A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x -direction in 0.3 sec. The…

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 ?
  1. $y=2 \cos (0.83 x-3.35 t) \mathrm{cm}$
  2. $y=2 \sin (0.83 x-3.5 t) \mathrm{cm}$
  3. $y=2 \cos (3.35 x-0.83 t) \mathrm{cm}$
  4. $y=2 \cos (0.13 x-0.5 t) \mathrm{cm}$

Solution

$\begin{aligned}
& \mathrm{v}=\frac{\text { distance }}{\text { time }} \\ & \mathrm{v}=\frac{12}{0.3}=4 \mathrm{~cm} / \mathrm{s} \\ & \mathrm{k}=\frac{2 \pi}{\lambda}=\frac{2 \pi}{7.5}=\frac{4 \pi}{15}=0.83 \\ & \mathrm{v}=\frac{\omega}{\mathrm{k}} \Rightarrow \omega=\mathrm{vk}=4 \times \frac{4 \pi}{15}=3.35
\end{aligned}$
So $y=A \cos (k x-\omega t)$

Asked in: JEE Main 2025 (02 Apr Shift 2)

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