Whether a listener hears
 maximum, constructive interference, a LOUD signal, or
 minimal, destructive interference, a WEAK signal
depends on the extreme path difference, or EPD, between the waves arriving at his position from each of two inphase, coherent sound sources.
EPD = L_{1}  L_{2}
LOUD constructive

WEAK destructive

mλ

½(2m  1)λ

where m {0, 1, 2, 3, ..... } for constructive interference and
m {1, 2, 3, ..... } for destructive interference.


Let's first examine a situation illustrating constructive interference.
Shown below are two inphase, coherent sound sources. This fact that each source emits the same wavelength can be verified by noting that the distance from a crest/compression to its next crest/compression is the same for both sources. That the sources are coherent can be readily seen by the fact that the sources emit their waves in unison  both release a trough, then a crest, then a trough, and so on. If "purple" wavefronts represent troughs/rarefactions and "teal" wavefronts represent crests/compressions, then point P is four wavelengths from the left source and three wavelengths from the right source. P would therefore be located in an antinode and a listener standing at point P would hear a LOUD signal. More simply, if the extreme path difference, EPD, between the two sources is a multiple of whole number of wavelengths, then P is in a region of constructive interference and a listener located at P would hear a LOUD, strong signal.
EPD = L_{1}  L_{2} EPD = 4λ  3λ EPD = 1λ
Consequently standing at P a listener would receive a LOUD, maximum signal.
Now consider a new situation illustrating destructive interference.
In this case, point Q is three wavelengths from the left source but three and onehalf wavelengths from the right source. Q would therefore be located in a nodal region and a listener standing at Q would hear minimal sound, a WEAK signal. More simply, if the extreme path difference, EPD, between the two sources is a multiple of an odd halfwavelength, then Q is in a region of destructive interference and a listener located at Q would hear a WEAK signal.
EPD = L_{1}  L_{2} EPD = 3λ  3½λ EPD = ½λ
Consequently standing at Q a listener would hear a WEAK, minimal signal.
Practice
