Question

Equation of a plane progressive wave is given by  y = 0.6 sin2π `(t - x/2)`. On reflection from denser medium its amplitude become `2/3` of the amplitude of the incident wave. The equation of the reflected wave is

विकल्प

• y = `0.6 sin 2pi (t + x/2)`

• y = `- 0.4 sin 2pi(t + x/2)`

• y = `0.4 sin 2pi (t + x/2)`

• y = `- 0.4 sin 2pi(t - x/2)`

Answer 1

y = `- 0.4 sin 2pi(t + x/2)`

Explanation:

There is a 180° phase reversal on reflection from denser medium.

Now consider new amplitude = `2/3 xx 0.6` = 0.4

Following reflection, the wave will proceed in the negative x-direction.

∴ Reflected wave equation is y = `0.4 sin 2pi [t + x/2 + pi]`

= `- 0.4 sin 2pi(t + x/2)`  .....[∵ sin (π + θ) = – sin θ]