Resultant Waves: Constructive interfence vs destructive

In summary, the problem involves two speakers, A and B, who emit sound waves from equidistant location Q and differ in distance from location P. Speaker A is closer to P than Speaker B. The problem asks to find the relationship between the amplitude of the resultant wave at both locations. The waves will interfere constructively at location Q, but may interfere destructively at location P depending on the path difference between the waves. Therefore, AQ ≥ AP.
  • #1
joej24
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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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  • #2
Almost correct.Those waves can interfere constructively too, if the path difference between them is integer multiple of the wavelength, so AQ ≥AP

ehild
 

1. What is the difference between constructive interference and destructive interference in resultant waves?

In constructive interference, two waves combine to form a resultant wave with greater amplitude, while in destructive interference, the waves cancel each other out and result in a wave with lower or zero amplitude.

2. How do you calculate the amplitude of the resultant wave in constructive interference?

The amplitude of the resultant wave in constructive interference is equal to the sum of the amplitudes of the individual waves.

3. What happens to the amplitude of the resultant wave in destructive interference?

In destructive interference, the amplitude of the resultant wave is equal to the difference between the amplitudes of the individual waves.

4. Can constructive interference and destructive interference occur at the same time?

Yes, it is possible for both constructive and destructive interference to occur simultaneously in different regions of a wave. This is known as partial interference.

5. How do resultant waves behave when two waves with similar amplitudes interfere?

Resultant waves will exhibit regular patterns of constructive and destructive interference, resulting in a wave with a varying amplitude known as an interference pattern.

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