JEE Mains · Physics · STD 11 - 14. waves and sound
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 ?
- 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 \(y=2 \cos (0.13 x-0.5 t) \mathrm{cm}\)
Answer & Solution
Correct Answer
(A) \(y=2 \cos (0.83 x-3.35 t) \mathrm{cm}\)
Step-by-step Solution
Detailed explanation
\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…
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