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Question

Two travelling waves y1=A sin [k(x - ct)] and y2=A sin [k(x+ct)] are superimposed on string. The distance between adjacent nodes is

A
cπ
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B
c2π
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C
π2k
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D
πk
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Solution

The correct option is D πk
Given two travelling waves y1=A sin [k(x - ct)] and y2=A sin [k(x+ct)]
Since stationary wave is formed due to interference of two identical waves, moving in opposite directions.
y1+y2=A sin [k(x - ct)]+A sin [k(x + ct)]=2A sin (kx)cos (kct)]

Wave number k=2πλ
wavelength (λ)=2πk
Distance between adjacent nodes will be,
Δx=λ2=(2πk)2
Δx=πk

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