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For a travelling haromonic wave , y=2.0c...

For a travelling haromonic wave , `y=2.0cos(10t-0.0080x+0.818)` where x and y are in cm and t is in sec. What is the phase difference between two points separated by (i) a distance of 0.5m (ii) time gap of 0.5s.

Text Solution

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Compare the given eqn. with standard form `y=rcos(omegat-kx+phi_(0))`
We find, `r=2.0cm, omega=10rad//s`,
`k=0.0080cm^(-1), phi_(0)=0.18rad. `
(i) When `Deltax=0.5m=50cm,`
`Deltaphi=-(2pi)/(lambda)Deltax=-kDeltax=0.0080xx50`
`=-0.4rad`
(ii) When `Deltat=0.5s,`
`Deltaphi=(2pi)/(T)Deltat=omega.Deltat=10xx0.5=5rad`
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