Given,
y1 = 10 sin (3πt + \(\frac{\pi}{4}\))
y2 = 5 (3 sin3πt + \(\sqrt 3\) cos3πt)
y2 = 15 sin3πt + \(5\sqrt 3\) cos3πt
Amplitude of y1 is A1 = 10
Amplitude of y2 is A2 = \(\sqrt{(15)^2+(5\sqrt3)^2}\)
A2 = \(\sqrt{225+(8.6)^2}\)
A2 = \(\sqrt{225+73.96}\)
A2 = \(\sqrt{298.96}\)
A2 = 17.29
Then ratio of amplitude is :
\(\frac{A_1}{A_2}\) = \(\frac{10}{17.29}\)
\(\frac{A_1}{A_2}\) = \(\frac{1}{\sqrt 3}\)
Hence,
Option (b) is correct.