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

Options

A. `y=0.6sin2pi(t+(x)/(2))`
B. `y=-0.4sin2pi(t+(x)/(2))`
C. `y=0.4sin2pi(t+(x)/(2))`
D. `y=-0.4sin2pi(t-(x)/(2))`

Answer

B

Explanation

Amplitude of reflected wave
`A_(r)=(2)/(3)xxA_(i)=(2)/(3)xx0.6=0.4` units
Given equation of incident wave
`y_(i)=0.6sin2pi(t-(x)/(2))`
Reflection from a denser medium results to phase change of `pi` and change in sign.
`therefore` Equation of reflected wave is
`y_(r)=A_(r)sin2pi(t+(x)/(2)+pi)`
So, `y_(r)=-0.4sin2pi(t+(x)/(2))[becausesin(pi+theta)=-sintheta]`