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(C) The first wave equation is ${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{3}} \right)$. The amplitude of this wave is $A_1 = 10$.The second wave equ

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$1:1$

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(C) The first wave equation is ${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{3}} ight)$. The amplitude of this wave is $A_1 = 10$.The second wave equation is ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$.We can rewrite this by multiplying and dividing by $2$:${y_2} = 5 	imes 2 \left( \frac{1}{2} \sin 3\pi t + \frac{\sqrt 3}{2} \cos 3\pi t ight)$.Using the trigonometric identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,where $\cos \frac{\pi}{3} = \frac{1}{2}$ and $\sin \frac{\pi}{3} = \frac{\sqrt 3}{2}$:${y_2} = 10 \left( \sin 3\pi t \cos \frac{\pi}{3} + \cos 3\pi t \sin \frac{\pi}{3} ight) = 10 \sin \left( 3\pi t + \frac{\pi}{3} ight)$.The amplitude of the second wave is $A_2 = 10$.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 ${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{3}} \right)$ 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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