Two waves represented by the following equations are travelling in the same medium $y_1 = 5\sin 2\pi (75t -…

Two waves represented by the following equations are travelling in the same medium $y_1 = 5\sin 2\pi (75t - 0.25x),$ $y_2 = 10\sin 2\pi (150t - 0.50x).$ The intensity ratio $\frac{I_1}{I_2}$ of the two waves is
  1. 1 : 2
  2. 1 : 4
  3. 1 : 8
  4. 1 : 16

Solution

Ratio of intensities, $\frac{I_1}{I_2} = \frac{A_1^2 \omega_1^2}{A_2^2 \omega_2^2} = \left(\frac{5}{10}\right)^2 \left(\frac{2\pi \times 75}{2\pi \times 150}\right)^2 = \frac{1}{16}$

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