The magic in my setting offers a lot of control, at the expense of energy equivalent to whatever the task you're doing. So, lifting a 5 pound box is equally as difficult with magic as it would be in real life, energy consumption wise. This hasn't been a problem yet, but it's raised some questions of energy cost for various spells - Specifically, how much energy would it take to create a really loud noise, in the most efficient way possible? Or, more generally, what is the most efficient way to create a really loud noise, all other circumstances being variable? An explosion? A sonic boom created by throwing something really, really fast?
The easiest would to impart your force onto the air molecules directly. Select an amount of air that you want to move and how much you want to accelerate it to create the shockwave. A cubic meter of air only has about one kilogram of mass. So about one Newton per kilometer an hour you want the blast wave to hit with. Two cubic meters of air suddenly moving at a hundred kilometers an hit would knock a man to hit feet probably. That'd be two hundred newtons. A hundred cubic meters of air suddenly moving at a hundred kilometers and hour would obliterate an average house so that's calculate out to about ten thousand newtons. Both of those numbers sound large, but they're actually quite small amounts of energy. https://en.m.wikipedia.org/wiki/Orders_of_magnitude_(force). A small alligators bite, applies enough force to blow down a house. Seems illogical, but air creates small pressures over entire surface areas. You'd have to move the air very close to when you want the damage. The force of the impact would decrease as you got further from the point of origin by a factor of distance squared.
I think some sort of explosion would be the most effective way to generate a really loud noise perception wise. A balloon popping is loud if you are nearby but since you are close to the sound brain figures out that it is not really a "huge" thing happening to create the sound. When you hear blasting at a distance it is not necessarily real loud but IMO you imagine it was very loud and something very significant closer to the source. So maybe it depends on the effect you want the sound to have on the listener.
Explosions create noise, if you want your voice heard, use harmonics. Deep sounds travel further and have easier time passing between mediums. A whales song is about as loud as a jet engine and can be heard for hundreds of miles, yet we can't hear it because it's below our perception.
I like newjerseyrunner's post but I still think you need to explain the purpose of the sound/noise, this would have an impact on how it is generated. A car playing deep bass notes rattles the windows on homes as it goes by, kind of like newjerseyrunner is suggesting. However if you have magic available to create this sound then "throwing your voice" may be a good technique, make the sound appear to be far away but loud at its source might be a useful effect. The ability to "march" the sound towards someone could also be effective for deception purposes. Also harmonics could play a part in this, certain frequencies make dogs howl, added noise, maybe certain frequencies in your world can be amplified by the surrounding environment. Harmonics caused a bridge to fail, wind blowing across it started it swinging and it kept building up until it collapsed - changed the way they engineered bridges, so how you can use the sound might play a big part in your situation, IMO. Another thought is if you can generate the sound at the opening to the ear of the person you are trying to impress, throwing your voice in reality in a magic setting, even a tiny amount of energy would seem incredibly loud.
