Two speakers S₁ and S₂ , powered by a common amplifier, are situated at y = 1.0 m and y = -1.0 m as shown in the figure. These speakers vibrate in phase at 600 Hz . A man is standing at a point on the X-axis located at a very large distance from the origin and begins to move parallel to the Y-axis. The speed of sound in air is given as 330 m s ⁻¹ . At what angle does the sound intensity decrease to a minimum for the

Step-by-step solution

The distance between the two speakers is d = 1.0 - (-1.0) = 2.0 m . The wavelength of the sound wave is given by: = v f = 330 600 = 0.55 m For a point at a very large distance, the path difference between the sound waves reaching the man at an angle is x = d . The sound intensity decreases to a minimum for the first time when the path difference is equal to 2 . d = 2 Substituting the values, we get: 2.0 = 0.55 2 = 0.275 2.0 = 0.1375 For small angles, (in radians), so 0.1375 rad . Converting to degrees: 0.1375 180^