I am really impressed with the amount of correct information here. Can I reorganise some of the information above?
ISOLATION, called soundproofing by amateurs, is about what needs to be done to ensure that noise levels can be reduced to acceptable levels. We are talking about mass, like earth, concrete, bricks, plasterboard, all common building materials, as well as lead and other effective but expensive materials.
ACOUSTIC TREATMENT, also called soundproofing by amateurs, is about making the sound that stays in the studio more accurate which in turn will make it sound more pleasant. Some of the treatment works to minimise too much reverb (bathrooms have more reverb than bedrooms) and other treatments work to ensure the sound is even across the entire audio spectrum. Foam*, egg boxes and carpets soak up only the highest frequencies, leaving an unbalanced frequency reponse; notice how a night club can sound good inside but but just bassy and boomy outside.
*foam, especially for Kim: while there are fire-hazardous and fire-retardant foams, in audio we primarily differentiate between open-cell and closed-cell foams. Open-cell foam has usable audio qualities but because foam is so expensive compared to fluffy insulation and gets sold so thin, many home studio builders use foam tiles too thin yet cannot change the laws of physics (frequencies' wavelengths) and so it only affects high frequencies. In professional studios the only foam you will find is the padding in chairs and headphones.
fd3 ...
Your son's electronic kit probably has mesh heads which make it quieter to play. Mesh heads (Remo SilentStroke and others) are available to fit to an acoustic kit to bring the volume level of the drums down to similarly low levels. There are quieter cymbals (Zildjian L80 and others) which have lots (hundreds) of holes in them to facilitate home acoustic kits that are not crazy loud.
In planning your shed, you would be wise to plan temperature and humidity control so that condensation and rot do not ruin wooden drums or cause your books to curl and mould to ruin the carpets, curtains and more.
Your son might be interested to look at my not yet finished studio in the WFH rejig topic (
part 1 and
part 2). Mine is a mixing studio and a rehearsal room all in one, so I have things he will not need but some aspects, such as the HVAC (heating, ventilation* and air conditioning) will be useful for him to understand.
*ventilation, especially for fruitcake: I mentioned the silencers in my WFH posts but did not explain how they work. Exactly as you say, the labrynth means air can flow freely but as sound likes to travel in straight lines, by the time the air has flowed through two silencers it is just air without the sound. This photo shows you my silencers before I closed them up.