A wave $y = a sin (w t - k x)$ on a string meets with another wave producing a node at $x = 0$ .Then the equation of the unknown wave is

y = a sin (w t + k x)

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y = a cos (k x - w t)

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y = - a cos (k x - w t)

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y = - a sin (k x + w t)

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Solution

The correct option is C $y = a cos (k x - w t)$
Equation of a wave
$y_{1} = a s i n (ω t - k x) . . . . . . (i)$
Let equation of another wave may be,
$y_{2} = a s i n (ω t + k x) . . . . . . (i i)$
$y_{3} = - a s i n (ω t + k x) . . . . . (i i i)$
If Eq(i) propagate with Eq(ii) ,we get
$y = 2 a c o s k x s i n ω t$
If Eq(i) , propagates with Eq(iii) , we get
$y = - 2 a s i n k x c o s ω t$
At x=0, y=0 , wave produce node.
So, Eq(iii) is the equation of unknown wave

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Similar questions

y = a s i n (ω t - k x)

y = a sin (ω t - k x)

x = 0

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

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

AIEEE 2002; UPSEAT 2004]

y = A s i n (k x + w t + 30^{\circ} + 180^{\circ})

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