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Equation of a plane progressive wave is ...

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

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
Amlitude of reflected wave
`" " A_(r)=(2)/(3)xxA=(2)/(3)xx0.6=0.4` units
Given equation of incident wave
`" " y_(i)=0.6sin2pi(t-(x)/(2))`
Equation of reflected waves is
`" " y_(r)=A_(r)sin2pi(t+(x)/(2)+pi) " " [ :. "At denser medium, phase changes by"pi]`
The positive sing in due to reversal of directio of propagation
So, `" " y_(r)=-0.4 sin 2 pi (t+(x)/(2))" " [:. sin (pi+theta)=-sin theta`]
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