12.4 Two loudspeakers, A and B , are driven by the same amplifier and emit sinus
ID: 2099438 • Letter: 1
Question
12.4 Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced by the loudspeakers is 206 Hz. Consider Point P between the speakers and along the line connecting them, a distance x to the right of speaker A. Both speakers emit sound waves that travel directly from the speaker to point P. a) For what values of x will destructive interference occur at point P? b) For what values of x will constructive interference occur at point P?
See Attached Link for Photo: http://course.physastro.iastate.edu/phys221/homework/written_homework/hw12.pdf
Explanation / Answer
Destructive interference will occur at all points where the path length difference is an integer number of wavelengths (including 0) plus 1/2 wavelength.
Assume speed of sound c = 343 m/s, then wavelength lambda = c/f = 1.665 m and lambda/4 = 0.41626 m. There are two locations between the speakers where there is interference. At the center the path lengths are equal. If you move lambda/4 from the center you increase one path by lambda/4 and decrease the other by the same amount, for a 1/2 lambda difference. If you then try to add 1 lambda to the difference to get to the next pair of points you have to move the points another lambda/2 which is beyond the speakers. So the locations are at 1.03 - 0.41626 and 1.03 + 0.41626 m.
B. For constructive interference you want a pathlength difference equal to lambda multiplied by an integer>=0. Then you have one constructive point at the center and, using similar logic as in A, two more at lambda/2 = 0.83252 m to either side. No more points can fit in that space. The locations are at 1.03 - 0.83252 and 1.03 + 0.83252 m.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.