Interference is the pattern produced when waves from two sources superpose. For a steady pattern that you can observe, the sources must be coherent: they have the same frequency and a constant phase difference. Two loudspeakers connected to the same signal generator are coherent. Two separate light bulbs are not.The result at a point depends on the path difference, the difference in the distances travelled by the two waves to reach that point. For two sources that are in phase:maximum (constructive): path difference = nλ
minimum (destructive): path difference = (n + ½)λ where n = 0, 1, 2 ... At a maximum the waves arrive in phase. At a minimum they arrive in antiphase and cancel.For the minima to be completely dark or silent, the two waves must also have equal amplitudes. Otherwise the cancellation is only partial.Worked example: two loudspeakers emit sound of wavelength 0.50 m in phase. At point X the distances to the speakers are 3.00 m and 4.25 m. The path difference is 1.25 m, which is 1.25 / 0.50 = 2.5 wavelengths. This is a whole number plus a half, so X is a minimum and the sound is quiet. At a point with a path difference of 1.50 m (3 wavelengths) the sound is loud.
Walking along a line in front of the speakers, you hear loud and quiet regions alternate. The same pattern can be shown with microwaves and a detector, or with water waves in a ripple tank.
Walking along a line in front of the speakers, you hear loud and quiet regions alternate. The same pattern can be shown with microwaves and a detector, or with water waves in a ripple tank.