to be in the oscillation state when it moves back and forth in repeating and a regular way. The fluctuations can be there between the extremes of the positions, quantity, force. Different oscillations occur because of different types of waves, like for example in the longitudinal wave the oscillation is parallel to the direction of waves.

Q2. What Do Waves Do?

Ans: Without the transport of matter the waves transport the energy, a wave in a conclusion can be defined as the disturbance that travels through a medium it can transport the energy from one place to another without transporting matter.

Q3. Define Types of Waves.

Ans: For the mechanical wave there are two types of waves transverse and longitudinal waves. The difference between conveys the motion of particles in a medium through waves travels.

Q4. Which Waves Cannot be Transferred?

Ans: In a solid, the mechanical waves cause oscillation of particles in the liquid, gas, and solid must have a medium to travel through. The oscillation is caused by electromagnetic waves in the magnetic and electric fields. It is very important for us to remember that all waves do not transfer matter instead they transfer energy.

Q5. What is a Restoring force in Chapter 15 of Class 11 Physics?

Ans: We have already studied about springs in Chapter 5 and Chapter 6 of Class 11 Physics. These springs exert a restoring force. For example, consider the propagation of sound waves in the air. These sound waves create disturbances in the surrounding medium and cause a change in physical quantities such as density, pressure, etc. Since we know that pressure is just force per unit area, a restoring force proportional to the disturbance is developed here too, just like in spring.

Q6. How can you demonstrate the propagation of Longitudinal waves in Chapter 15 of Class 11 Physics?

Ans: Physics is all about learning new things that have real-life applications. For example, let us take a long pipe with a piston at one end. Assume that this pipe is filled with air. Moving the piston backwards and forwards will generate a pulse. This pulse will generate condensations and rarefactions in the surrounding medium. If you repeat this motion, a sinusoidal wave will be formed and as we all know, longitudinal waves travel in a sinusoidal manner.

Q7. What is an example of a Transverse wave in Chapter 15 of Class 11 Physics?

Ans: Sound waves can be classified into longitudinal and transverse waves. Let us see an example of a transverse wave. Pull a stretched string in such a manner that it vibrates and generates a pulse. You can even attach one side of this string to the wall. Each segment of the string vibrates and oscillates about its equilibrium position. This is perpendicular to the direction of wave propagation and results in the formation of a transverse wave.

Q8. How do I determine the speed of a travelling wave in Chapter 15 of Class 11 Physics?

Ans: There is a mathematical formula that has been derived to determine the speed of a travelling wave. It has been formulated as a general relation that is applicable to all progressive waves. The speed of a travelling wave depends on a number of factors including the elastic properties of the surrounding medium. To know more and refer to the solutions of this topic, check out Chapter 15 of Class 11 Physics Revision Notes provided by Vedantu. The notes and solutions are present on Vedantu's official website ( and mobile app for free of cost.

Q9. What is the principle of superposition of waves in Chapter 15 of Class 11 Physics?

Ans: The principle of superposition of waves has been extensively discussed in Chapter 15 of Class 11 Vedantu Revision Notes. It is basically a phenomenon that explains what happens when two waves overlap each other. When the generated pulses overlap, the resultant displacement can be defined as the algebraic sum of the displacement caused due to each individual pulse. This is the superposition of waves. It does not matter whether the individual displacement is positive or negative.