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(C) The amplitude of the first wave $y_1 = 10 \sin(3\pi t + \pi/3)$ is $A_1 = 10$.For the second wave,$y_2 = 5 \sin 3\pi t + 5\sqrt{3} \cos 3\pi t$. T

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$1 : 1$

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(C) The amplitude of the first wave $y_1 = 10 \sin(3\pi t + \pi/3)$ is $A_1 = 10$.For the second wave,$y_2 = 5 \sin 3\pi t + 5\sqrt{3} \cos 3\pi t$. This is of the form $y = a \sin \omega t + b \cos \omega t$,where the amplitude $A_2 = \sqrt{a^2 + b^2}$.Here,$a = 5$ and $b = 5\sqrt{3}$.$A_2 = \sqrt{5^2 + (5\sqrt{3})^2} = \sqrt{25 + 75} = \sqrt{100} = 10$.The ratio of their amplitudes is $\frac{A_1}{A_2} = \frac{10}{10} = 1:1$.

The displacement equations of two waves are given as $y_1 = 10 \sin(3\pi t + \pi/3)$ and $y_2 = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)$. What is the ratio of their amplitudes?

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