Question

A plane sound wave passes from medium 1 into medium 2. The speed of sound in medium 1 is 200 m/s and in medium 2 is 100 m/s. The ratio of amplitude of the transmitted wave to that of incident wave is

• A. $\frac{3}{4}$
• B. $\frac{4}{5}$
• C. $\frac{5}{6}$
• D. $\frac{2}{3}$

Answer 1

Answer: (D)

$\frac{2}{3}$

Ratio of amplitude of the transmitted wave to that of incident wave is known as transmission coefficient $\left(T\right)$.

When a wave is transmitted from medium 1 to 2, then $T=\frac{2n_1}{n_1+n_2}$ .........(1)

where $n$ is the refractive index of the respective medium.

Now as $\frac{n_1}{n_2}=\frac{v_2}{v_1}$

Thus $\frac{n_1}{n_2}=\frac{100}{200}⟹n_2=2n_1$

From (1), $T=\frac{2n_1}{n_1+2n_1}=\frac{2}{3}$