Question

For a wave, y = 0.0002 sin`[2pi(110"t"-x/3)+pi/3]` is travelling in a medium. The energy per unit volume being transferred by wave if density of medium is 1.5 kg/m³, is ______.

Options

• 14 × 10^-4 J m^-3

• 143.2 × 10^-4 J m^-3

• 14.3 × 10^-4 J m^-3

• 1.43 × 10^-4 J m^-3

Answer 1

For a wave, y = 0.0002 sin`[2pi(110"t"-x/3)+pi/3]` is travelling in a medium. The energy per unit volume being transferred by wave if density of medium is 1.5 kg/m³, is 143.2 × 10^-4 J m^-3.

Explanation:

Y = 0.0002sin `[2pi(110"t"-x/3)+pi/3]`         ...(i)

ρ = 1.5 kg/m³

The general form of wave is given by 

Y =  A sin (ωt ± kx ± Φ_o)                         ...(ii)

By comparing eqn. (i) and (ii), we get

A = 0.0002 m

A = 2 × 10^-4 m

ω = 220 π

The energy per unit volume being transferred by wave is 

E_o = `1/2rho"A"^2omega^2`

E_o = `1/2xx1.5xx(2xx10^-4)^2xx(220pi)^2`

E_o = `1/2xx1.5xx4xx10^-8xx48.400xx9.8596`

E_o = 1.433 × 10^-2 J m^-3

E_o = 143.2 × 10^-4 J m^-3