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Let's say that I have a neighbor who has a big dog that barks at 80 dB. between him and me, there is a big wall, vegetations, etc. The sounds are absorbed, there is isolation so from my place what I will hear is a bark of only 60 dB.

Now, I also have a dog, exactly the same and it barks at 80 dB too.

If what I hear is 60 dB, does my neighbor hear 60 dB too from my dog? No matter what separates us? No matter the shape of the wall or its material ? is it always "symmetric"? I guess the answer is 'yes' but I'm wondering if it's so trivial

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PS: If you have a better idea to the title of that question, feel free to edit

EDIT

Since it's more a thought experiment, you should consider that the two dogs are twins

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    $\begingroup$ An acoustical diode will disprove your question. Just search the internet and look how it works (I'm no expert in the field but It seems from one of those things that if you try to be clever/a bit of a smart-ass you could find a solution :) ) $\endgroup$ – Ofek Gillon Dec 26 '19 at 23:00
  • $\begingroup$ didn't know something like that existed, intersting : ) $\endgroup$ – snoob dogg Dec 26 '19 at 23:01
  • $\begingroup$ An analogy - optical filters sometime require consideration of which side should face the source. Sound direction could matter if there is nonlinear absorption involved. So if the nonlinear material is, say, on the right and the sound is coming from the right, it will first encounter nonlinear absorption. If the sound is coming from the left, it might first be attenuated enough to not undergo as much nonlinear absorption in the material on the right, thus leading to a different result on the left side of the wall compared to the right side. Maybe an acoustic person can comment. $\endgroup$ – Not_Einstein Dec 27 '19 at 3:01
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    $\begingroup$ An obvious counter-example would be if the things between the houses consisted of a microphone (next to one dog) wired to an amplifier and an powerful loudspeaker (next to the other dog). $\endgroup$ – abligh Dec 28 '19 at 18:58
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It is not always "symmetric" (technically, this property is called reciprocity)!

However, assuming the medium between the two dogs is linear and microscopically reversible, your intuition is correct. Under these assumptions, it is actually a theorem, due to Lord Rayleigh, that if you exchange the source of the sound and the point at which you measure it, the sound level is unchanged. (“ Some general theorems relating to vibrations,” Proc. London Math. Soc. 4, 357–368. https://doi.org/10.1112/plms/s1-4.1.357). In electromagnetism, this is known as Lorentz reciprocity.

Now if we break one of these assumptions, we can avoid the consequences. For instance, imagine there is a very strong wind going westward, going faster than the speed of sound. Then, barks emitted by the west dog will never reach the east dog, while the opposite is possible. Such a system is called non-reciprocal.

This is an extreme, but straightforward example. You can get around reciprocity in subtler ways. Read https://science.sciencemag.org/content/343/6170/516 for a recent reference on the subject.

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As it is only a thought experiment, analogies will do.

Imagine for a moment you're dealing with light rather than sound.

There are ways to make a surface "see through" from one side but not the other, such as glass squash courts; and theatrical effects using gauze either lit directly (well, at an angle) from the front to make it appear solid, or left unlit so a bright scene can show through it from behind.

It isn't that hard to imagine some fine structure that might reflect sound waves preferentially coming from one direction, like the design of the one-way transparency coatings on glass.

Naturally I have no idea if this holds up in reality.

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