A standing wave is formed by the superposition of two waves trave… - Vidyadip

MCQ

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by $y\left( {x,t} \right) = 0.5\sin\, \left( {\frac{{5\pi }}{4}x} \right)\,\cos\, \left( {200\,\pi t} \right)$. What is the speed of the travelling wave moving in the positive $x$ direction .... $m/s$ ? ($x$ and $t$ are in meter and second, respectively.)

✓
$160$
B
$90$
C
$180$
D
$120$

✓

Answer

Correct option: A.

$160$

a
Given, $y(x, t)=0.5 \sin \left(\frac{5 \pi}{4}x\right) \cos (200 \pi t)$

comparing with equation $-y(x, t)=2 a sin\mathrm{kx} \cos \omega \mathrm{t}$

$\omega=200 \pi, k=\frac{5 \pi}{4}$

speed of travelling wave

$v=\frac{\omega}{k}=\frac{200 \pi}{5 \pi / 4}=160 \mathrm{m} / \mathrm{s}$

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