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 will the man experience a maximum of sound intensity fo

Step-by-step solution

The distance between the two speakers S₁ and S₂ 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 from the origin at an angle with the X-axis, the path difference between the sound waves reaching the man from S₁ and S₂ is: x = d The man starts from the X-axis ( = 0^ ), where there is a central maximum. As he moves parallel to the Y-axis, he will experience the first maximum of sound intensity when the path difference equals one