The dependence of disturbances due to two wav | vedclass

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(A) From the graph,for the first wave (solid line),the amplitude $A_1 = 1$ and the time period $T_1 = 2$ units.For the second wave (dotted line),the a

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$1 : 1$

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(A) From the graph,for the first wave (solid line),the amplitude $A_1 = 1$ and the time period $T_1 = 2$ units.For the second wave (dotted line),the amplitude $A_2 = 2$ and the time period $T_2 = 4$ units.The intensity $I$ of a wave is given by $I = 2 \pi^2 \rho v f^2 A^2$,where $f = 1/T$.Thus,$I \propto (A/T)^2$.Therefore,the ratio of intensities is $\frac{I_1}{I_2} = \left( \frac{A_1}{A_2} \cdot \frac{T_2}{T_1} \right)^2$.Substituting the values: $\frac{I_1}{I_2} = \left( \frac{1}{2} \cdot \frac{4}{2} \right)^2 = (1)^2 = 1 : 1$.

The dependence of disturbances due to two waves on time is shown in the figure. The ratio of their intensities $I_1 / I_2$ will be

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