A progressive wave gets reflected at a boundary such that the ratio of amplitudes of the reflected and incident wave is `1 :2`. Find the percentage of energy transmitted .

Explanation

To solve the problem, we need to find the percentage of energy transmitted when a progressive wave is reflected at a boundary with a given ratio of amplitudes for the reflected and incident waves.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The ratio of the amplitudes of the reflected wave (Ar) to the incident wave (Ai) is given as:
\[
\frac{Ar}{Ai} = \frac{1}{2}
...