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Q.

A wave y = a sin (ωt–kx) on a string meets another  wave propagating along negative x-axis, producing  a  node at x = 0. The equation of the unknown wave is

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a

\large y\, = \, - a\cos \left( {kx - wt} \right)

b

\large y\, = \,a\cos \left( {kx - wt} \right)

c

\large y\, = \, - a\sin \left( {kx + wt} \right)

d

\large y\, = \,a\sin \left( {wt + kx} \right)

answer is D.

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Detailed Solution

y = y1+y2

Here, \large {y_1}\, = \,a\sin \left( {\omega t - kx} \right)

At x = 0, y is zero for all values of t.

\large \therefore   Since the other wave is moving along negative x-axis.

\large {y_2}\, = \, - a\sin \left( {\omega t + kx} \right)\,\,

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