Q. Two sound waves travel in the same direction in a medium. The amplitude of each wave is $A$ and the phase difference between the two waves is$120{^\circ}$. The resultant amplitude will
A) $\sqrt{2}A$
B) $2A$
C) $3A$
D) $A$
Explanation
(d) Here, $A_{1} = A,A_{2} = A,\phi = 120{^\circ}$
The amplitude of the resultant wave is
$A_{R} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2A_{1}A_{2}\cos\phi}$
$= \sqrt{A^{2} + A^{2} + 2AA\cos\ 120{^\circ}}$
$= \sqrt{A^{2} + A^{2} - A^{2}}\ \ \ \ \ \ \ \ \left\lbrack \because\cos{120{^\circ} = - \frac{1}{2}} \right\rbrack$
$\therefore A_{R} = A$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.