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A standing wave pattern is formed on a s...

A standing wave pattern is formed on a string One of the waves if given by equation `y_1=acos(omegat-kx+(pi)/(3))` then the equation of the other wave such that at `x=0` a node is formed.

A

`y_(2)=a sin(omega t+kx+(pi)/(3))`

B

`y_(2)=a cos(omega t+kx+(pi)/(3))`

C

`y_(2)=a cos(omega t+kx+(3pi)/(3))`

D

`y_(2)=a cos (omega t+kx+(4pi)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
D
A standing …………
At `x = 0` the phase difference should be `pi` .
`:.` the correct option is D.
Altermate solution
`y_(2)=a cos (omega t+ kx + phi 0)`
`:. y = y_(1)+y_(2) = a cos (omega t - kx + (pi)/(3))+a cos (omega t+kx+ phi_(0))`
`= 2a cos [omega t+((pi)/(3)+varphi_(0))/(2)]xxcos [kx +(varphi_(0)-(pi)/(3))/(2)]`
`:. y = 0 at x = 0` for ant `t`
`implies kx +(varphi_(0)-(pi)/(3))/(2) = (pi)/(2) at x = 0`
`:. phi_(0) = (4pi)/(3)`. Hence `y_(2) = a cos (omega t + kx +(4pi)/(3))`
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