Resource Lesson Interference: In-phase Sound Sources
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|

 LOUDconstructive WEAKdestructive mλ ½(2m - 1)λ

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

Two loud speakers are facing each other at opposite ends of a room. They are in-phase 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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