Whether a listener hears

 

depends on the extreme path difference, or EPD, between the waves arriving at his position from each of two in-phase, coherent sound sources.
 

EPD = |L1 - L2|   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.   Interference Physlet

 

 

Shown below are two in-phase, 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 = |L₁ - L₂|
EPD = |4λ - 3λ|
EPD = 1λ

Consequently standing at P a listener would receive a LOUD, maximum signal.

 

 

 

In this case, point Q is three wavelengths from the left source but three and one-half 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 half-wavelength, then Q is in a region of destructive interference and a listener located at Q would hear a WEAK signal.

 

EPD = |L₁ - L₂| 
EPD = |3λ - 3½λ| 
EPD = ½λ

Consequently standing at Q a listener would hear a WEAK, minimal signal.