Two identical loudspeakers, S1 and S2, are driven in phase by the same audio signal of frequency 680Hz. The speakers are placed 3.0m apart on a horizontal line. A listener initially stands at point A on the perpendicular bisector of the line joining the speakers, 8.0m directly in front of the midpoint, and then walks parallel to the line S1S2 toward S2 as shown.
Assume the speed of sound in air is 340ms−1 and reflections from walls are negligible.
(a) Calculate the wavelength of the sound emitted by the speakers.
(b) Determine the smallest lateral distance d the listener must walk from point A toward S2 to first experience a point of minimum sound intensity. Show all reasoning that leads to your answer.
(c) After moving the distance found in part (b), the listener continues walking in the same direction. How much farther must the listener travel to reach the next position of maximum sound intensity? Explain.
(d) If the listener instead walks toward S1 starting again from point A, will the first minimum occur at the same or a different distance than in part (b)? Justify quantitatively.