Sound WavesHardBloom L3

Question

The equations of S.H.M. of medium particle due to sound waves propagating in a medium are given by s1 = 2 sin (200πt) and s2 = 5 sin (150πt). The ratio of average intensities of sound at these points is :

Options

A.4 : 25
B.9 : 100
C.8 : 15
D.64 : 225

Solution

Sol. I = $\frac{1}{2}\rho A^{2}w^{2}v$

As medium is same so ρ and v are same

So $\frac{I_{1}}{I_{2}} = \left( \frac{A_{1}\omega_{1}}{A_{2}\omega_{2}} \right)^{2}$ = $\left( \frac{2 \times 200\pi}{5 \times 150\pi} \right)^{2}$ = $\frac{64}{225}$

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