DL=|L₂-L₁|=xx l

Displacements of air particles at P

The interference of the two waves at P is fully constructive if their path length difference DL = |L₂-L₁| is an integer multiple of the wavelength l.
DL = n l,                   n = 0, 1, 2, ...     (fully constructive interference)
The interference of the two waves at P is fully destructive if their path length difference DL = |L₂-L₁| is a half-integer multiple of the wavelength l.
DL  = (n+0.5) l,         n = 0, 1, 2, ...     (fully destructive interference)
Review wave interference in chapter 1

Click on S₁, S₂, or P and drag them to change the two waves path length difference DL = |L₂-L₁|.

Consider a point P where we want to detect the sound from the sources. Let L₁ be the distance from P to S₁ and L₂ be the distance from P to S₂. We assume that L₁ and L₂ are much greater than the distance between the sources so that we can approximate the waves as traveling in the same direction at P.

interference

Wave 2

L₂

L₁

Wave 1

Consider two sound point sources S₁ and S₂. S₁ emits wave 1 and S₂ emits wave 2. The two waves have identical wavelength l. The phase of wave 1 at S₁ is the same as the phase of wave 2 at S₂. Because of this, the two sources are said to be in phase.