In a stationary wave pattern that forms as a result of reflection of waves from an obstacle the ratio of the amplitude at an antinode and a node is  $\beta =1.5$ what percentage of the energy passes across the obstacle

         

Amplitude at antinodes $a_1+a_2$  and at nodes $a_1-a_2$   

We have been given $\beta =\frac{a_1+a_2}{a_1-a_2}= 1.5$

solving $\frac{a_1}{a_2}= 5$     i.e,  $a_2=\frac{a_1}{5}$   intensity of  the reflected wave $I_2=\frac{I_1}{25}$

percentage of energy reflected  $\frac{I_1}{25}\frac{100}{I_1}=4$  so percentage  of energy transmitted across the obstacle= 96