Discussion Forum

Four harmonic waves of equal frequencies and equal intensities I₀   have phase angles    $0,\frac{\pi}{3},\frac{2\pi}{3}$ and $\pi$. When they are superposed, the intensity of the resulting wave is  nI₀. The value of n is

Answer:

Explanation:

Let individual amplitudes are A₀ each. Amplitude can be added by vector method.

 A₁ = A₂ = A₃ = A₄ = A₀ 

Resultant  of  A₁  and  A₄ is zero, Resultant   of  A₂  and  A₃  is   

    $A=\sqrt{A_{0}^{2}+A_{0}^{2}+2A_{0}A_{0}\cos 60^{0}}=\sqrt{3}A_{0}$

 This is also the net resultant.

Now,               $I\propto A^{2}$

    $\therefore$                    Net intensity will become 3I₀

         $\therefore$          Answer is 3.