Ncert Exercises & Solutions

Equation of a plane progressive wave is given by $y = 0.6 \sin 2 π (t - \frac{x}{2})$ . On reflection from a denser medium, its amplitude becomes $\frac{2}{3}$ rd of the amplitude of the incident wave. The equation of the reflected wave is:

1. $y = 0.6 \sin 2 π (t + \frac{x}{2})$

2. $y = - 0.4 \sin 2 π (t + \frac{x}{2})$

3. $y = 0.4 \sin 2 π (t + \frac{x}{2})$

4. $y = - 0.4 \sin 2 π (t - \frac{x}{2})$

(2) Hint: There would be a phase difference in the incident wave due to reflection.

Step 1: Find the amplitude of the reflected wave.

The amplitude of the reflected wave,

A_{r} = \frac{2}{3} \times A_{i} = \frac{2}{3} \times 0.6 = 0.4 units

Given the equation of the incident wave,

y_{i} = 0.6 \sin 2 π (t - \frac{x}{2})

Step 2: Find the equation of the reflected wave.

Equation of the reflected wave is,

y_{r} = A_{r} \sin 2 π (t + \frac{x}{2} + π)

[

∵

At a denser medium, the phase changes by

π

]

The positive sign is due to the reversal of direction of propagation.

So,

y_{r} = - 0.4 \sin 2 π (t + \frac{x}{2})

[∵ \sin (π + θ) = - sinθ]

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