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  • Two waves represented by the following equations are travelling in the same medium. <img alt="\mathrm{\begin{aligned} & y_1=5 \sin 2 \pi(75 t-0.25 x) \\ & y_2=10 \sin 2 \pi(150 t-

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

\mathrm{\begin{aligned} & y_1=5 \sin 2 \pi(75 t-0.25 x) \\ & y_2=10 \sin 2 \pi(150 t-0.50 x) \end{aligned}}

The intensity ratio \mathrm{\frac{I_{1}}{I_{2}}} of the waves is-

Option: 1

1:2


Option: 2

1:4


Option: 3

1:8


Option: 4

1:16


Answers (1)

best_answer

Use,\mathrm{I_1=A_1{ }^2 \omega^2, I_2=A_2{ }^2 \omega_2{ }^2}

\mathrm{ \begin{aligned} \frac{I_1}{I_2}=\frac{A_1{ }^2 \omega_1^2}{A_2{ }^2 \omega_2^2} & =\left(\frac{A_1}{A_2}\right)^2\left(\frac{\omega_1}{\omega_2}\right)^2 \\ & =\left(\frac{5}{10}\right)^2\left(\frac{2 \pi \times 75}{2 \pi \times 150}\right) \\ \frac{I_1}{I_2} & =\frac{1}{16} \quad \text { Ans. } \end{aligned} }

Posted by

Sanket Gandhi

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