Question

The displacement of the medium in a sound wave is given by the equation; $y_1=Acos(ax+bt)$ where A, a & b are positive constants. The wave is reflected by an obstacle situated at x = 0, The intensity of the reflected wave is 0.64 times that of the incident wave. The equation for the reflected wave is $y_2=\pm \frac{s}{10}Acos(ax-bt)$. Find $s$ :

Answer 1

The intensity of the wave is directly proportional to the square of the amplitude.

Thus $I\propto A^2$

where $I$ and $A$ represent the intensity and amplitude respectively.

Thus $\frac{I_R}{I_I}=\frac{A_R^2}{A_I^2}$

Given: $A_I=A{A}_R=\frac{s}{10}A{I}_R=0.64I_I$

$\frac{(\frac{s}{10}A{)}^2}{A^2}=\frac{0.64I_I}{I_I}$

$⟹s=8$