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Interference of Sound Waves 
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#1
Nov1307, 08:37 PM

P: 150

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from speaker A. Take the speed of sound in air to be 344 m/s.
What is the closest you can be to speaker B and be at a point of destructive interference? __________ I am having the hardest time trying to visualize the problem. I know that destructive interference occurs when the difference in path lengths traveled by sound waves is a half integer number of wavelengths. So I need to know the wavelength of the sound which is just 2m. I also know that in general if d_a and d_b are paths traveled by two waves of equal frequency that are originally emitted in phase, the condition for destructive interference is d_ad_b=n(wavelength)/2 where wavelength is what I calculated it to be (2m) and n=any nonzero odd integer. I think I need to know what the value of n is that corresponds to the shortest distance d_b to solve my prob. (is d_a=8m? then what is d_b?) I'm going around in circles and getting nowhere. Please help! 


#2
Nov1307, 09:18 PM

P: 48

Take n=1 for shortest distance from speaker B.



#3
Nov1307, 09:23 PM

Sci Advisor
HW Helper
P: 1,772

Usually, it is important to know the distance between the two speakers. Is this not given?
Then you can move B wherever you like. If you are 8 m from A, and wavelength is 2 m, the sound form A has traveled 4 full integer multiples of the wavelength. You must place B at a location such that the sound will arrive 1/2 wavelength out of phase. One full wavelength? or less? how much less? 


#4
Nov1307, 09:35 PM

P: 150

Interference of Sound Waves
apparently n=1 is not the right answer.
all info has been given. gahh. i need help. Yes, sound from A has traveled 4X the wavelength of sound emitted by the loud speakers. Sound from B must be moved so that the sound arrives 1/2 wavelength out of phase (d_ad_b=n(wavelength)/2) so are you telling me the same thing that Vijay told me, that n=1? 


#5
Nov1307, 10:27 PM

P: 150

am i approaching this the wrong way???? ..Nobody??



#6
Oct2108, 12:43 AM

P: 1

The correct answer is 1.00m.
Hint: The closest you can be to B. (lamda/2) 


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