Superposition of 2 Similar Frequencies from Separate Sources

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When two sounds of similar frequencies are emitted from separate sources, they create an interference pattern characterized by constructive and destructive interference, resulting in beats. The sound pressure levels from each source can be described as functions of time and space, leading to an interesting spatial interference pattern. Despite the separation, listeners will still perceive the beat frequency at any single point over time. This phenomenon can be observed in real-life scenarios, such as musicians tuning instruments, where the elimination of beats indicates successful tuning. Understanding this concept involves considering the problem in terms of vector fields and superposition principles.
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If 2 sounds of similar freq are emited from the same source you get beats, but what happens if two sounds of similar freq are emited from separate sources. I realize that its just superposition but i can't figure out what it would be like in the space between the two sources.
Im happy to initially assume that the 2 amplitude are the same and only consider the 2d plane between the two sources.
Is this easy to solve?
Is this problem best considerd in vector fields? if so then how?
 
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The two frequencies do not have to be from the same source to get beats.
 
Beats happen because of constructive and destructive interference. You can describe the sound pressure level from each source as a function of time and space. If the sources are not in the same place then you will have an interesting interference pattern in space, but even so if you listen for a while at any single point you will hear the beat frequency.
 
Again there will be beats. An everyday illustration: Go somewhere where you can watch musicians manually tuning instruments, with respect to another instrument. The standard or reference instrument is one source, and the one being tuned is another, separated by some space. Tuning is done, the beats are gone - and as soon as beats are gone, they know, it's tuned

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