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

Answer

B

Explanation

Here amplitude of incident wave is `a _(i) =0.6 ` unit amplitude of reflected wave would be,
`a _(r) = 2/3 a _(i) = 2/3 xx 0.6 =0.4 ` unit
Equation of incident wave,
`y _(i) = 0.6 sin 2pi (t - (x)/(2))` (As per the statement)
`therefore y _(i) =0.6 sin (2pi t -pi x )`
When above wave gets reflected from the surface of denser medeium, its phase increases by `pi` rad. Also, x is to be replaced by `(-x).` Hence, equation of reflected wave would be,
`y _(r) = 0.4 sin [ (2pi t + pix )+pi ]`
`=- 0.4 sin (2pi t +pi x )`
`therefore y _(r) =- 0.4 sin {2pi (t + (x)/(2)) }`