Question

A) You attend an open-air concert with a friend on a hot day with an air temperature of 25.3°C, and the arena has two speakers, one on each side of the stage. Suppose you sit in a seat which is 7 meters from one speaker and 9.1 meters from the other, and your friend sits in a seat 7 meters from one speaker and 8.75 meters from the other. If a musician plays a single 494 Hz tone through the speakers, then under ideal conditions, which one of you would hear the tone at its loudest? Which one would not hear it at all? Consider the speakers to be point sources. (15 pts)

Answer 1

where The speed of sound at room temperature is approximately 346 m/s Now the wavelength of the 494 Hz tone will be cu the speed of sound and a is the wavelength v is the frequency 494 1 ~ 0.7m uk 346 ula Both - 7 Now, consider the first case Im and a. lm are an integer multiple of a because 0.7 x 10 and 0.7813=9.1 Hence the two waves will be exactly in phase when they arrive the listener. Therefore the listener will loudest tone. hear the y Care ③ Case (2) Consider the second case 7m is an integes multiple of a 8.75m= 124.7 + 1x ot Case ① wave frouts exactly match sound wave highs 2. lows wave know this term suggests that the coming from the other end will be half wavelengths ahead! And we that a difference of half wavelengths corresponds to destructive interference ie. the waves will concel each other Hence the second listener your friend) will not hear anything

If you have any further doubts, please feel free to comment. Please upvote if my answer helped.