A large room contains two speakers that are 3 meters apart. The sound intensity I of one speaker is twice that of the other, as shown in the figure. (To print an enlarged copy of the graph, go to MathGraphs.com.) Suppose the listener is free to move about the room to find those positions that receive equal amounts of sound from both speakers. Such a location satisfies two conditions: (1) the sound intensity at the listener’s position is directly proportional to the sound level of a source, and (2) the sound intensity is inversely proportional to the square of the distance from the source. (a) Find the points on the x-axis that receive equal amounts of sound from both speakers. (b) Find and graph the equation of all locations (x, y) where one could stand and receive equal amounts of sound from both speakers.
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