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Question

Equation of plane progressive wave is given by $$y = 0.6 sin 2\pi\left(t - \dfrac{x}{2}\right)$$. 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=0.6sin2π(t+x2)
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B
y=0.4sin2π(t+x2)
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C
y=0.4sin2π(t+x2)
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D
y=0.4sin2π(tx2)
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Solution

The correct option is B $$y =- 0.4 sin 2\pi\left(t + \dfrac{x}{2}\right)$$
Amplitude of reflected wave $$= \dfrac{2}{3} \times 0.6 = 0.4$$
On reflection from a denser medium there is phase change of $$\pi$$.
$$\therefore$$ Equation of reflected wave is
$$y = 0.4 sin 2\pi\left(t + \dfrac{x}{2} + \pi\right) = - 0.4 sin 2\pi\left(t + \dfrac{x}{2}\right)$$

Physics

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