Question

Equation of a plane progressive wave is given by `"y" = 0.6  "sin"2pi ("t" - "x"/2)`. On reflection from 48. denser medium its amplitude become `2/3` of the amplitude of the incident wave. The equation of the reflected wave is ____________.

Options

• `"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

Equation of a plane progressive wave is given by `"y" = 0.6  "sin"2pi ("t" - "x"/2)`. On reflection from 48. denser medium its amplitude become `2/3` of the amplitude of the incident wave. The equation of the reflected wave is `"y" =-0.4  "sin"2pi ("t" + "x"/2)`.

Explanation:

On reflection from denser medium, there is a phase reversal of 180°

`"Now, new amplitude" = 2/3 xx 0.06 = 0.4`

After reflection, wave will travel along negative x - direction

`therefore "Equation of reflected wave is"`

`  "y" = 0.4  "sin" 2pi ["t" + "x"/2 +pi]`

`= -0.4  "sin" 2pi ("t" + "x"/2)`   .....`[because  "sin"  (pi + theta) = -"sin" theta]`