Question

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

• A. $25\%$
• B. $49\%$
• C. $58\%$
• D. $72\%$

Answer 1

Answer: (B)

$49\%$

the ratio of the amplitude at an antinode to the amplitude at node is 6, so
$\frac{a_i+a_r}{a_i-a_r}=6$
or, $\frac{a_r}{a_i}=5/7$
Now, the energy is proportional to the square of the amplitudes.
So, $\frac{E_r}{E_i}=25/49=51\%$
So the rest will be the transmitted energy, i.e. $49\%$.