Question

Please show steps and show equations used

3. (In this problem, use 344 m/'s for the speed of sound in air.) Two identical loudspeakers are located on the x- axis: loudspeaker A is at the origin; loudspeaker B is at x-+3.00 m·The loudspeakers are driven by the same amplifier and produce sound waves with a frequeney of 401 Hz. A small microphone is moved along the positive y-axis. (a) (2 pts) In general, for constructive interference, what is the relation between path-length (b) (6 pts) At what position(s) on the+y-axis will there be maximum sound intensity (constructive (c) (2 pts) If the frequency of the source is decreased sufficiently, there will be no positions of difference and wavelength? (One equation /sentence should be sufficient to answer.) interference)? destructive interference along the ty-axis. How low must the frequency be for the arrangement ala given in this problem? Y. 101 YP, こn +3.00 m- Bx

Answer 1

For constructive inter fences there should be on phase difference between the two waves or the phase difference should be an integral multiple of 2 pi I e phase difference pi = n 2 pi n = 0, 1, 2, 3 phase of 2 pi path length difference = delta L for constructive delta L = n lambda n = 0, 1, 2 let us consider there in constructive inter faience at a point y an the + y asin squareroot 3^2 + y^2 - y = n lambda lambda = y/- velocity f - frequency = 344/401 m = 0.86579 m \r\n squareroot 9 + y^2 - y = n 344/401) 9 + y^2 = n^2 (344/401)^2 + y^2 + 2ny (344/401) 9 + y^2 = n^2 (344/401)62 + y^2 + 2ny (344/401) y = 9 - n^2 (344/401)^2/n (688/401) for n = 1 y = 4.8167 m fa n = 2 y = 1.765 m for n = 3 y = 0.4618 m for n = 4 y in - ve