The equation of displacement of two waves are given as
` y_(1) = 10 sin( 3 pi t + (pi)/(3)) , y_(2) = 5 [ sin 3 pi t + sqrt(3) cos 3 pi t]`
Then what is the ratio of their amplitudes

Explanation

To find the ratio of the amplitudes of the two waves given by the equations \( y_1 = 10 \sin(3 \pi t + \frac{\pi}{3}) \) and \( y_2 = 5 [\sin(3 \pi t) + \sqrt{3} \cos(3 \pi t)] \), we can follow these steps:

### Step 1: Identify the amplitude of the first wave
The first wave is given by:
\[ y_1 = 10 \sin(3 \pi t + \frac{\pi}{3}) \]
In this equation, the amplitude \( A_1 \) is the coefficient of the sine function, which is:
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