Question

The equation of displacement of two waves are given as y₁ = 10 sin $\left( 3\pi t + \frac{\pi}{3} \right)$; y₂ = 5 $\lbrack\sin 3\pi t + \sqrt{3}\cos 3\pi t\rbrack$

Then what is the ratio of their amplitudes

• A. 1 : 2
• B. 2 : 1
• C. 1 : 1
• D. None of these

Answer 1

Answer: (C)

1 : 1

Answer 2

y₂ = 5 $\lbrack\sin 3\pi t + \sqrt{3}\cos 3\pi t\rbrack$ = 5 $\sqrt{1 + 3}\sin\left( 3\pi t + \frac{\pi}{3} \right)$= 10 sin $\left( 3\pi t + \frac{\pi}{3} \right)$

So, A₁ = 10 and A₂ = 10