Two coherent narrow slits emitting sound of wavelength in the same phase are situated parallel to one another with a small separation of 2 . The sound is detected by sliding a detector along the screen positioned at a distance D ( ) from the slit S₁ , as depicted in the figure. Determine the distance x such that the intensity at P matches the intensity at O .

Step-by-step solution

The path difference at point O is given by: x_O = S₁O - S₂O = D - (D - 2 ) = 2 Since the path difference is an integer multiple of the wavelength, constructive interference occurs at O , resulting in maximum intensity. For the intensity at point P to match the intensity at O , constructive interference must also occur at P . The path difference at P is: x_P = S₁P - S₂P = D^2 + x^2 - (D - 2 )^2 + x^2 As x increases, the path difference decreases from 2 towards 0 . The next maximum intensity occurs when the path diff