A plane undamped harmonic wave progates in a medium. Find the mean space density of energy becomes equal to `W_(0)` at an instant `t=t(0)+T//6`, where `t_(0)` is the instant when amplitude is maximum at this location and T is the time period of oscillation.

A plane undamped harmonic wave progates in a medium. Find the mean spa

1.	A plane undamped harmonic wave progates in a medium. Find the mean space density of energy becomes equal to `W_(0)` at an instant `t=t(0)+T//6`, where `t_(0)` is the instant when amplitude is maximum at this location and T is the time period of oscillation.
Answer» Let us consider the wave `Y=A cos(omegat-kx)`, then its energy density (energy per unit volume)is given by `W=pA^(2)omega^(2) sin ^(2) (omegat-kx)` `[`where `p` is of medium, for string waves, `mu =pS]`. Let us consider `x=0`, `t_(0)=0` at which amplitude is maximum At `t=t_(0)+(T)/(6)` And `t=A cos[(omegaT)/(6)]` and the energy density is `w=pA^(2)omega^(2)sin^(2)[(omegaT)/(6)]=pA^(2)omega^(2)sin^(2)(pi)/(3)` `W=(pA^(2)omega^(2))(3)/(4)` From given data, `W=W_(0)` `impliespA^(2)omega^(2)=(4)/(3)W_(0)=(2W_(0)/(3)`

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A plane undamped harmonic wave progates in a medium. Find the mean space density of energy becomes equal to `W_(0)` at an instant `t=t(0)+T//6`, where `t_(0)` is the instant when amplitude is maximum at this location and T is the time period of oscillation.

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