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 ..........

Equation of a plane progressive wave is given by y = 0.6 sin 2pi (t -

1.	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 ..........
Answer» `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))` Solution :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)) }`