Question

In interference of two waves, two individual amplitudes are $A_0$ each and the intensity is $I_0$ each. The resultant amplitude at a point where phase difference between two waves is ${60}^{\circ }$ is

• A. $\sqrt{2}{A}_0$
• B. $\sqrt{3}{A}_0$
• C. $A_0$
• D. $2A_0$

Answer 1

The correct option is B $\sqrt{3}{A}_0$

Given:
Amplitudes of two waves, $A_1=A_2=A_0$

Intensities of two waves, $I_1=I_2=I_0$

Phase difference between two waves, $\varphi ={60}^{\circ }$

The formula for the resultant amplitude is given by,

$A=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \varphi }$

$=\sqrt{A_0^2+A_0^2+2A_0^2\cos {60}^{\circ }}$

$=\sqrt{3}{A}_0$

The resultant amplitude at a point where phase difference between two waves is ${60}^{\circ }$ is $\sqrt{3}{A}_0.$

Hence, option $\left(\text{B}\right)$ is correct.

Why this question? This question has been asked to test your retention skill for formulas of interference. Here, intensity has been given to confuse you. Sometimes the given data cannot be used.