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 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.
|
|
Let's first examine a situation illustrating constructive interference.
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.
Now consider a new situation illustrating destructive interference.
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.
Practice
|