Question

A travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i,a_r$ and $a_t$ be the amplitudes of incident wave, reflected wave and transmitted wave and $I_i,I_r$ and $I_t$ be the corresponding intensities. Then, choose the correct alternative.

• A. $\frac{I_i}{I_r}={\left(\frac{a_i}{a_r}\right)}^2$
• B. $\frac{I_i}{I_t}={\left(\frac{a_i}{a_t}\right)}^2$
• C. $\frac{I_r}{I_t}={\left(\frac{a_r}{a_t}\right)}^2$
• D. All of these

Answer 1

The correct option is A $\frac{I_i}{I_r}={\left(\frac{a_i}{a_r}\right)}^2$

Relation between intensity and amplitude of wave,
$\frac{I_1}{I_2}={\left(\frac{a_1}{a_2}\right)}^2$
The above relation is valid only when properties like density of medium, speed of wave, etc. remains the same.
$(I=\frac{1}{2}\rho v{\omega }^2{a}^2)$
In incident and reflected waves medium is same, therefore other properties are same. Hence,
$\frac{I_i}{I_t}={\left(\frac{a_i}{a_r}\right)}^2$