Two waves having the same frequency \( (\nu) \) and the same amplitude \( (A) \) have a phase difference of \( 2\pi/3 \). If these waves superpose, the resultant amplitude will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( A \)
Two waves of the same frequency and the same amplitude \( a \) superpose with a phase difference \( \phi \). The resultant amplitude is then \( 2a\cos(\phi/2) \). Here each wave has amplitude \( A \) and \( \phi=2\pi/3 \).
\( \begin{aligned} A_R &= 2A\cos\left(\frac{\phi}{2}\right) \\ &= 2A\cos\left(\frac{\pi}{3}\right) \\ &= 2A\times\frac{1}{2} \\ &= A \end{aligned} \)
NCERT (2026-27):
Coherent and Incoherent Addition of Waves – “… the displacement produced by S2 would be
\( y_2=a\cos(\omega t+\phi) \)
and the resultant displacement will be given by
\( \begin{aligned} y &= y_1+y_2 \\ &= a\,[\cos\omega t+\cos(\omega t+\phi)] \\ &= 2a\cos(\phi/2)\cos(\omega t+\phi/2) \end{aligned} \)
The amplitude of the resultant displacement is 2a cos (φ/2) …”