Why does convolution reverb work?

I've just begun learning about signal processing on my own, and after reading about convolution I'm curious about why convolution reverb works. That is given a recorded impulse $$\hat{f}$$ and an audio signal $$g$$, why does the convolution $$h = \hat{f} \circledast g$$ produce an audio signal which sounds like the signal $$g$$ was recorded in the environment $$\hat{f}$$ was recorded (based on $$\hat{f}$$)? If this question is better suited for sound design/physics stack exchange, feel free to redirect me!

• The room is an LTI system (sort of), so the impulse response is sufficient to characterize it and convolution is the way to calculate the output. Are you looking for a mathematical proof? Dec 15, 2021 at 10:05
• @Hilmar I'm not really looking for a mathematical proof, but perhaps a detailed description on why the the convolution works physically when we look at the small details of the formula. That is, why in order to replicate how the sound $g$would have sounded in the room $\hat{f}$ was recorded, we begin by multiplying and summing the first pressure values of $g$ by the last pressure values of the recorded $\hat{f}$. I do accept the high-level description of the phenomenon as systems, but I would just like to examine the situation in low-level. Dec 15, 2021 at 15:22

• @ZRHan While I do accept the high-level description of the situation, do you happen to know any source which examines the phenomenon in low-level? I mean that why in order to replicate how the sound ggwould have sounded in the room $\hat{f}$ was recorded, we begin by multiplying and summing the first pressure values of $g$ by the last pressure values of the recorded $\hat{f}$? Dec 15, 2021 at 15:24