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A travelling wave y=A sin(ω t-kx) is superposed on y=A sin(ω t+kx). The resultant is
Asked in JEE Main Re-Scheduled 2011 · Nodes, antinodes and harmonics
- (1) a wave travelling along the +x direction
- (2) a wave travelling along the -x direction
- (3) a standing wave with nodes at x=(nλ)/2, n=0,1,2,…
- (4) a standing wave with nodes at x=(n+1/2)λ/2, n=0,1,2,…
Answer: (4) a standing wave with nodes at x=(n+1/2)λ/2, n=0,1,2,…
Step-by-step solution
Adding gives y=2A sin ω t cos kx, a standing wave.
Nodes are where cos kx=0, i.e. kx=(n+1/2)π.
With k=(2π)/λ this is x=(n+1/2)λ/2.
Why the other options are wrong
- (1) Two equal waves in opposite directions cannot give a travelling wave.
- (2) The same objection applies.
- (3) These are the positions of the antinodes for this pair, not the nodes.
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