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CGPET 2016 Solved Paper

Section: Physics

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Question : 7 of 150

Marks: +1, -0

A wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed with anotherwave to form stationary wave such that thepoint $x = 0$ is a node. The equation for theother wave is

$a \sin(kx + \omega t)$
$-a \cos (\omega l + kx)$
$-a \cos (kx - \omega t)$
$-a \sin(kx - \omega t)$

Solution:

At

x = 0

, the equation for other wave will be

-\cos (\omega t - kx)

Because the wave will propagate in the oppositedirection with phase difference of π

Negative sign will be used as the boundary is rigid.or

y = y_1 + y_2

y = a [\cos (kx - \omega t) - \cos(kx - \omega t)]

At,

x=0,\; y=0

\therefore y_2

miust be

[-a \cos(kx + \omega t)]

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