Chapter 14: Waves Short Questions | physics Class 11 CBSE

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Chapter 14: Waves Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Define a wave. How do waves differ from the flow of matter?

A wave is a disturbance that propagates through a medium transporting energy and information from one point to another without any net transfer or flow of matter as a whole.
In a wave, the particles of the medium oscillate about their mean positions but do not travel with the wave; for example, cork pieces on a disturbed water surface move up and down but do not drift away from the centre.
By contrast, a flow of matter (such as a stream or wind) involves actual bodily movement of the medium from one place to another; sound in air is a wave whereas wind is a flow.

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Question 2

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State the three types of waves recognised in physics and give one example of each.

Mechanical waves require a material medium for propagation and are governed by Newton's laws; example: sound waves in air or waves on a stretched string.
Electromagnetic waves do not require a medium and can travel through vacuum at speed c ≈ 3 × 10^8 m/s; example: light waves, X-rays, and radio waves.
Matter waves are associated with material particles such as electrons and protons and arise from quantum mechanical description; example: electron waves used in electron microscopes.

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Question 3

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Distinguish between transverse and longitudinal waves with one example each.

In a transverse wave, the particles of the medium oscillate perpendicular to the direction of wave propagation; example: a sinusoidal wave travelling along a stretched string where string elements move up and down while the wave moves horizontally.
In a longitudinal wave, the particles oscillate along (parallel to) the direction of wave propagation, producing alternate compressions and rarefactions; example: sound waves in air.
Transverse waves can propagate only in media that sustain shearing stress (solids), while longitudinal waves can propagate in all elastic media including fluids.

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Question 4

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Write the standard equation for a sinusoidal progressive wave moving in the positive x-direction and identify each term.

The equation is y(x, t) = a sin(kx − ωt + φ), where a is the amplitude representing the maximum displacement of medium particles from equilibrium.
k = 2π/λ is the angular wave number (propagation constant) with SI unit rad m⁻¹, and ω = 2π/T is the angular frequency with SI unit rad s⁻¹.
The quantity (kx − ωt + φ) is called the phase of the wave, and φ is the initial phase angle that depends on the choice of origin and initial time.

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Question 5

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Define wavelength and angular wave number. State the relation between them.

Wavelength (λ) is the minimum distance between two points in the medium that have exactly the same phase at a given instant; it equals the distance between two consecutive crests or troughs.
Angular wave number k (also called propagation constant) is defined as k = 2π/λ; its SI unit is radian per metre (rad m⁻¹).
Physically, k represents 2π times the number of complete waves that can be accommodated per unit length of the medium.

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Question 6

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Define period and frequency of a wave. Write the relation connecting angular frequency ω, period T, and frequency ν.

Period T is the time taken by any element of the medium to complete one full oscillation as the wave passes over it.
Frequency ν is the number of complete oscillations per second; it is the reciprocal of period: ν = 1/T, measured in hertz (Hz).
The angular frequency ω is related to T and ν by ω = 2π/T = 2πν; it has SI unit rad s⁻¹.

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Question 7

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Derive the expression for the speed of a progressive wave in terms of angular frequency and angular wave number.

To find speed, consider a fixed phase point on the wave where kx − ωt = constant; as time increases, x must also increase to keep the phase constant.
Differentiating: k Δx − ω Δt = 0, which gives dx/dt = ω/k. This is the speed at which the fixed phase point (e.g., a crest) moves, so v = ω/k.
Using ω = 2πν and k = 2π/λ, we get v = ω/k = (2πν)/(2π/λ) = λν = λ/T, which is the general relation for all progressive waves.

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Question 8

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Write the formula for speed of a transverse wave on a stretched string and explain the significance of each quantity.

The speed of a transverse wave on a stretched string is v = √(T/μ), where T is the tension in the string (in newtons) and μ is the linear mass density (mass per unit length, in kg m⁻¹).
The speed increases with tension because greater tension provides a stronger restoring force that accelerates the wave, and decreases with linear mass density because a heavier string has greater inertia.
Crucially, this speed depends only on the properties of the medium (T and μ) and is independent of the frequency or wavelength of the wave.

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Question 9

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State Newton's formula for the speed of sound in a gas and explain why it gives a value about 15% lower than the experimental value.

Newton assumed that compression and rarefaction during sound propagation are isothermal processes, giving bulk modulus B = P (gas pressure), and hence v = √(P/ρ). For air at STP this yields about 280 m/s.
The experimental value is approximately 331 m/s. Newton's formula underestimates the speed by about 15% because the assumption of isothermal process is incorrect.
Sound propagation is actually adiabatic because pressure variations occur so rapidly that there is no time for heat exchange with surroundings, so the correct bulk modulus is B = γP, not P.

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Question 10

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State the Laplace correction and write the corrected formula for speed of sound in a gas.

Laplace pointed out that sound propagation involves adiabatic (not isothermal) changes because pressure variations are too rapid for heat exchange to maintain constant temperature.
For an adiabatic process, the effective bulk modulus is Badiabatic = γP, where γ = Cp/Cv is the ratio of specific heats at constant pressure and constant volume.
The corrected (Laplace) formula for speed of sound in a gas is v = √(γP/ρ); for air γ = 7/5, and this gives v ≈ 331.3 m/s at STP, in excellent agreement with the measured value.

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Question 11

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State the principle of superposition of waves and write its mathematical expression.

The principle of superposition states that when two or more waves travel simultaneously through the same medium, the net displacement of any element is the algebraic sum of the individual displacements due to each wave acting independently.
Mathematically, if y1(x,t), y2(x,t), ..., yn(x,t) are individual wave displacements, the resultant is y(x, t) = y1(x,t) + y2(x,t) + ... + yn(x,t) = Σ fi(x − vt).
The principle implies that each wave retains its own identity (shape, frequency, speed) after overlapping with others; it is the basis for interference, standing waves, and beats.

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Question 12

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Explain constructive and destructive interference using the formula for resultant amplitude.

When two waves of equal amplitude a and frequency, differing in phase by φ, are superposed, the resultant amplitude is A(φ) = 2a cos(φ/2).
Constructive interference occurs when φ = 0 (or an integral multiple of 2π), making cos(φ/2) = 1 and the resultant amplitude maximum at 2a; the two waves reinforce each other.
Destructive interference occurs when φ = π, making cos(φ/2) = 0 and the resultant amplitude zero; the two waves completely cancel each other, giving zero displacement everywhere at all times.

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Question 13

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What happens when a wave pulse is reflected at a rigid boundary? Explain the reason for this behaviour.

At a rigid boundary, the reflected wave suffers a phase change of π (180°) compared to the incident wave; if the incident wave is yi = a sin(kx − ωt), the reflected wave is yr = −a sin(kx + ωt).
The reason is that the displacement at a rigid boundary must be zero at all times (boundary condition); this is possible only if the reflected and incident waves differ by a phase of π, so that their algebraic sum is always zero at the boundary.
Dynamically, as the pulse reaches the wall, it exerts a force on the wall; by Newton's third law, the wall exerts an equal and opposite force on the string, generating the phase-reversed reflected pulse.

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Chapter 14: Waves | Short Questions

Define a wave. How do waves differ from the flow of matter?

State the three types of waves recognised in physics and give one example of each.

Distinguish between transverse and longitudinal waves with one example each.

Write the standard equation for a sinusoidal progressive wave moving in the positive x-direction and identify each term.

Define wavelength and angular wave number. State the relation between them.

Define period and frequency of a wave. Write the relation connecting angular frequency ω, period T, and frequency ν.

Derive the expression for the speed of a progressive wave in terms of angular frequency and angular wave number.

Write the formula for speed of a transverse wave on a stretched string and explain the significance of each quantity.

State Newton's formula for the speed of sound in a gas and explain why it gives a value about 15% lower than the experimental value.

State the Laplace correction and write the corrected formula for speed of sound in a gas.

State the principle of superposition of waves and write its mathematical expression.

Explain constructive and destructive interference using the formula for resultant amplitude.

What happens when a wave pulse is reflected at a rigid boundary? Explain the reason for this behaviour.

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