A wave represented by the equation $Y = A c o s (k x - ω t)$ is superimposed with another wave to form a stations wave such that the point x=0 is a node. The equation of the other wave is

- A s i n (k x + ω t)

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- A c o s (k x + ω t)

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A s i n (k x + ω t)

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A c o s (k x + ω t)

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Solution

The correct option is C $- A c o s (k x + ω t)$
Given wave is : $A c o s (k x - ω t) = A [c o s k x c o s ω t + s i n k x s i n ω t]$
Since we need node at $x = 0$ , we need to cancel $c o s k x$ term in the sum of given wave and superimposed wave
Hence superimposed wave is of the form

$(- A c o s k x c o s ω ω t + A s i n k x s i n ω t) = - A [c o s k x c o s ω t - s i n k x s i n ω t] = - A c o s (k x + ω t)$

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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 = a cos (k x - ω t)

y_{1} = A sin (k x - ω t)

y_{2} = A cos (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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