Sound wave interference destructive interference problem?

[Douna2nd]

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

 

[CWatters]

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?

 

[Douna2nd]

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 ?

 

[Redbelly98]

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

 

[Douna2nd]

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 ?.