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(C) The intensity $I$ of a wave is directly proportional to the square of its amplitude $a$,i.e.,$I \propto a^2$.Given the equations for the two parti

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$4:1$

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(C) The intensity $I$ of a wave is directly proportional to the square of its amplitude $a$,i.e.,$I \propto a^2$.Given the equations for the two particles:${y_1} = 0.06 \sin 2\pi (1.04t + {\phi _1})$${y_2} = 0.03 \sin 2\pi (1.04t + {\phi _2})$The amplitudes are ${a_1} = 0.06$ and ${a_2} = 0.03$.The ratio of the intensities is given by:$\frac{{{I_1}}}{{{I_2}}} = \frac{{a_1^2}}{{a_2^2}} = \left( \frac{{0.06}}{{0.03}} \right)^2 = (2)^2 = \frac{4}{1}$.Therefore,the ratio of the intensities is $4:1$.

The relation between time and displacement for two particles is given by
${y_1} = 0.06 \sin 2\pi (1.04t + {\phi _1})$
${y_2} = 0.03 \sin 2\pi (1.04t + {\phi _2})$
The ratio of the intensity of the waves produced by the vibrations of the two particles will be

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The relation between time and displacement for two particles is given by${y_1} = 0.06 \sin 2\pi (1.04t + {\phi _1})$${y_2} = 0.03 \sin 2\pi (1.04t + {\phi _2})$The ratio of the intensity of the waves produced by the vibrations of the two particles will be