A transverse wave $\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$ moves on a stretched string from one…

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. $5 \mathrm{~m}$
  2. $10 \mathrm{~m}$
  3. $15 \mathrm{~m}$
  4. $20 \mathrm{~m}$

Solution

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

Asked in: MHT CET 2023 (11 May Shift 1)

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