Resultant Waves: Constructive interfence vs destructive

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SUMMARY

The discussion focuses on the interference of sound waves emitted by two speakers, A and B, positioned equidistant from location Q but at different distances from location P. The speakers are in phase, leading to constructive interference at location Q. However, at location P, the differing distances result in a potential for destructive interference unless the path difference is an integer multiple of the wavelength, allowing for constructive interference as well. The conclusion is that the amplitude of the resultant wave at location P will be less than or equal to that at location Q, depending on the path difference.

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Homework Statement


Let's say that there are 2 speakers, A and B. They are equidistant from location Q and differ in distance from Location P. Speaker A is closer to Location P than Speaker B is to Location P. Both speakers emit sound waves and are in phase with each other.

The problem asks me to find the relationship between the amplitude of the resultant wave at both Locations.


Homework Equations





The Attempt at a Solution


I understand that since they are equidistant from Location Q, they are in sync and will interfere constructively. But since they differ in distance from Location P, the waves will not be in sync. Since they are not in sync, does this mean that the waves will interfere destructively? The resultant wave can also interfere constructively, but the amplitude will not be as great as the amplitude of the resultant wave at Location Q.

So either way, AQ > AP

Is this reasoning correct?
 
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Almost correct.Those waves can interfere constructively too, if the path difference between them is integer multiple of the wavelength, so AQ ≥AP

ehild
 

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