Please Prove the fact that intensity is directly proportional to amplitude of the wave...

- Intensity is the power transferred per unit area, where the area is an imagined surface that is perpendicular to the direction of propagation of the energy The energy of a wave  depends on its amplitude and frequency. 

 

- Considering a mechanical wave,

a particle on a wave oscillates with simple harmonic motion,

its maximum velocity is given by 

 

v=2π×frequency×amplitude

 

- The intensity of a wave is defined as the amount of energy that passes

though unit area perpendicular to the wave direction in unit time.

 

- If the amplitude is doubled the maximum velocity is doubled.

- The kinetic energy = ×mass×velocity²

- Thus on doubling the velocity you quadruple the kinetic energy,

that further quadrupling the intensity of the wave.