Question

Two sinusoidal waves each of amplitude $2A$, travel in the same direction in a medium. If the phase difference between the two waves is ${120}^{\circ }$, then find the resultant amplitude of the superimposed wave.

• A. $3\sqrt{2}A$
• B. $2A$
• C. $\sqrt{2}A$
• D. $3A$

Answer 1

The correct option is B $2A$

Given that,
Amplitude of each wave is $2A$
Phase difference between two sinusoidal waves $\left(\varphi \right)={120}^{\circ }$

The resultant amplitude is given by
$A_r^2=A_1^2+A_2^2+2A_1{A}_2\cos \varphi$
From the given data,

$A_r=\sqrt{{\left(2A\right)}^2+{\left(2A\right)}^2+2\left(2A\right)\left(2A\right)\cos \left({120}^{\circ }\right)}$

$\Rightarrow A_r=\sqrt{8A^2+8A^2\times (-\frac{1}{2})}$

$\Rightarrow A_r=\sqrt{4A^2}=2A$

Hence option (b) is correct.