Two coherent sound sources are at distances x1 = 0.2 m and x2 = 0.48 m from a point. Calculate the intensity of the resultant wave at that point, if the frequency of each wave is f = 400 Hz and velocity of wave in the medium is v = 448 ms-1. The intensity of each wave is I0 = 60 Wm-2.

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Aicharya · Accepted Answer

Sol. Path difference, $\Delta x = x_2 - x_1 = 0.48 - 0.2 = 0.28\ \mathrm{m}$ Now, phase difference, $\phi = \dfrac{2\pi}{\lambda}\,\Delta x = \left(\dfrac{2\pi f}{v}\right)\Delta x$ $= \dfrac{2\pi(400)(0.28)}{448} = \dfrac{\pi}{2}$ Now, intensity of resultant wave, $ I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$ or $ I = I_0 + I_0 + 2I_0\cos\left(\dfrac{\pi}{2}\right)$ $ = 2I_0 = 2(60) = 120\ \mathrm{Wm}^{-2}$ Answer: $120\ \mathrm{Wm}^{-2}$

Two coherent sound sources are at distances x1 = 0.2 m and x2 = 0.48 m from a point. Calculate the intensity…

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