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Two transverse waves A and B superimpose...

Two transverse waves A and B superimposed to produce a node at x = 0. If the equation of wave A si `y= a cos (kx-omegat)`, then the equation of wave B is

A

`y=asin(omegat+kx)`

B

`y=asin(omega-kx)`

C

`y-asin(omegat+kx)`

D

`y=-asin(omegat-kx)`

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of a wave is
`Y = a sin (omega t-kx)` …(i)
Let the eqyations of another wave be
Either `Y = a sin (omega t-kx)` …(ii)
or , `Y = - a sin (omega t-kx)` …(iii)
If (i) superposes on with (ii), then we get :
`Y = 2a coskx sin omega t` ...(iv)
If (i) superposes on with (iii) , then we get : `Y = -2a sin kx cos omega t` ..(v)
After putting x = 0 in (iv) and (v) , respectively , we get :
y=0 at x=0 For equation (v)
Hence , (iii) is an equation of the unknown wave .
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