Are these practice questions for Waves based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Physics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Waves free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Waves mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Waves for full coverage.

How many practice questions are there for Waves?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Waves Class 11 Physics Practice Questions with Answers

easy

Define the phenomenon of beats.

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easy

Define a transverse wave and provide one example.

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easy

A musician tuning a guitar string against a reference tone of

440 \text{ Hz}

hears beats. Justify why the complete disappearance of beats indicates that the string is perfectly in tune.

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easy

A pulse is sent down a string tied to a freely moving ring at the other end. Justify the phase of the reflected pulse relative to the incident pulse.

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easy

Define a transverse wave and provide one example.

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easy

List the three main categories of waves described in your text.

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easy

Name the general category of waves that requires a material medium for its propagation.

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easy

State the principle of superposition of waves.

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easy

A wave pulse traveling on a string encounters a fixed, rigid boundary. Analyze the phase change of the wave pulse upon reflection.

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easy

Apply the principle of superposition to determine the resultant amplitude of a wave when two identical waves with amplitude '

a

' interfere perfectly destructively.

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easy

Justify why transverse waves can propagate through solids but not through ideal fluids like gases or liquids.

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easy

Calculate the speed of a transverse wave in a steel cable that has a tension of

500

N and a linear mass density of

0.05 \text{ kg/m}

.

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easy

Compare transverse waves and longitudinal waves based on the direction of particle oscillation relative to the direction of energy propagation.

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easy

Justify why transverse waves require a medium with shear modulus to propagate, and why this prevents them from travelling through ideal fluids like gases.

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easy

A progressive wave is described by the equation

y(x, t) = 0.04 \sin(20\pi x - 5\pi t)

, where

x

and

y

are in meters and

t

is in seconds. Calculate the amplitude, wavelength, and frequency of the wave.

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easy

Recall the formula that relates the speed of a progressive wave (

v

) to its wavelength (

\lambda

) and frequency (

\nu

).

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easy

Recall the mathematical relationship between wavelength (

\lambda

) and angular wave number (

k

), and the relationship between time period (

T

) and angular frequency (

\omega

).

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easy

Define the phenomenon of 'beats'.

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easy

Contrast a progressive (traveling) wave and a stationary (standing) wave with respect to the transfer of energy.

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easy

Define nodes and antinodes as they relate to stationary waves.

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medium

For a string of length

L

fixed at both ends, list the frequencies for the first three harmonics (fundamental, second, and third) in terms of the wave speed

v

and length

L

.

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medium

Calculate the speed of sound in helium gas at a pressure of

1.0 \times 10^5 \text{ Pa}

and a density of

0.18 \text{ kg/m}^3

. For helium, a monatomic gas, the ratio of specific heats is

\gamma = 5/3

.

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medium

Identify the phase change that a transverse wave pulse undergoes upon reflection from a rigid boundary.

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medium

A progressive wave is represented by

y(x, t) = 0.02 \sin(10x - 40t + \pi/3)

, with all quantities in SI units. Calculate the displacement of a particle located at

x = 0.5

m at time

t = 0.1

s.

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medium

Explain the fundamental difference between transverse and longitudinal waves. Provide one example for each.

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medium

List the physical quantities represented by the symbols in the displacement relation for a progressive wave, given by the equation

y(x, t) = a \sin(kx - \omega t + \phi)

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medium

A guitarist wants to produce a note with a specific frequency but finds the string is slightly out of tune. Propose a method to adjust the frequency of the note produced by the string without changing the string itself. Justify your proposal based on the physics of wave speed on a string and the relationship between frequency, wavelength, and speed for standing waves. Evaluate the practical limitations of your proposed method.

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medium

Recall the formula for the speed of a transverse wave on a string. Find the speed of a wave on a string with linear mass density

\mu = 0.025 \text{ kg/m}

under a tension of

T = 100 \text{ N}

.

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medium

Describe how standing waves are formed. Define the terms 'node' and 'antinode' in the context of standing waves.

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medium

Examine the function

y(x,t) = A \log(x^2 - v^2t^2)

. Can this function represent a travelling wave? Justify your answer.

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medium

Create a wave function

y(x, t)

that represents a transverse wave travelling in the negative x-direction with an amplitude of

0.05 \text{ m}

, a wavelength of

0.4 \text{ m}

, and a frequency of

10 \text{ Hz}

. Justify the sign chosen for the

\omega t

term in your function.

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medium

A transverse wave on a string is described by the equation

y(x, t) = 0.04 \sin(20\pi x - 50\pi t)

, where

x

and

y

are in meters and

t

is in seconds. Calculate the wavelength and the period of this wave.

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medium

Two waves are described by

y_1 = a \sin(kx - \omega t)

and

y_2 = a \cos(kx - \omega t)

. Justify whether these two waves will produce interference with maximum possible amplitude.

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medium

Design a system using two identical wave sources to demonstrate both constructive and destructive interference at a specific point in space. Specify the required phase relationship between the sources and their placement relative to the observation point for each type of interference. Formulate the mathematical conditions for the path difference.

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medium

A

1.5

m long string has a mass of

30 \times 10^{-3} \text{ kg}

and is fixed at both ends. If the string vibrates in its fundamental mode with a frequency of

50

Hz, solve for the tension in the string.

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medium

Two waves traveling in the same direction are described by

y_1(x, t) = 0.02 \sin(4x - 50t)

and

y_2(x, t) = 0.02 \sin(4x - 50t + \pi/3)

. Apply the principle of superposition to calculate the amplitude of the resultant wave.

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medium

Define wavelength, period, and frequency of a wave and state the relationship between wave speed, frequency, and wavelength.

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medium

Compare the reflection of a wave pulse from a rigid boundary and a free (or open) boundary. Focus on the phase change of the reflected pulse in each case.

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medium

Describe the phase change that occurs when a wave on a string is reflected from (a) a rigid boundary and (b) an open or free boundary.

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medium

Design an experiment to determine the speed of a transverse wave on a stretched string. Justify your choice of equipment and the formula you would use to calculate the speed.

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medium

A student uses Newton's formula

v = \sqrt{P/\rho}

to calculate the speed of sound in air and gets a value that is about 15% lower than the experimentally measured value. Critique the student's method by identifying the flawed physical assumption and justify why Laplace's correction is necessary.

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medium

A student claims that for a progressive wave described by

y(x, t) = a \sin(kx - \omega t)

, the speed of any particle in the medium is constant and equal to the wave speed

v = \omega/k

. Critique this statement. Is it correct? Justify your answer by deriving the expression for the particle velocity.

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medium

Recall the formula for the speed of a transverse wave on a stretched string and identify the two physical properties of the string that determine this speed.

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medium

Recall the general mathematical expression for a sinusoidal wave travelling in the positive x-direction.

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medium

Two tuning forks produce sound waves of frequencies

256

Hz and

260

Hz. Calculate the beat frequency. Analyze what would happen to the beat frequency if the second tuning fork's frequency was increased to

262

Hz.

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medium

Name the two properties of a stretched string that determine the speed of a transverse wave travelling along it.

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medium

Newton's formula for the speed of sound,

v = \sqrt{P/\rho}

, was found to be inaccurate. Laplace's correction, which assumed adiabatic processes, yielded

v = \sqrt{\gamma P/\rho}

, a much more accurate value. Evaluate the physical reasoning behind Laplace's assumption and justify why the compressions and rarefactions in a sound wave are better described as adiabatic rather than isothermal.

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medium

Explain the primary difference between transverse and longitudinal waves, providing one example for each.

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medium

Analyze how the speed of sound in air increases with temperature. Use the formula

v = \sqrt{\frac{\gamma P}{\rho}}

and the ideal gas law to demonstrate this relationship.

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medium

An organ pipe of length

50 \text{ cm}

is open at both ends. It resonates with a source of frequency

1020 \text{ Hz}

. Given the speed of sound in air is

340 \text{ m/s}

, calculate which harmonic mode of the pipe is excited. Would resonance occur with the same source if one end of the pipe were closed?

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medium

Analyze the relationship

v = \nu \lambda

. If a sound wave travels from air into water, its frequency remains constant. Compare the wave's speed and wavelength in water to its speed and wavelength in air.

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medium

Two students are debating the applicability of the wave equation

y(x, t) = a \sin(kx - \omega t)

. Student A argues it only represents transverse waves, where

y

is the perpendicular displacement. Student B claims it can also represent longitudinal waves. Evaluate both arguments and justify your conclusion.

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medium

Two musicians are tuning their sitars. One plays a note at a frequency of

440 \text{ Hz}

. The other sitar produces 4 beats per second with the first one. Propose two possible frequencies for the second sitar and formulate a method by which the second musician can determine which of the two frequencies is correct without using a frequency counter.

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medium

A

1.0 \text{ m}

long steel rod is clamped at its midpoint and is made to vibrate in its fundamental longitudinal mode at a frequency of

2500 \text{ Hz}

. First, calculate the speed of sound in steel. Second, calculate the wavelength of the sound wave produced in air by these vibrations, assuming the speed of sound in air is

340 \text{ m/s}

.

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medium

An ambulance siren has a frequency of

500

Hz. Analyze the apparent frequency heard by a stationary observer when the ambulance is approaching them at a speed of

30 \text{ m/s}

. The speed of sound in air is

340 \text{ m/s}

. Apply the Doppler effect formula to calculate this apparent frequency.

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medium

Evaluate the statement: 'In a stationary wave, no energy is transported along the medium.' Is this statement entirely correct? Justify your answer by considering the energy within a single segment between two consecutive nodes.

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medium

A wave travelling on a string has a wavelength of

0.5 \text{ m}

and a frequency of

120 \text{ Hz}

. Recall the formula for wave speed and calculate its value.

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medium

Compare the requirements of a medium for the propagation of transverse waves versus longitudinal waves.

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medium

A guitar string with a length of

0.8 \text{ m}

has a mass of

4.0 \times 10^{-3} \text{ kg}

. Calculate the tension required in the string for a transverse wave to travel at a speed of

400 \text{ m/s}

.

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medium

Examine the factors affecting the speed of sound in a gas, as described by the formula

v = \sqrt{\frac{\gamma P}{\rho}}

. Explain why the speed of sound increases with temperature.

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medium

A pipe open at both ends has a fundamental frequency

f_o

. When one end is closed, the fundamental frequency becomes

f_c

. Formulate a relationship between

f_o

and

f_c

. Justify why only odd harmonics are present in the closed pipe.

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medium

Analyze why a musician tuning an instrument listens for the disappearance of beats rather than their presence.

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hard

Summarize the key differences between a progressive wave and a stationary wave based on amplitude, phase, and energy transfer.

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hard

Explain the principle of superposition of waves. Describe the conditions for fully constructive and fully destructive interference for two sinusoidal waves of the same amplitude and frequency.

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hard

Describe how a standing wave is formed and explain why it is called a 'stationary' wave. Also, write the general equation for a standing wave.

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hard

A student suggests that since the speed of sound in a gas is given by

v = \sqrt{\gamma P/\rho}

, increasing the pressure of the gas at constant temperature will increase the speed of sound. Critique this reasoning. Is the conclusion correct? Justify your answer by considering the ideal gas law.

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hard

Explain why the speed of sound is generally higher in solids and liquids than in gases, using the formula

v = \sqrt{B/\rho}

.

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hard

Design a setup using a string fixed at both ends, a variable tension mechanism, and a wave driver to demonstrate the first three harmonics. Formulate the relationship you would expect between the tension

T

and the frequency

v

for the fundamental mode, and propose a method to verify this relationship graphically.

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hard

Two piano strings are supposed to be tuned to a frequency of

440

Hz. One string is slightly out of tune and when played together with the correctly tuned string, 4 beats per second are heard. The tension in the out-of-tune string is increased slightly, and the beat frequency is observed to decrease to 2 beats per second. Solve for the original frequency of the out-of-tune string.

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hard

The transverse displacement of a string of length

1.2 \text{ m}

fixed at both ends is given by

y(x, t) = 0.05 \sin(5\pi x) \cos(40\pi t)

, where

x, y

are in meters and

t

is in seconds. Calculate the wavelength, frequency, and speed of the two traveling waves that form this standing wave. Also, determine the tension in the string if its linear mass density is

2.0 \times 10^{-2} \text{ kg/m}

.

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hard

You are given two tuning forks with frequencies

v_A

and

v_B

. When sounded together, they produce

5 \text{ Hz}

of beats. After loading fork B with a small amount of wax, the beat frequency decreases to

2 \text{ Hz}

. If the frequency of fork A is

v_A = 256 \text{ Hz}

, formulate an expression and determine the original frequency of fork B,

v_B

. Justify your reasoning.

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hard

Two tuning forks, A and B, produce

4

beats per second when sounded together. The frequency of fork A is known to be

256 \text{ Hz}

. When a small piece of wax is attached to fork B, the beat frequency decreases to

2 \text{ Hz}

. Analyze this situation to calculate the original frequency of fork B.

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hard

Propose a modification to a standard single-measurement resonance tube experiment to yield a more accurate value for the speed of sound, specifically by accounting for the 'end correction'. Justify your proposed method.

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hard

The equation for a standing wave on a string is given by

y(x, t) = 0.1 \sin(4\pi x) \cos(100\pi t)

, where

x

and

y

are in meters and

t

is in seconds. Analyze this wave to determine the amplitude, wavelength, and frequency of the two travelling waves that superpose to form it. Also, calculate the distance between two consecutive nodes.

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hard

Design an experiment to determine the speed of sound in air using the principle of resonance in an air column. Justify your choice of apparatus and formulate the procedure to minimize experimental errors.

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hard

A progressive wave is described by

y_i(x, t) = a \sin(kx - \omega t)

. It travels towards a rigid boundary at

x=0

. Formulate the mathematical expression for the reflected wave,

y_r(x, t)

, and justify the phase change upon reflection.

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hard

Examine the formation of a standing wave. Two waves

y_1 = a \sin(kx - \omega t)

and

y_2 = a \sin(kx + \omega t)

travel in opposite directions. Apply the principle of superposition to derive the equation of the resulting standing wave and identify the general positions of nodes and antinodes.

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hard

Explain the key differences between a progressive wave and a stationary wave with respect to (i) energy transfer, (ii) amplitude of particles, and (iii) phase relationship between particles.

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hard

Create a mathematical model for a standing wave on a string of length

L = 2 \text{ m}

fixed at both ends. The wave speed is

v = 100 \text{ m/s}

. Formulate the equation for the third harmonic (

n=3

) and determine the locations of its nodes and antinodes. Justify the boundary conditions used in your model.

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hard

The equation for a stationary wave is given by

y(x, t) = 0.04 \sin(5\pi x) \cos(40\pi t)

, where

x

and

y

are in meters and

t

is in seconds. Evaluate this wave by deconstructing it into its two constituent travelling waves. Formulate the equations for these two waves and justify their directions of travel, amplitudes, and speeds.

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hard

A pipe of length

85

cm is open at both ends. It produces a note of frequency

300

Hz. The speed of sound in air is

340 \text{ m/s}

. Calculate which harmonic mode of the pipe is resonating. Then, analyze what the fundamental frequency of this pipe would be if one end were closed.

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hard

Explain Newton's formula for the speed of sound in a gas and describe the correction that was later introduced by Laplace.

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hard

Compare the speed of sound in Helium (

He

) and Nitrogen (

N_2

) gas at the same temperature and pressure. Helium is monatomic (

\gamma_{He} = 5/3

) and Nitrogen is diatomic (

\gamma_{N_2} = 7/5

). The molar mass of Helium is

4 \text{ g/mol}

and Nitrogen is

28 \text{ g/mol}

. Calculate the ratio of the speed of sound in Helium to that in Nitrogen (

v_{He}/v_{N_2}

).

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hard

Evaluate the effect of changing the following parameters on the speed of a transverse wave on a stretched string: (a) doubling the tension

T

, (b) halving the length of the string while keeping the mass constant, and (c) replacing the string with another of the same material but twice the radius. Justify your conclusions using the formula

v = \sqrt{T/\mu}

.

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hard

Explain Newton's formula for the speed of sound in a gas and describe the Laplace correction that was made to it.

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WavesClass 11 Physics Practice Questions