How Does Destructive Interference Occur Between Two Loudspeakers?

[anubis01]

Homework Statement

Two identical loudspeakers are located at points A and B, 2.00 m apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of 784 Hz. Take the speed of sound in air to be 344 m/s . A small microphone is moved out from point B along a line perpendicular to the line connecting A and B

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a)At what distances from B will there be destructive interference

b)At what distances from B will there be constructive interference

c)If the frequency is made low enough, there will be no positions along the line BC at which destructive interference occurs. How low must the frequency be for this to be the case?

Homework Equations

λ=v/f

The Attempt at a Solution

λ=v/f=344/784=0.4388 m

okay so first I labelled the distance from A to C as dA and from B-C as dB.

http://e.imagehost.org/0070/Capture.jpg

and to see when its destructive or constructive you would input odd or even numbers respectivley. Now I still have a wrong answer with this method and I suspect its the way I derived dB. Can anyone help me figure out what's wrong. As always any help is appreciated.

 

[Doc Al]

Now I still have a wrong answer with this method and I suspect its the way I derived dB.

Your derivation looks fine to me. What were your actual answers? Perhaps you made an arithmetic mistake somewhere.

 

[anubis01]

Your derivation looks fine to me. What were your actual answers? Perhaps you made an arithmetic mistake somewhere.

okay for destructive interference I use odd numbers for 3 and this needs to be done 5 times with values of 2 sig figs in ascending order.

for n=1 db=9m n=3 db=2.7m n=5 db=1.3 n=7 db=0.53m n=9 db=0.028 then entering in ascending order answer is

0.028,0.53,1.3,2.7,9.0

 

[Doc Al]

I just checked the first couple (n = 1, 3) and your answers look good to me.

 

[anubis01]

Okay I got the right answer thanks for the help.