Resource Lesson
Interference: Inphase Sound Sources
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Whether a listener hears
maximum, constructive interference, a LOUD signal, or
minimal, destructive interference, a WEAK signal
depends on the
e
xtreme
p
ath
d
ifference, 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.
Interference Physlet
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
Two loud speakers are facing each other at opposite ends of a room. They are inphase and emit tones having the exact same frequency of 68 hz. If needed, you may use the speed of sound to be 340 m/sec.
If the distance between the speakers is 15 meters, find all positions where a detector could be placed and receive a LOUD (maximum) signal.
If the distance between the speakers is 15 meters, find all positions where a detector could be placed and receive a WEAK (minimal) signal.
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