Two plane monochromatic waves propagating in the same direction with amplitudes 3 A and 5 A and differing in phase by $\frac{2π}{3}$, superimpose. The amplitude of the resulting wave will be:

$\sqrt{19}A$

The correct answer is Option (3) → $\sqrt{19}A$

The general formula for the amplitude of the resultant wave when two wave superimposes -

$A_{res}=\sqrt{{A_1}^2+{A_2}^2+2A_1A_2\cos(\phi)}$

where,

$A_1$, Amplitude of first wave = 3A

$A_2$, Amplitude of second wave = 5A

$Δ\phi$, Phase difference between two waves = $\frac{2\pi}{3}$

$A_{res}=\sqrt{(3A)^2+(5A)^2+2(3A)(5A)\cos\frac{2\pi}{3}}$

$=\sqrt{9A^2+25A^2-15A^2}$

$=\sqrt{19}A$