Question

Two sinusoidal plane waves of same frequency having intensities $I_0$ and ${16I}_0$ are travelling in the same direction. The resultant intensity at a point at which waves meet with a phase difference of 0 radian is

• A. ${17I}_0$
• B. ${16I}_0$
• C. ${25I}_0$
• D. ${20I}_0$

Answer 1

The correct option is C ${25I}_0$

Given : $I_1=I_o$ and $I_2=16I_o$
Resultant intensity is maximum at a point at which waves meet with a phase difference of 0 radian.
Maximum intensity $I_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$
$\therefore$ $I_{max}=(\sqrt{I_o}+\sqrt{16I_o}{)}^2$
Or $I_{max}=(\sqrt{I_o}+4\sqrt{I_o}{)}^2$
$⟹I_{max}=(5\sqrt{I_o}{)}^2=25I_o$