Hi scotty,
i have a question, about the engine cover with the emblem of the car, in my case its 2016 mazda 3, and about hood liner
i noticed the under side of the engine cover has a foamy material, almost spongy, what is it made for?
is it safe to remove?
and will removing it make the engine sound more distinct?
same question goes about the hood liner, does it serve any purpuse? can i remove it for saving weight and hearing the engine's sound more?
can i remove it for saving weight
You won't reduce weight significantly.

I'm not gonna speak for @scottykilmer, but he has referenced a number of times in videos that the "stupid beauty cover" is a waste. I suspect most of the users here will agree.
My contrarian take is that there are benefits beyond aesthetics, if small. For one, the insulating material is going to protect the hood and the paint thereon. Second, airflow in the engine bay was optimized by the engineers to have the cover in place. And regarding noise, even though you may want engine noise, most of the noise reduction is going to be the clackety kind of sounds from the engine top (which I suspect is not what you want to hear more of; what you want is more of the low-pitched growl, which is primarily coming from the lower part of the motor and exhaust).
I always keep my engine's clothes on. But probably doesn't make much difference either way.
can i remove it for saving weight
The cover weighs the same as a couple of soft drinks . It's going to make absolutely zero difference to your performance.
hearing the engine's sound more
you want hear the annoying buzz of a 150hp 4 banger?

Back in may when I had moved up to new york and first got my car inspected, one of the local mechanics that has decades of experience, said to ditch the beauty cover.
He said up here in the cold weather, the mice like to hide under it, and chew away at everything. They may still get in there, but it doesn't make it as easy to hide.
I hate taking the thing off to check stuff like power steering fluid anyway.
Beauty covers removed.
The stupid beauty cover seems to have become more prominent when cars switched from distributors to coil on plug.
I don’t know if that just a correlation, or causation.
