Question

Two waves having equation $x_1=a\sin (\omega t+{\varphi }_1)$ and $x_2=a\sin (\omega t+{\varphi }_2)$ If in the resultant wave the frequency and amplitude remains equals to amplitude of superimposing waves. Then phase difference between them-

• A. $\frac{\pi }{6}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{8}$

Answer 1

The correct option is B $\frac{2\pi }{3}$

$x_1=asin(\omega t+{\varphi }_1)$

$x_2=asin(\omega t+{\varphi }_2)$

$△\varphi$ = phase difference = ${\varphi }_1-{\varphi }_2$

Resulatant amplitude $\Rightarrow a=\sqrt{(a{)}^2+(a{)}^2+2a^{2}cos△\varphi }$

$\Rightarrow a^2=2a^2+2a^{2}cos△\varphi$

$cos△\varphi =-\frac{1}{2}$

$△\varphi =\frac{2\pi }{3}$

Option B