The equation of a plane progressive wave is y = 0.4sin8π (t - x/20). If wave is reflected from a surface, ​

Question

The equation of a plane progressive wave is y = 0.4sin8π (t - \(\frac{x}{20}\) ). If wave is reflected from a surface, and its amplitude remains half of previous value, then determine the equation of the reflected wave if (i) it is reflected from a rigid plane, (ii) free plane.

Answer 1

Incident wave y = 0.4 sin8π(t - \(\frac{x}{20}\))

(i) From rigid surface path difference of π will be produced. Amplitude of the reflected wave
a' =\(\frac{a}{2} = \frac{0.4}{2} = 0.2\) 

∴ Equation of the reflected wave