What is the ratio of the amplitudes of the wa | vedclass

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(C) Given $y_1 = 10 \sin(3\pi t + \frac{\pi}{3})$. The amplitude $A_1 = 10$.For $y_2 = 5[\sin 3\pi t + \sqrt{3} \cos 3\pi t]$,we multiply and divide b

Vedclass · Accepted Answer

$1 : 1$

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(C) Given $y_1 = 10 \sin(3\pi t + \frac{\pi}{3})$. The amplitude $A_1 = 10$.For $y_2 = 5[\sin 3\pi t + \sqrt{3} \cos 3\pi t]$,we multiply and divide by $2$ inside the bracket:$y_2 = 5 	imes 2 [\frac{1}{2} \sin 3\pi t + \frac{\sqrt{3}}{2} \cos 3\pi t]$Using the 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 [\sin 3\pi t \cos(\frac{\pi}{3}) + \cos 3\pi t \sin(\frac{\pi}{3})]$$y_2 = 10 \sin(3\pi t + \frac{\pi}{3})$.The amplitude $A_2 = 10$.Therefore,the ratio of amplitudes is $\frac{A_1}{A_2} = \frac{10}{10} = 1:1$.

What is the ratio of the amplitudes of the waves $y_1 = 10 \sin(3\pi t + \frac{\pi}{3})$ and $y_2 = 5[\sin 3\pi t + \sqrt{3} \cos 3\pi t]$?

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