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

Correct answer: A. y=2 (0.83 x-3.35 t) cm aligned & v= distance time & v=(12)/(0.3)=4 cm / s & k=(2 π)/(λ)=(2 π)/(7.5)=(4 π)/(15)=0.83 & v= ω k ω=vk=4 × (4 π)/(15)=3.35 aligned So y=A (k x-ω t)

JEE Main 20252 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 2 April
Shift: Evening Shift
Subject: Physics
Chapter: Waves and Sound

JEE Main 2025 · 2 April · Evening Shift · Physics · Waves and Sound

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm...

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

t=0 \mathrm{sec}

and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave ?

Options

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

Correct answer

A. $y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$

Step-by-step solution

\begin{aligned}& \mathrm{v}=\frac{\text{ distance }}{\text{ time }} \\ & \mathrm{v}=\frac{12}{0.3}=4 \mathrm{ cm} / \mathrm{s} \\ & \mathrm{k}=\frac{2 \pi}{\lambda}=\frac{2 \pi}{7.5}=\frac{4 \pi}{15}=0.83 \\ & \mathrm{v}=\frac{\omega}{\mathrm{k}} \Rightarrow \omega=\mathrm{vk}=4 \times \frac{4 \pi}{15}=3.35\end{aligned}

y=A \cos (k x-\omega t)

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