Superposition of Sound Waves


An oscillator drives two loudspeakers 35.0 cm apart, which vibrate in phase at a frequency of 2.00 kHz. What is the smallest nonzero angle, q, (in degrees) at which a distant observer hear maximum sound intensity?


For a distant observer, the first maximum in sound level occurs at an angle such that the angle is the wavelength divided by the distance between the speakers. That is the condition that makes the difference in path length from the two speakers to the observer, one wavelength. We know that the speed of sound is about 343 m/s so a 2000Hz sound wave has a 343/2000 meter wavelength = 0.1715 meter. Then sine q is 0.1715/0.35 = 0.49, so q is 29.34 degrees.