Question

In a stationary wave that from as a result of reflection of waves from an obstacle, the ratio of the amplitude at an antinode to the amplitude at node is 6. What percentage of energy is transmitted?

Answer 1

Let the incident amplitude be $a$ and reflected be $b$. Hence, as per the question, $\frac{a+b}{a-b}=6$. Hence, $\frac{a}{b}=\frac{7}{5}$.

Since energy is proportional to square of amplitude, ratio of reflected energy will be $\frac{7^2-5^2}{7^2}100=\frac{2400}{49}\approx 49$.