Two travelling waves produces a standing wave represented by equa… - Vidyadip

MCQ

Two travelling waves produces a standing wave represented by equation,

${y}=1.0\, {mm} \cos \left(1.57 \,{cm}^{-1}\right) {x} \sin \left(78.5\, {s}^{-1}\right) {t}$

The node closest to the origin in the region ${x}>0$ will be at ${x}=\ldots \ldots \ldots\, {cm}$

A
$3$
✓
$1$
C
$5$
D
$7$

✓

Answer

Correct option: B.

$1$

b
For node

$\cos \left(1.57 {cm}^{-1}\right) {x}=0$

$\left(1.57 {cm}^{-1}\right) {x}=\frac{\pi}{2}$

${x}=\frac{\pi}{2(1.57)} {cm}=1\, {cm}$

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