Question

In the standing waves that form as a result of reflection of waves from an obstacle, the ratio of the amplitude at antinode to the amplitude at a node is s. The fraction of the energy that passes past the obstacle is:

• A. $\frac{4}{s^2}$
• B. $\frac{s+1}{s-1}$
• C. $(\frac{s+1}{s-1}{)}^2$
• D. non of the above.
  

Answer 1

The correct option is D non of the above.

Let $A_0$ be amplitux of original wave

$A_r$ be amplitux of reflected wave

$s/a$

$\frac{A_0+A_r}{A_0-A_r}=S$

Applying comp. and dive.

$\frac{A_0+A_r+A_0-A_r}{A_0+A_r-A_0+A_r}=\frac{s+1}{s-1}$

$\Rightarrow A_r=\frac{s-1}{s+1}{A}_0$

Now

$4\propto A^2$

$\therefore$ Req ratio

$\frac{A_0^2-A_r^2}{A_0^2}=1-{\left(\frac{s-1}{s+1}\right)}^2$

$=\frac{2s}{(s+1{)}^2}$

Remark: Non of option is correct