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A wave y = a sin ( $ω$ t–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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$\large y\, = \, - a\cos \left( {kx - wt} \right)$

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

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

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

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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