Two travelling waves produces a standing wave represented by equation. y = (1 . 0mm) [(1 . 57 cm ^ - 1 )x] [(78 . 5 s ^ - 1 )t] . The node closest to the origin in the region x > 0 will be at x = . . . . . . (incm) .

Correct answer: 1 At Node, y = 0 ⇒ (1.57x) (78.5t) = 0 ⇒ ( 1.57x ) = 0 ⇒ 1.57x = (π)/(2) ⇒ x = 1cm

JEE Main 202126 AugustMorning Shift

JEE Main 2021 · 26 August · Morning Shift · Physics · Waves and Sound

Two travelling waves produces a standing wave represented by...

Two travelling waves produces a standing wave represented by equation.

y = \left(1 . 0mm\right)\cos \left[\left(1 . 57{cm}^{- 1}\right)x\right]\sin \left[\left(78 . 5{s}^{- 1}\right)t\right]

. The node closest to the origin in the region

x > 0

will be at

x = . . . . . . \left(\text{in}cm\right) .

At Node,
$y = 0$

$⇒ \cos \left(1.57x\right)\sin \left(78.5t\right) = 0$

$⇒ \cos ( 1.57x ) = 0$

$⇒ 1.57x = \dfrac{\pi}{2}$

$⇒ x = 1cm$