Question 386: Waves

Question

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 $$t$$ in second, then the length of the string is

Accepted Answer

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

Answer

5 m

Answer

10 m

Answer

15 m

Answer

20 m

Waves

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

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