Question

The equations of displacement of two waves are
$y_1=10sin\left[3\pi t+\frac{\pi }{3}\right]$ and $y_2=5\left[sin3\pi t+\sqrt{3}cos3\pi t\right]$
The ratio of their amplitudes is

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

Answer 1

Answer: (C)

Here, $y_1=10sin\left(3\pi t+\frac{\pi }{3}\right)$
$\therefore$ Amplitude of this wave is $A_1=10$
and $y_2=5\left[sin3\pi t+\sqrt{3}cos3\pi t\right]$
$=10\left[\frac{1}{2}sin3\pi t+\frac{\sqrt{3}}{2}cos3\pi t\right]$
$=10\left[cos\frac{\pi }{3}sin3\pi t+sin\frac{\pi }{3}cos3\pi t\right]$
$=10sin\left(3\pi t+\frac{\pi }{3}\right)$
$\therefore$ Amplitude of this wave is $A_2=10$
Their corresponding ratio is
$\frac{A_1}{A_2}=\frac{10}{10}=1$