Question

The equations of displacement of two waves are
$y_{1}=10\,sin\left[3\pi t+\frac{\pi}{3}\right] $ and $ y_{2}=5\left[sin\,3\pi t+\sqrt{3}cos\,3\pi t\right]$
The ratio of their amplitudes is

• A. $1 : 2$
• B. $2 : 1$
• C. $1 : 1$
• D. $1 : 5$

Answer 1

Answer: (C)

Here, $y_{1}=10\,sin\left(3\pi t+\frac{\pi}{3}\right)$
$\therefore $ Amplitude of this wave is $A_{1}=10$
and $y_{2}=5\left[sin\,3\pi t+\sqrt{3}\,cos\,3\pi t\right]$
$=10\left[\frac{1}{2}sin\,3\pi t+\frac{\sqrt{3}}{2}cos\,3\pi t\right]$
$=10\left[cos \frac{\pi}{3}sin \,3\pi t+sin \frac{\pi}{3}cos \,3\pi t\right]$
$=10\,sin\left(3\pi t+\frac{\pi}{3}\right)$
$\therefore $ Amplitude of this wave is $A_{2}=10$
Their corresponding ratio is
$\frac{A_{1}}{A_{2}}=\frac{10}{10}=1$