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 . If he continues walking along the same line past the first maximum, h

Step-by-step solution

The wavelength of the sound wave is given by: = v f = 330 600 = 0.55 m The distance between the two speakers S₁ and S₂ is: d = 1.0 - (-1.0) = 2.0 m For an observer at a very large distance from the origin, the path difference x at an angle from the X-axis is: x = d For a maximum (constructive interference), the path difference must be an integer multiple of the wavelength: x = n d = n Substituting the values, we get: 2.0 = n(0.55) = 0.275 n Since the maximum value of is 1 (as 90^ when the man moves to infinity para