Suppose to have two speakers $A$ and $B$ one in front of the other, producing coherent sound waves with the same frequency $f$ and power $P$. In different positions on the line connecting the speakers there is constructive and distructive interference.

Where the interference is constructive, at distances $r_{A,max}$ from $A$ and $r_{B,max}$ from $B$, the intensity of the resulting wave is $$I_{MAX}=(\sqrt{I_A}+\sqrt{I_B})^2=\frac{P}{4 \pi} \bigg(\frac{1}{r_{A,max}}+\frac{1}{r_{B,max}}\bigg)^2$$

Where the interference is distructive, at distances $r_{A,min}$ from $A$ and $r_{B,min}$ from $B$, the intensity of the resulting wave is $$I_{MIN}=(\sqrt{I_A}-\sqrt{I_B})^2=\frac{P}{4 \pi}\bigg(\frac{1}{r_{A,min}}-\frac{1}{r_{B,min}}\bigg)^2$$

So I can consider the ratio


In a exercise with a similar situation I found $q<1$, which means $I_{MAX}<I_{MIN}$ and this seems strange because the intensity in a minimum would be greater than one in a maximum. Is that possible?

It seems to me that the resulting frequency is greater when the distances between speakers are similar, indipendently from the fact that I have a constructive or distructive interference but how can I obtain a lower intensity in a maximum than in a minimum?

I report the exercise to show the problem

An observer $O$ is between two speakers $A$ and $B$ emitting at same frequency and power. The distance between the speakers is $d=2m$ and $O$ is at distance $r_{A,max}=0.5 m$ from $A$ when he hears the maximum. The observer moves of a distance $0.2 m $ and hears a minimum. Find the ratio $q$.

It is not specified if the observer moves towards $A$ or $B$ but, if I consider that it moves towards the nearest speaker, $A$, then I get $q<1$, infact



1 Answer 1


The maximum and minimum are "local" values. As you move closer to A (at 0.2 m you are MUCH closer to A than to B) the amplitude of A is much larger - so although there may be destructive interference between A and B at that point, this is by no means perfect interference, and the resulting amplitude is still quite large (lot of A minus a little of B).

Whether that analysis agrees with your equations is something I don't quite have the time to figure out right now... So if you think I don't make sense please tell me why.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.