NCERT Solutions for Class 11 Physics Chapter 14 – Waves

Waves is a core and high-weightage chapter in Class 11 Physics that explains the propagation of energy through disturbances. This chapter covers key topics such as types of waves, wave motion, wave speed, transverse and longitudinal waves, superposition principle, reflection of waves, standing waves, beats, and Doppler effect—all essential for school exams and competitive exams like JEE and NEET.

NCERT Solutions for Class 11 Physics Chapter 14 – Waves are prepared strictly according to the latest CBSE syllabus and exam pattern. The solutions are written in simple, step-by-step language with clear diagrams, graphs, and solved numericals, helping students build strong conceptual clarity and score well in Class 11 examinations.

NCERT Solutions for Class 11 Physics Chapter 14 – Waves

Waves
Medium
Q.
A transverse harmonic wave on a string is described by y( x,t ) = 3.0 sin( 36t + 0.018 x +  π 4 ) Where x and y are in cm andtin s. The positive direction ofxis from left to right. ( a ) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation? ( b ) What are its amplitude and frequency? ( c ) What is the initial phase at the origin? ( d ) What is the least distance between two successive crests in the wave? MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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aaaaaa@CA58@
Waves
Medium
Q.
Explain why (or how):
(a) In a sound wave, a displacement node is a pressure antinode and vice versa,
(b) Bats can ascertain distances, directions, nature, and sizes of the obstacles without any “eyes”,
(c) A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
(d) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and
(e) The shape of a pulse gets distorted during propagation in a dispersive medium.
Waves
Medium
Q.
Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about 4.0 km s–1, and that of P wave is 8.0 km s–1. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?
Waves
Medium
Q.
A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km h–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m s–1.
Waves
Difficult
Q.
One end of a long string of linear mass density 8.0 × 10–3 kg m–1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t =0, the left end (fork end) of the string x = 0 has zero transverse displacement (y =0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm.
Write down the transverse displacement y as function of x and t that describes the wave on the string.
Waves
Medium
Q.
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 produced by the whistle equal to 1/20 or 0.05 Hz?
Waves
Difficult
Q.
A travelling harmonic wave on a string is described  by y( x, t )=7.5 sin( 0.0050x + 12t +  π 4 ) ( a ) What are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation? ( b ) Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point att =2 s, 5 s and 11 s. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@8A2F@
Waves
Medium
Q.
A train, standing in a station-yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with at a speed of 10 m s–1. What are the frequency, wavelength, and speed of sound for an observer standing on the station’s platform? Is the situation exactly identical to the case when the air is still and the observer runs towards the yard at a speed of 10 ms–1? The speed of sound in still air can be taken as 340 m s–1.
Waves
Medium
Q.
A train, standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air.
(i) What is the frequency of the whistle for a platform observer when the train
(a) approaches the platform with a speed of 10 ms–1,
(b) recedes from the platform with a speed of 10 ms–1?
(ii) What is the speed of sound in each case? The speed of sound in still air can be taken as 340 m s–1.
Waves
Medium
Q.
Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?
Waves
Medium
Q.
For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs?
In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?
Waves
Medium
Q.
A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is 340 m s–1).
Waves
Medium
Q.
A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?
Waves
Medium
Q.
A metre-long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the tube length is 25.5 cm or 79.3 cm. Estimate the speed of sound in air at the temperature of the experiment. The edge effects may be neglected.
Waves
Medium
Q.
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is 3.5 × 10–2 kg and its linear mass density is 4.0 × 10–2 kg m–1. What is (a) the speed of a transverse wave on the string, and (b) the tension in the string?
Waves
Medium
Q.
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a traveling wave, (ii) a stationary wave or (iii) none at all:
(a) y = 2 cos (3x) sin (10t)
(b) y = 2 x−vt MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeqabeqabiqaceGabeqabeWabeqaeeaakeaajugGbiaabIcacaqGIbGaaeykaiaaysW7ruavP1wzZbItLDhis9wBH5gaiuaacaWF5bGaaGjbVlaa=1dacaaMe8Uaa8NmamaakaaakeaajugGbiaa=HhacqGHsislcaWF2bGaa8hDaaWcbeaaaaa@4842@
(c) y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
(d) y = cos x sin t + cos 2x sin 2t
Waves
Medium
Q.
(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same
(a) frequency,
(b) phase,
(c) amplitude? Explain your answers.
(ii) What is the amplitude of a point 0.375 m away from one end?
Waves
Medium
Q.
The transverse displacement of a string (clamped at its both ends) is given by
y(x,t) = 0.06 sin  2π 3  x cos (120 πt) MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeqabeqabiqaceGabeqabeWabeqaeeaakeaaruavP1wzZbItLDhis9wBH5gaiuaacaWF5bacfeGaa4hkaiaa=HhacaWFSaGaa8hDaiaa+LcacaaMe8Uaeyypa0JaaGjbVlaa=bdacaWFUaGaa8hmaiaa=zdacaaMe8Uaa83Caiaa=LgacaWFUbGaaGjbVpaalaaabaGaa8NmaGGaaiab9b8aWbqaaiaa=ndaaaGaaGPaVlaa=HhacaaMe8Uaa83yaiaa=9gacaWFZbGaaGPaVlaa+HcacaWFXaGaa8Nmaiaa=bdacaaMe8Uae0hWdaNaa8hDaiacObOFPaaaaa@5F0C@
Where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 ×10–2 kg.
Answer the following:
(a) Does the function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What are the wavelength, frequency, and speed of each wave?
(c) Determine the tension in the string.
Waves
Medium
Q.
For the travelling harmonic wave
y (x, t) = 2.0 cos 2p (10t – 0.0080x + 0.35)
Where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
(a) 4 m,
(b) 0.5 m,
 MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeqabeqabiqaceGabeqabeWabeqaeaaakqaabeqaaerbuLwBLnhiov2DGi1BTfMBaGqbaKqzagGaa8hkaiaa=ngacaWFPaGccaaMe8+aaSaaaeaajugGbiabeU7aSbGcbaqcLbyacaWFYaaaaOGaa8hlaaqaaiaa=HcacaWFKbGaa8xkaiaaysW7daWcaaqaaiaa=ndacqaH7oaBaeaacaWF0aaaaGqbbKqzagGaa4Nlaaaaaa@4(c)  λ 2 , (d)  3λ 4 . MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9q8qqQ8frFve9Fve9Ff0dmeqabeqabiqaceGabeqabeWabeqaeaaakqaabeqaaKqzagGaaeikaiaabogacaqGPaGccaaMe8+aaSaaaeaajugGbiabeU7aSbGcbaqefqvATv2CG4uz3bIuV1wyUbacfaqcLbyacaWFYaaaaOGaa8hlaaqaaiaabIcacaqGKbGaaeykaiaaysW7daWcaaqaaiaa=ndacqaH7oaBaeaacaWF0aaaaGqbbKqzagGaa4Nlaaaaaa@4BA1@
Waves
Difficult
Q.
A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall?

NCERT Solutions for Class 11 Physics Chapter 14 – Waves

Q. 1) Explain why (or how):

  • (a) In a sound wave, a displacement node is a pressure antinode and vice versa.
  • (b) Bats can ascertain distances, directions, nature, and sizes of the obstacles without any "eyes".
  • (c) A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes.
  • (d) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases.
  • (e) The shape of a pulse gets distorted during propagation in a dispersive medium.

Ans:

(a) Node is a point where the amplitude of oscillation is the minimum and pressure is the maximum. On the contrary, antinode is a point where the amplitude of oscillation is the maximum and pressure is the minimum. Therefore, in a sound wave, a displacement node is a pressure antinode and vice versa.

(b) Bats emit ultrasonic sound waves of very high-frequency. When these waves are reflected by obstacles in their path, the bat receives a reflected wave and estimates the nature, direction, distance and size of an obstacle.

(c) Although a violin note and a sitar note have the same frequency, but the overtones and their strengths are different. Thus, we can differentiate the notes produced by a sitar and a violin even if they have the same frequency of vibration.

(d) Solids have both elasticity of shape and elasticity of volume (shear modulus). Longitudinal waves require the elasticity of shape in the medium for their propagation. Transverse waves propagate in the medium with elasticity of volume. Thus, the solids can support both longitudinal and transverse wave whereas, gases have only the volume elasticity, therefore, the transverse waves cannot propagate through gases.

(e) A sound pulse is a combination of waves having different wavelengths. The shape of wave pulse gets distorted due to propagation of waves in a dispersive medium with different velocities.

Q. 2) 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 produced by the whistle equal to 1/20 or 0.05 Hz?

Ans:

(a) A narrow sound pulse has neither a definite wavelength nor a definite frequency. However, its speed remains the same, which is equal to the speed of sound in that medium.

(b) If the pulse rate is 1 after every 20 seconds, it does not mean that the frequency of note produced by the whistle is 0.05 Hz. Rather, it implies that, 0.05 Hz is the frequency of the repetition of the short pip of the whistle.

FAQs: Class 11 Physics Chapter 14 – Waves

Q1. Is Waves important for exams?
Yes, it is a high-weightage chapter for Class 11 and competitive exams.

Q2. Which topics are most important in this chapter?
Wave speed, standing waves, superposition, beats, and Doppler effect.

Q3. Are numericals asked from this chapter?
Yes, wave equation, beats, and Doppler effect numericals are common.

Q4. Are diagrams important here?
Yes, wave profiles and standing wave diagrams are frequently asked.

Q5. How do NCERT Solutions help?
They provide NCERT-aligned, exam-ready explanations with solved numericals and diagrams.