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MHT CET · Physics · Waves and Sound

A transverse wave \(\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})\) moves on a stretched string from one end to another end in 0.5 second. If \(x\) and \(y\) are in \(\mathrm{cm}\) and \(\mathrm{t}\) in second, then the length of the string is

  1. A \(5 \mathrm{~m}\)
  2. B \(10 \mathrm{~m}\)
  3. C \(15 \mathrm{~m}\)
  4. D \(20 \mathrm{~m}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(15 \mathrm{~m}\)

Step-by-step Solution

Detailed explanation

Given \(Y=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})\)
Comparing with standard equation,
\(
\begin{aligned}
\mathrm{Y} & =\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t}), \\
\therefore \quad \mathrm{k} & =0.01 / \mathrm{cm} \\
\omega & =30 \mathrm{rad} / \mathrm{s}
\end{aligned}
\)
\(
\begin{aligned}
\text { Velocity } \mathrm{v} & =\frac{\omega}{\mathrm{k}}=\frac{30}{0.01}=3000 \mathrm{~cm} / \mathrm{s} \\
\therefore \quad \text { Length } \mathrm{L} & =\mathrm{v} \times \mathrm{t}=30 \times 0.5 \\
& =15 \mathrm{~m}
\end{aligned}
\)