A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x -direction in 0.3 sec . The crest P is at x=0 at t=0 sec and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

Physics · Transverse waves

JEE Main 2025 — 2 April, Evening Shift — Question 60

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$ -direction in 0.3 sec . The crest $P$ is at $x=0$ at $t=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

Option A:
$y=2 \cos (3.35 x-0.83 t) \mathrm{cm}$
Option B:
$y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$
Correct
Option C:
$y=2 \sin (0.83 x-3.5 t) \mathrm{cm}$
Option D:
$y=2 \cos (0.13 x-0.5 t) \mathrm{cm}$

Answer: B

Step-by-step solution

$\lambda=7.5 \mathrm{~cm}$ $\lambda=\frac{2 \pi}{K}$

$K=\frac{2 \pi}{7.5}=0.83 \mathrm{~cm}^{-1}$

$v=\frac{1.2}{0.3}=\frac{\omega}{K}$

$\omega=4 \times 0.83=3.35$

At $t=0, x=0$ ,

there is a crest $\therefore \quad y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 2 April, Evening Shift
Subject: Physics
Chapter: Transverse waves
Topic: Introduction, wave parameters and wave Equation