Serway & Jewett — Superposition and Standing Waves: Problem 6

Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of \(f = 21.5\text{ Hz}\) (Fig. P17.6) in an area where the speed of sound is \(344\text{ m/s}\). (a) Show that a receiver at point A records a minimum in sound intensity from the two speakers. (b) If the receiver is moved in the plane of the speakers, show that the path it should take so that the intensity remains at a minimum is along the hyperbola \(9x^2 - 16y^2 = 144\) (shown in red-brown in Fig. P17.6). (c) Can the receiver remain at a minimum and move very far away from the two sources? If so, determine the limiting form of the path it must take. If not, explain how far it can go.