Question

Two sound waves are represented by the following equations::
$y_1=10\sin (2\pi t-0.03x)$ and
$y_2=5\left\{\sin \right(3\pi t-0.03x)+\sqrt{3}\cos (3\pi t-0.03x\left)\right\}$
Then the ratio of their amplitude is given by -

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

Answer 1

The correct option is A $1:1$

$y_1=10\sin (2\pi t-0.03x)$

$y_2=5\{sin(3\pi t-0.03x)+\sqrt{3}cos(3\pi t-0.03x)\}$

$y_2=5\times 2\{\frac{1}{2}\sin (3\pi t-0.03x)+\frac{\sqrt{3}}{2}\cos (3\pi t-0.03x)\}$

$=10\{{\cos 60}^0\sin (3\pi t-0.03x)+{\sin 60}^0\cos (3\pi t-0.03x)\}$

$=10\sin (3\pi t-0.3x+{60}^0)$

Ratio of amplitudes $=10:10$

$=1:1$ (A)

Answer