Question

Two waves represented by the following equations are travelling in the same medium

$y_{1}=5sin 2\pi \left(75 t - 0 .25 x\right)$

$y_{2}=10sin 2\pi \left(150 t - 0.50 x\right)$

The intensity ratio $\frac{I_{1}}{I_{2}}$ of the two waves is

• A. $1:2$
• B. $1:4$
• C. $1:8$
• D. $1:16$

Answer 1

Answer: (D)

$I=\frac{1}{2}ρω^{2}A^{2}v$
$\frac{I_{1}}{I_{2}}=\frac{\omega _{1}^{2} A_{1}^{2}}{\omega _{2}^{2} A_{2}^{2}}$
$\frac{I_{1}}{I_{2}}=\left(\frac{75}{150}\right)^{2}\left(\frac{5}{10}\right)^{2}$
$\frac{I_{1}}{I_{2}}=\frac{1}{16}$