A wave represented by the equation $y = a cos (k x - ω t)$ is superposed with another wave to form stationary wave such that the point $x = 0$ is a node. The equation for the other wave is

a sin (k x + ω t)

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- a cos (k x - ω t)

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- a cos (k x + ω t)

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- a sin (k x - ω t)

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Solution

The correct option is A $- a cos (k x + ω t)$
Let us take $y_{1} = a cos (k x - ω t)$
Let the other wave equation be $y_{2} = - a cos (k x + ω t)$
On superposition
$y = y_{1} + y_{2} = a cos (k x - ω t) - a cos (k x + ω t)$
$= a [cos k x cos ω t + sin k x sin ω t - cos k x cos ω t + sin k x sin ω t]$
$y = 2 a sin k x sin ω t$
At $x = 0$ we get $sin k x = 0$
$\Rightarrow y = 0$
$∴ x = 0$ is a node.

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Similar questions

A wave represented by the given equation y = a cos ( kx - $ω$ t ) is superposed

with another wave to form a stationary wave such that the point x = 0 is a

node. The equation for the other wave is

AIIMS 1998; SCRA 1998; MP PET 2001; KCET 2001;

AIEEE 2002; UPSEAT 2004]

y_{1} = A sin (k x - ω t)

y_{2} = A cos (k x - ω t)

Y = A c o s (k x - ω t)

y = α c o s (k x - ω t)

y = \frac{1}{\sqrt{a}} sin (k x - ω t) \pm \frac{1}{\sqrt{b}} cos (k x - ω t)

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