Can I increase pressure with sound waves?

An ideal sound wave will alternately increase, then decrease, the pressure locally - with no mean shift in pressure. However, there is a small amount of dissipation of sound energy - meaning that the gas will slowly heat if subjected to sound. So if your container has a fixed volume, it is possible to (slightly) heat the gas inside with sound; theoretically this would increase the pressure.

It is not a very practical mechanism except in very specific circumstances.

This is exactly what happens in a shockwave, so setting an explosion off would do the trick! Doing it without an explosion is not very feasible though.

The hard part of trying to find the resonant frequency line that is that objects that are vibrating at their resonant frequency have a tendency to act like a speaker because they interact with the molecules of the air. At the point where you start getting "interesting" results, it may be ear-splitting loud. Sounds that we are used to hearing are tiny compared to the forces you'd be looking at.

A gas or a liquid would not develop a resonant frequency, but the chamber you put them in might have one, so we'll just start from the assumption that you have already found the resonant frequency to play with and ignore it for the rest of the though experiment. It won't be important. Let's pick a pressure which is meaningful: 970 mmHg. This is the most pressure a man can exhale against a static load -- like blowing into a a balloon that's giving you too much resistance. If I convert that pressure into the SI unit for pressure, the Pascal, we get 130,000Pa. Using this calculator, I would need a sound volume of 196dB to attain that!

That sort of pressure is unattainable using sound waves in air. A .30-06 rifle going off right next to your ear is 171dB, 3,00 times weaker than the sound you'd need for this experiment (remember that dB is a logarithmic scale). You actually hit a limit around 194dB. At 194dB, you can no longer form an undistorted wave because the trough of the wave actually creates a perfect vacuum. So to create a modest pressure, one you could create using your own lungs and diaphragm, you would actually need a louder sound than the air supports!

But it does work. The trick is that blast waves don't try to create a nice sinusoidal sound wave. They merely create a large pressure gradient, pushing the air into a range where it is no longer effective to treat it as a linear transmission medium. In fact, modern nuclear devices use this when they go off. They use a large number of carefully shaped conventional explosives around the outside of the weapon to generate a shockwave which actually compresses the solid nuclear fuel in the middle. They do some really clever tricks to focus this shockwave such that at the center you get enough compression to increase the density of the fuel past critical density and it starts the chain reaction.