loudspeakers, resting on the same horizontal plane, are driven by the same ampli
ID: 2090339 • Letter: L
Question
loudspeakers, resting on the same horizontal plane, are driven by the same amplifier and emit sinusoidal waves in phase. The speakers are 2 meters apart. The frequency of the sound waves produced by the speakers is 206Hz. At what distances from the first speaker, in the direction of the second speaker, will there be constructive and destructive interference. Assume sound produced by both speaker travels in the direction of the opposite speaker. I realize there is an answer to this question already posted, although I do not understand how to get the destructive interference value for x when n=1.Explanation / Answer
Constructive interference occurs when the difference of the distances of each source from point P is
an integer number of wavelengths. The interference is destructive when this difference of path lengths is a half
The wavelength is ? = v f = (344 m s) (206 Hz) =1.67 m. Since P is between the speakers, x must be
in the range 0 to L, where L = 2.00 m is the distance between the speakers.
The difference in path length is ?l = (L ? x) ? x = L ? 2x, or x = (L ? ?l )/ 2. For destructive
interference, ?l = (n + (1 2))?, and for constructive interference, ?l = n?.
(a) Destructive interference: n = 0 gives ?l = 0.835 m and x = 0.58 m. n =1 gives ?l = ?0.835 m and x =1.42 m.
No other values of n place P between the speakers.
(b) Constructive interference: n = 0 gives ?l = 0 and x =1.00 m. n =1 gives ?l =1.67 m and x = 0.17 m. n = ?1
gives ?l = ?1.67 m and x =1.83 m. No other values of n place P between the speakers.
(c) Treating the speakers as point sources is a poor approximation for these dimensions, and sound reaches these
points after reflecting from the walls, ceiling, and floor.
Points of constructive interference are a distance ? / 2 apart, and the same is true for the points of destructive interference
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