Equation of a plane progressive wave is given by y = 0.6 sin 2π(t – x/2). On reflection from a denser medium its amplitude becomes …

Q: Equation of a plane progressive wave is given by y = 0.6 sin 2π(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 = 0.6 sin 2π(t + x/2)

(b) y = – 0.4 sin 2π(t + x/2)

(c) y = 0.4 sin 2π(t + x/2)

(d) y = – 0.4 sin 2π(t – x/2)

Solution : After reflection from denser surface , the phase of wave changes by π radian .So reflected wave is given by $\displaystyle y = \frac{2}{3} \times 0.6 sin 2\pi(t + x/2 + \pi) $

$\displaystyle y = – 0.4 sin 2\pi(t + x/2 ) $

Correct option is (b)