Question

Two waves, $y_1=2a\cos \omega t$ and $y_2=3a\cos (\omega t+\frac{\pi }{2})$ meet at a point. The amplitude of the resultant wave is

• A. $a$
• B. $5a$
• C. $3.6a$
• D. $2.5a$

Answer 1

The correct option is C $3.6a$

Given:
$y_1=2a\cos \omega t$
$y_2=3a\cos (\omega t+\frac{\pi }{2})$
So, the amplitudes of wave are,
$A_1=2a$ and $A_2=3a$
Also, phase difference,
$\alpha =\frac{\pi }{2}$
We know that resultant amplitude of superposition of two waves is given by,
$A=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \alpha }$
$\Rightarrow A=\sqrt{(2a{)}^2+(3a{)}^2+2\times 2a\times 3a\times \cos \frac{\pi }{2}}$
$\Rightarrow A=\sqrt{13a^2}=3.6a$