Question

The equation of displacement of two waves are given as
$y_1=10sin(3\pi t+\frac{\pi }{3})$
$y_2=5(sin3\pi t+\sqrt{3}cos3\pi t)$
Then, the ratio o f their amplitude will be

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

Answer 1

The correct option is B $1:1$

$y_2=5(sin3\pi t+\sqrt{3}cos3\pi t)$
$=10(\frac{1}{2}sin3\pi t+\frac{\sqrt{3}}{2}cos3\pi t)$
$=10(sin3\pi t.cos\frac{\pi }{3}+cos3\pi t.sin\frac{\pi }{3})$
$=10sin(3\pi t+\frac{\pi }{3})$
Now, amplitude of first wave $=10$
Amplitude of second wave $=10$
Ratio $=1:1$