Question

Two sinusoidal plane waves of same frequencies having intensities $I_0$ and ${4I}_0$ are travelling in the same direction . The resultant intensity at a point at which waves meet with a phase difference of zero radian is

• A. $I_0$
• B. ${5I}_0$
• C. ${9I}_0$
• D. ${3I}_0$

Answer 1

Answer: (C)

${9I}_0$

When two waves of same frequencies meet at a point with no phase difference, then the resultant amplitude is the sum of the individual ones.

Intensity is proportional to the square of the amplitude.

Hence $I_0=k{A}_1^2$ and $4I_0=k{A}_2^2$ where k is the constant of proportionality.

Hence $A_1=\sqrt{k^{-1}{I}_0}$ and $A_2=2\sqrt{k^{-1}{I}_0}$

Resultant amplitude is $A_R=A_1+A_2=3\sqrt{k^{-1}{I}_0}$

Resultant intensity $9I_0$