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:
Answer & explanation
Correct answer: option 3
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 = $\frac{2\pi}{3}$
$A_{res}=\sqrt{(3A)^2+(5A)^2+2(3A)(5A)\cos\frac{2\pi}{3}}$
$=\sqrt{9A^2+25A^2-15A^2}$
$=\sqrt{19}A$