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Progressive Waves and the Displacement Relation for JEE: 25 solved questions

Real JEE paper questions on progressive waves and the displacement relation, part of waves. Each opens with the options, the correct answer and a step-by-step solution. Papers run from 2003 to 2026. No sign-in needed to read them.

What this topic asks

• Wave parameters from the equation — 14 questions
• Identifying a travelling wave — 9 questions
• Particle velocity and wave velocity — 2 questions

All 25 questions with solutions

• The equation of a plane progressive wave is y=5 cos π(200t-x/(150)), where x and y are in cm and t in seconds… JEE Main 2nd April 1st Shift 2026
• A sinusoidal wave of wavelength 7.5 cm travels 1.2 cm along the x-direction in 0.3 s. A crest P is at x=0 whe… JEE Main 2nd April 2nd Shift 2025
• The displacement of a wave is x(t)=5 cos (628t+π/2) m. If the wave velocity is 300 m s⁻¹, its wavelength is (… JEE Main 4th April 2nd Shift 2025
• The equation of a wave on a string is y=sin(20π x+10π t), with x and t in SI units. The minimum distance betw… JEE Main 7th April 2nd Shift 2025
• The equation of a transverse wave on a string is y(x,t)=4.0 sin [20×10⁻³x+600t] mm, where x is in mm and t in… JEE Main 23rd Jan 2nd Shift 2025
• A plane progressive wave is given by y=2 cos 2π(330t-x) m. The frequency of the wave is JEE Main 8th April 2nd Shift 2024
• A travelling wave is described by y(x,t)=0.05 sin(8x-4t) m, with all quantities in SI units. The velocity of… JEE Main 24th Jan 1st Shift 2023
• A transverse wave is represented by y=2 sin(ω t-kx) cm. The wavelength, in cm, for which the wave velocity eq… JEE Main 26th July 2nd Shift 2022
• In the wave equation y=0.5 sin (2π)/λ(400t-x) m, the velocity of the wave is JEE Main 28th July 1st Shift 2022
• A longitudinal wave is represented by x=10 sin 2π(nt-x/λ) cm. The maximum particle velocity is four times the… JEE Main 29th June 1st Shift 2022
• Which equation correctly represents a travelling wave of wavelength λ=4.0 cm and frequency u=100 Hz moving al… JEE Main 30th June 1st Shift 2022
• A sound wave of frequency 245 Hz travels at 300 m s⁻¹ along the positive x-axis, and each point of the medium… JEE Main 17th March 2nd Shift 2021
• Which of the following equations represents a travelling wave? JEE Main 24th Feb 2nd Shift 2021
• For a transverse wave travelling along a straight line, the distance between two crests is 5 m and the distan… JEE Main 4th Sept 1st Shift 2020
• [Figure: a snapshot at t=0 of a wave on the x-axis: the curve leaves the origin going downward, reaches a tro… JEE Main 12th April 1st Shift 2019
• A travelling harmonic wave is y(x,t)=10⁻³ sin(50t+2x), with x and y in metres and t in seconds. Which stateme… JEE Main 12th Jan 1st Shift 2019
• The disturbance of a wave moving in the positive x-direction is y=1/(1+x²) at t=0 and y=1/(1+(x-1)²) at t=2 s… JEE Main (year not legible in the scan)
• The transverse displacement of a wave on a string is y(x,t)=e^-(ax²+bt²+2√ab xt). This represents JEE Main 2011
• A wave travelling along the x-axis is y(x,t)=0.005 cos(α x-β t). If the wavelength is 0.08 m and the time per… JEE Main 2008
• The displacement of a particle in a medium is y=10⁻⁶ sin (100t+20x+π/4) m, with t in seconds and x in metres.… JEE Main 2004
• The displacement of a wave travelling in the x-direction is y=10⁻⁴ sin (600t-2x+π/3) m, with x in metres and… JEE Main 2003
• A transverse wave on a string is y=3 sin (36t+0.018x+π/4), where x and y are in cm and t in seconds. The leas… JEE Main 5th April 1st Shift 2026
• A transverse harmonic wave on a string is y(x,t)=5 sin(6t+0.003x), where x and y are in cm and t in seconds.… JEE Main 10th April 1st Shift 2023
• The equation of a wave is y=10⁻² sin 2π(160t-0.5x+π/4), where x and y are in metres and t in seconds. The spe… JEE Main 11th April 1st Shift 2023
• The disturbance of a wave propagating in the positive x-direction is y=1/((1+x)²) at t=0 and y=1/(1+(x-2)²) a… JEE Main 20th July 1st Shift 2021