Overview
Wave Motion is a compact but formula-heavy chapter in Grade XII Physics, typically worth 5–8 marks across MCQs, theory, and numericals in NEB board papers. The syllabus is built around two core ideas: the progressive (travelling) wave and the stationary wave, with everything else — mathematical forms, derivations, and calculations — flowing from how these two are defined and how one gives rise to the other.
The most consistent theory question is some version of “derive the expression for a stationary wave by superposing two identical progressive waves travelling in opposite directions,” which appears almost every year, sometimes as a full derivation and sometimes broken into “write the progressive wave equation” followed by “hence obtain the stationary wave equation.” A close second is a question asking for the condition(s) under which stationary waves are formed — students are expected to state that two waves of the same frequency, amplitude, and speed must travel in opposite directions through the same medium and superpose. Numericals mostly test whether a student can start from the general progressive wave equation y = a sin(ωt − kx) and correctly extract amplitude, frequency, time period, or velocity by comparing coefficients — these are quick marks once the standard form is memorized. A concept worth internalizing early: a stationary wave is not a “wave” in the travelling sense at all — it stores energy at fixed points (antinodes) rather than transporting it, and this distinction is exactly what most derivation and reasoning questions are built around.
Below is the full set of MCQs, theory questions, and numerical problems from past NEB board exams, organized by course and question type.
Common Mistakes Students Make
- Confusing the progressive wave equation with the stationary wave equation. Progressive wave: y = a sin(ωt − kx), which shifts in space and time. Stationary wave: y = 2a cos(kx) sin(ωt), which has fixed nodes and antinodes and doesn’t shift. Remember: Stationary = Split into two separate factors (a space part and a time part).
- Forgetting the exact condition for stationary wave formation. Two waves must be identical in frequency, amplitude, and speed, and must travel in opposite directions in the same medium — leaving out any one of these conditions costs marks in theory answers.
- Misreading ω and k from the equation when calculating frequency, velocity, or time period. A sign error or mixing up ω (angular frequency) with k (wave number) is the most common way students get the numerical right in method but wrong in the final answer.
MCQs
What is the distance between node and antinode in a stationary wave in terms of wavelength?
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Which of the following is a mechanical wave?
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Which of the following is an example of transverse wave?
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When sound travels from air to water, which remains constant?
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What is the distance between two consecutive particles in a wave which are in the same phase?
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Distance between two consecutive nodes in a standing wave is
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The frequency of tuning fork is 384 Hz and velocity of sound in air is 352 m/s. How far the sound has traverse while fork complete 36 vibrations?
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When sound wave is refracted from air to water, which of the following will remain unchanged?
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The distance between any two consecutive antinodes in a stationary wave is
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Theoretical questions
Differentiate between progressive and stationary waves. [2]
What are stationary waves? Prove that the distance between two consecutive nodes in it is equal to half of the wavelength. [3]
A plane progressive wave equation is given by [latex]y = 0.2sin(512\pi t – \frac{25}{8}\pi x)[/latex] where y is in centimeters, x in meters and t in seconds. What is the speed of the wave?
How do transverse waves differ from longitudinal waves?
Can longitudinal wave be polarized? Explain.
How are stationary waves formed?
Distinguish between progressive waves and stationary waves.
We can’t hear echo in a small room. Why?
Frequency is the most fundamental property of a wave. Why?
If you are walking on the moon surface, can you hear the cracking sound behind you? Explain.
Distinguish between progressive waves and standing waves?
How is a progressive wave different from a stationary wave? Derive an equation for a progressive wave.
OR Define progressive waves. Derive an equation to represent this wave.
What is a wave motion? Derive progressive wave equation in a medium.
Numerical problems
A transverse wave equation is given by y = 0.02 Sin(30t – 4x), where x and y are in meter and t is in sec. Calculate the speed of the wave. [2] Ans: [latex]7.5\ ms^{-1}[/latex]
A wave has the equation (x in metres and t in seconds) Y = 0.02sin(30t – 4x). Find
i. Its frequency, speed and wave length.
ii. The equation of wave with double amplitude but travelling in the opposite direction. Ans: 4.77 Hz, 1.57 m, 7.5 ms-1, y = 0.04sin(30t + 4x)
A sound wave of frequency 400 Hz is travelling in air at a speed of 320 ms-1. Calculate the difference in phase between two points on the wave 0.2 m apart in the direction of travel. Ans:1.57 radian
The equation of motion of a wave is y = 1.2sin(3.5t – 0.5x), where distance and time are expressed in meter and second respectively. Determine the amplitude, frequency, wavelength and velocity of the wave. Also, find the maximum speed of particles in that medium and the equation of a wave with double amplitude and frequency but travelling exactly in the opposite direction of the given wave. Ans: 1.2m, 0.56 Hz, 12.57 m, 7.04 ms-1, 4.2 ms-1, 2.4sin(7.04t+0.5x)