For a wave y = 0.0002 sin `[2pi (110 t -(x)/(3))+(pi)/(3)]`
is travelling in a medium. Find energy per unit volume being transferred by wave if density of medium is `1.5 kg//m^(3)`.

Options

A. `14 xx 10^(-4)J//m^(3)`
B. `143.2 xx 10^(-4) J//m^(3)`
C. `14.3 xx 10^(-4) J//m^(3)`
D. `1.43 xx 10^(-4) J//m^(3)`

Answer

B

Explanation

We know `E_(0)=2pi^(2)rhoA^(2)v^(2)=(1)/(2)rhoA^(2)omega^(2)`
`=(1)/(2)xx15xx(0.02)^(2)(220pi)^(2)xx10^(-4)`
`E_(0)=143.2xx10^(-4)J//m^(3)`
`therefore (dy//dt)/(dy//dx)=(- omegaAcos(kx-omegat))/(kAcos(kx-omegat))`
`(dx)/(dt)=-(omega)/(k)=-v`
`therefore (dy)/(dt)=-v((dy)/(dx))`
i.e. particle velocity = - (wave speed) `xx` slope. And slope at x = 0 and t = 0 is positive in figure. Therefore, particle velocity is in negative y - directiond. Therefore, (d) is correct option.