Chapter 14: Waves Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 1

Logic Check

Assertion (A): Waves transport energy from one point to another without any net transfer of matter. Reason (R): In a wave, the particles of the medium oscillate about their equilibrium positions and do not travel with the wave.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 2

Logic Check

Assertion (A): Transverse waves cannot propagate through gases. Reason (R): Gases do not possess a shear modulus of elasticity and therefore cannot sustain shearing stress.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 3

Logic Check

Assertion (A): The speed of a transverse wave on a stretched string increases when the tension is increased. Reason (R): The speed of transverse waves on a string is given by v = √(T/μ), which shows speed is directly proportional to √T.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 4

Logic Check

Assertion (A): The speed of sound in air is independent of the atmospheric pressure at constant temperature. Reason (R): For an ideal gas at constant temperature, pressure is inversely proportional to volume, so P/ρ remains constant, making v = √(γP/ρ) independent of P.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 5

Logic Check

Assertion (A): Newton's formula for the speed of sound gives a value about 15% lower than the experimental value. Reason (R): Newton assumed sound propagation to be an adiabatic process, but it is actually isothermal.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 6

Logic Check

Assertion (A): The speed of sound is greater in solids than in gases. Reason (R): Solids have a much higher bulk modulus than gases, and the increase in bulk modulus far outweighs the increase in density.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 7

Logic Check

Assertion (A): When two waves of equal and opposite displacements completely overlap, the string is momentarily flat with zero displacement. Reason (R): At the instant the string is flat, all the energy has been destroyed.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 8

Logic Check

Assertion (A): At a rigid boundary, a reflected wave has a phase change of π. Reason (R): The displacement at a rigid boundary must be zero at all times, which is satisfied only if the incident and reflected waves differ by a phase of π.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 9

Logic Check

Assertion (A): In a standing wave, the amplitude of oscillation is the same at all points of the string. Reason (R): In a standing wave, all particles oscillate with the same angular frequency ω.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 10

Logic Check

Assertion (A): The distance between two consecutive nodes in a standing wave is λ/2. Reason (R): Nodes are positions where sin(kx) = 0, which occur at x = nλ/2, so consecutive nodes are separated by λ/2.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 11

Logic Check

Assertion (A): A pipe closed at one end and open at the other produces only odd harmonics. Reason (R): The boundary conditions (node at closed end, antinode at open end) allow only wavelengths λ = 4L/(2n+1), corresponding to odd multiples of the fundamental frequency.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 12

Logic Check

Assertion (A): The beat frequency heard when two tuning forks of 512 Hz and 516 Hz are sounded together is 4 Hz. Reason (R): Beat frequency equals the average of the two frequencies.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 13

Logic Check

Assertion (A): The speed of a mechanical wave is determined by the medium, not by the source of the wave. Reason (R): The frequency of the wave is determined by the medium, while the speed is determined by the source.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 14

Logic Check

Assertion (A): The function y = 2 cos(3x) sin(10t) represents a standing wave. Reason (R): In this function, x and t appear in separate factors rather than in the combined form (kx ± ωt), so the wave pattern does not travel.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 15

Logic Check

Assertion (A): In a harmonic progressive wave, all particles of the medium have the same amplitude. Reason (R): In a progressive wave, all particles execute simple harmonic motion with the same amplitude a as given by the wave equation y = a sin(kx − ωt).

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 16

Logic Check

Assertion (A): Sound travels faster in warm air than in cold air. Reason (R): The speed of sound in a gas is directly proportional to the square root of its absolute temperature.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 17

Logic Check

Assertion (A): A standing wave does not transfer energy along the string. Reason (R): In a standing wave, energy oscillates between kinetic and potential forms at fixed locations but there is no net energy flow in any direction.

Reasoning Options

ByteNotes

Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 18

Logic Check

Assertion (A): At an open end of an organ pipe, there is a pressure node and a displacement antinode. Reason (R): At the open end, air is free to move (maximum displacement possible) and the pressure equals atmospheric pressure (no pressure variation).

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 19

Logic Check

Assertion (A): The fundamental frequency of a pipe open at both ends is double that of a pipe closed at one end, for the same pipe length. Reason (R): For an open pipe, the fundamental wavelength is 2L; for a closed pipe, it is 4L. Since v = νλ, the frequencies are v/2L and v/4L respectively.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 20

Logic Check

Assertion (A): Increasing the humidity of air increases the speed of sound. Reason (R): Water vapour has a smaller molar mass than dry air; humid air has a lower average molar mass, and since v = √(γRT/M), speed increases when M decreases.

Reasoning Options

ByteNotes

Chapter sections

Chapter 14: Waves | Assertion-Reason

Assertion (A): Waves transport energy from one point to another without any net transfer of matter. Reason (R): In a wave, the particles of the medium oscillate about their equilibrium positions and do not travel with the wave.

Assertion (A): Transverse waves cannot propagate through gases. Reason (R): Gases do not possess a shear modulus of elasticity and therefore cannot sustain shearing stress.

Assertion (A): The speed of a transverse wave on a stretched string increases when the tension is increased. Reason (R): The speed of transverse waves on a string is given by v = √(T/μ), which shows speed is directly proportional to √T.

Assertion (A): The speed of sound in air is independent of the atmospheric pressure at constant temperature. Reason (R): For an ideal gas at constant temperature, pressure is inversely proportional to volume, so P/ρ remains constant, making v = √(γP/ρ) independent of P.

Assertion (A): Newton's formula for the speed of sound gives a value about 15% lower than the experimental value. Reason (R): Newton assumed sound propagation to be an adiabatic process, but it is actually isothermal.

Assertion (A): The speed of sound is greater in solids than in gases. Reason (R): Solids have a much higher bulk modulus than gases, and the increase in bulk modulus far outweighs the increase in density.

Assertion (A): When two waves of equal and opposite displacements completely overlap, the string is momentarily flat with zero displacement. Reason (R): At the instant the string is flat, all the energy has been destroyed.

Assertion (A): At a rigid boundary, a reflected wave has a phase change of π. Reason (R): The displacement at a rigid boundary must be zero at all times, which is satisfied only if the incident and reflected waves differ by a phase of π.

Assertion (A): In a standing wave, the amplitude of oscillation is the same at all points of the string. Reason (R): In a standing wave, all particles oscillate with the same angular frequency ω.

Assertion (A): The distance between two consecutive nodes in a standing wave is λ/2. Reason (R): Nodes are positions where sin(kx) = 0, which occur at x = nλ/2, so consecutive nodes are separated by λ/2.

Assertion (A): A pipe closed at one end and open at the other produces only odd harmonics. Reason (R): The boundary conditions (node at closed end, antinode at open end) allow only wavelengths λ = 4L/(2n+1), corresponding to odd multiples of the fundamental frequency.

Assertion (A): The beat frequency heard when two tuning forks of 512 Hz and 516 Hz are sounded together is 4 Hz. Reason (R): Beat frequency equals the average of the two frequencies.

Assertion (A): The speed of a mechanical wave is determined by the medium, not by the source of the wave. Reason (R): The frequency of the wave is determined by the medium, while the speed is determined by the source.

Assertion (A): The function y = 2 cos(3x) sin(10t) represents a standing wave. Reason (R): In this function, x and t appear in separate factors rather than in the combined form (kx ± ωt), so the wave pattern does not travel.

Assertion (A): In a harmonic progressive wave, all particles of the medium have the same amplitude. Reason (R): In a progressive wave, all particles execute simple harmonic motion with the same amplitude a as given by the wave equation y = a sin(kx − ωt).

Assertion (A): Sound travels faster in warm air than in cold air. Reason (R): The speed of sound in a gas is directly proportional to the square root of its absolute temperature.

Assertion (A): A standing wave does not transfer energy along the string. Reason (R): In a standing wave, energy oscillates between kinetic and potential forms at fixed locations but there is no net energy flow in any direction.

Assertion (A): At an open end of an organ pipe, there is a pressure node and a displacement antinode. Reason (R): At the open end, air is free to move (maximum displacement possible) and the pressure equals atmospheric pressure (no pressure variation).

Assertion (A): The fundamental frequency of a pipe open at both ends is double that of a pipe closed at one end, for the same pipe length. Reason (R): For an open pipe, the fundamental wavelength is 2L; for a closed pipe, it is 4L. Since v = νλ, the frequencies are v/2L and v/4L respectively.

Assertion (A): Increasing the humidity of air increases the speed of sound. Reason (R): Water vapour has a smaller molar mass than dry air; humid air has a lower average molar mass, and since v = √(γRT/M), speed increases when M decreases.

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