y = a,cos,(kx -omega t) superposes on another | vedclass

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Question

Stationary wave is formed by superposition of two identical wave travelling in opposite direction. Given, wave is $y=a \cos (k x-\omega t).$

The ot

Vedclass · Accepted Answer

$-a\,cos\,(kx + \omega t)$

Vedclass · Answer

Stationary wave is formed by superposition of two identical wave travelling in opposite direction. Given, wave is $y=a \cos (k x-\omega t).$

The other wave can't be $y=-a \cos (k x-\omega t)$ as their directions are not opposite. The other possible cosine function can be:

$y=-a \cos (k x+\omega t)$

Their directions are opposite to each other

$	herefore $ $y_{s} =a \cos (k x-\omega t)-a \cos (k x+\omega t) $

$=2 a \sin k x \sin \omega t$

At $x=0, y_{s}=0$

Hence, a nocle is formed at $\mathrm{x}=0$

$	herefore $ The equation of other wave $=-a \cos (\mathrm{kx}+\omega \mathrm{t}).$

$y = a\,cos\,(kx -\omega t)$ superposes on another wave giving a stationary wave having node at $x = 0$ . What is the equation of the other wave

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