Two identical speakers in an auditorium are placed 10.0m apart above the stage.

Question

Two identical speakers in an auditorium are placed 10.0m apart above the stage. The amplifier system introduces a 690 Hz buzzing noise to the sound, which annoys some audience members. Use v=343 m/s as the speed of sound in air.
a) what is the wavelength of the noise? (I found it to be .497m)
b) If you are sitting 15m directly in front of one of the speakers, will you hear the noise loudly???

I got that the frequency will be lower at 115.02 Hz but it's wrong. Apparently it's constructive? Please help if you could write out the steps so I can see where I went wrong it would be much appreciated!

Explanation / Answer

Given Two speakers are at a distance of , d = 10 m Frequency of the noise , f = 690 Hz Speed of sound in air , v = 343 m/s a) The realtion between wavelength and frequency is             v = f            = v / f = 343 m/s / 690 Hz            = 0.497 m b) The condition for constructive interference is         r2 - r1 = n    ---1     where r2 is the distance from the first speaker to the person    and r1 is the distance from the second speaker to the person given r1 = 15 m and r2 = (10m)^2 + (15m)^2 = 18.02 m Taking eq 1,       18.02 m - 15 m =         = 3.02 m The frequency , f = v /                            = 343 m/s / 3.02 m = 113.5 Hz

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