Question 263: Waves

Question

The equation of wave is $y=60 \sin (1200 t-6 x)$, where ' $y$ ' is in micron, ' $t$ ' is in second and ' $x$ ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

Accepted Answer

$$ y=60 \sin (1200 t-6 x) \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...(i)$$
For particle velocity $\mathrm{v}_{\mathrm{p}}$,
$$ \begin{aligned} & \frac{d y}{d t}=60 	imes 1200 \cos (1200 t-6 x) \ & \left(v_pight)_{\max }=72000 \mu \mathrm{~m} / \mathrm{s} \end{aligned} $$
Comparing (i) with standard equation of progressive wave, the constant
$$ \mathrm{k}=\frac{2 \pi}{\lambda}=6 \Rightarrow \lambda=\frac{\pi}{3} $$
Comparing (i) with standard equation of progressive wave,
$$ 2 \pi n=1200 \Rightarrow n=\frac{600}{\pi} $$
We know, Wave velocity $\mathrm{v}=\mathrm{n} \lambda$
Substituting the values, we get:
$$ \begin{array}{ll}  & v=\frac{600}{\pi} 	imes \frac{\pi}{3}=200 \mathrm{~m} / \mathrm{s} \ 	herefore & \frac{\left(v_pight)_{\max }}{v}=\frac{72000 \mu \mathrm{~m}}{200}=\frac{72000 	imes 10^{-6}}{200}=3.6 	imes 10^{-4} \end{array} $$

Answer

36

Answer

$3.6 	imes 10^{-5}$

Answer

$3.6 	imes 10^{-4}$

Answer

$3.6 	imes 10^{-6}$

Waves

The equation of wave is y=60 \sin (1200 t-6 x), where ' y ' is in micron, ' t ' is in second and ' x ' is in metre. The ratio of maximum particle velocity to the wave velocity of wave propagation is

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