Sound wave interference destructive interference problem?

AI Thread Summary
Two identical loudspeakers, spaced 2 meters apart, emit sound waves at a frequency of 440 Hz and a velocity of 320 m/s. To achieve destructive interference at a point C, the path difference between the waves from the speakers A and B must equal half a wavelength. The wavelength is calculated as 0.727 meters, leading to a path difference of 0.364 meters for destructive interference. The discussion emphasizes the geometric relationship between points A, B, and C to determine the length of BC. Ultimately, the problem illustrates the concept of sound wave interference and the conditions required for destructive interference.
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Homework Statement



Two identical loud speakers placed at A and B 2m apart produce sound waves of frequency 440 HZ and with a velocity 320 m/sec a small microphone was used and placed at C along a perpendicular line from AB if there will be a destructive interference at C find the length of BC, please break the answer down for me and explain it in details,


Homework Equations


i guess v=f x wave length
path difference (m+0.5)wavelength


The Attempt at a Solution


I'll start by getting the wave length = velocity/frequency = 320/440= 8/11 but then what ? i don't see any way that could led me to length of BC
 
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Destructive interference occurs where a peak from one speaker meets a trough from the other. So perhaps draw circles of appropriate radius centered on a and b?
 
i don't understand how can a wave coming from speaker A interfere with wave coming from B at C ! maybe draw a line from A to C and make some sort of triangle, but i don't see where this may get me ?
 
Yes, draw a line from A to C. And, also draw a line from B to C.

If there is destructive interference, there is something you can say about the lengths of those two line segments.

p.s. Welcome to Physics Forums :smile:
 
Hey, ! Thanks, and i finally got the answer when i was in the physics class, and our teacher was like who got this ? and some guy raised his hand and told him the answer and how there are infinite answers because C could be anywhere, and I'm really sad that i got really shy and didn't have the nerve to say in a loud voice the answer and our teacher kept on praising this guy and telling him how smart he is and i got REALLY SUPER jealous, but it's not that hard anyway eh ?.
 
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