The major problem with ultrasound as a mechanism of purification is that it doesn't break molecules. Heat at least denatures proteins and breaks hydrogen bonds, but ultrasound is of a just smaller order of magnitude of energy at the atomic scale, which can be of the order of the adhesive forces holding the liquid together, but not of stronger molecular bonds.
But I think you can do it a different way: use a sound waves intensity gradient to move the biological impurities in the water to a part of the container, by having them walk down an effective potential gradient, like optical tweezers move molecules. This requires only that the density/stiffness of the molecules be different from water, so that the sound energy at a given mode is different inside the molecules than in the water. If it is greater, the molecule will move to the regions of greater intensity. If it is less, it will move towards the regions of smaller intensity. By arranging the sound wave to have an intensity gradient, you can make all the molecules segregate towards/away from the microphone, leaving water in the middle with only ionic or small molecule impurities, which are not affected by the sound.
You can flush the sides away, and repeat to make a purer water. This might work for getting rid of prions, which aren't disinfected by boiling.
This article is the only thing I found that might be relevant, but it is paywalled:
I think this might be a very useful idea.
Whether any form of wave can pass through an object depends on how strongly that wave is reflected, scattered or absorbed.
Sound waves are certainly reflected by a wall, otherwise you wouldn't hear an echo from it, but not all the sound is reflected so some travels into the wall. Whether the sound is scattered and/or absorbed in the wall depends on what the wall is made from. Remember that sound is a mechanical vibration. The sound hitting the wall makes the wall vibrate and the other side of the wall makes the air on the other side vibrate. A good solid wall won't disperse the vibrations too much, so you will get some sound through it. A wall filled with e.g. fibreglass insulation, will absorb the sound far more, so it will transmit less sound.
Light is also reflected by a wall, otherwise you wouldn't be able to see it. How much light is reflected depends on the wall: a white painted wall will reflect more of the light than a black painted one. However the dominant interaction with the wall is probably scattering. If the wall was made of glass then obviously the light would pass through it. A concrete wall is made from miniscule grains of calcium carbonate and aluminosilicates, and while these materials are transparent to visible light, reflections from all those grain boundaries scatter light strongly. If a concrete wall was very thin e.g. 0.1 mm you would still get some light transmission through it.
Response to Zeynel's comment:
Consider a microphone. Sound waves consist of to and fro oscillations of air molecules, and if you sit at a fixed point in space these to and fro oscillations create oscillating pressure changes. A microphone works because when the pressure is high is pushes the sensor in the microphone back, and when the pressure is low it pulls it forward. The end result is to make the sensor in the microphone oscillate in time with the wave, and in the microphone this movement is used to create an oscillating electric field.
A microphone is designed to be very sensitive to changes in air pressure, and a wall is not. Nevertheless, even a solid wall is elastic in the sense that it deforms when you push on it. So a wall will also move in response to the oscillating pressure created by a sound wave. It will move much, much less than a microphone sensor, but it will move. If the side of the wall facing the sound wave oscillates then obviously the of the wall will oscillate as well. This behaves like a loudspeaker, i.e. the opposite of a microphone, as the oscillating surface of the wall creates an oscillating pressure in the air next to it, and this creates a sound wave. That's how the sound gets through the wall.
Re your last comment "if we said some of the sound waves passes through the wall": you need to remember that a sound wave is not a thing. It's just the movement of something else. In air a sound wave is a movement of the atoms in air, and in a wall a sound wave is the movement of the atoms in the wall. It's true to say that the sound wave passes through the wall, but it's the vibration that moves through the wall not anything you could point to. In this respect sound is completely different to light, where in principle you could follow a photon as it moves between different media.
Best Answer
It’s true.
Unless new technology is just shockingly and suddenly better now and some advanced system can, but I seriously doubt it. Water is one of the hardest things for even expert human sound techs with computers to deal with, let alone computer-based real-time cancellation systems.
The reason is that the rate of change of the sounds is very high - higher order derivatives included. Most human- and machine-made sounds have a steady rise and fall rate after the initial uptake, and almost always a constant second derivative (the rate of getting louder/quieter is increasing/decreasing steadily), so the system can track that and predict the next several waves pretty accurately. Secondly, the sound of running water is made of innumerable components, unlike the one or two dozen that make ambient indoor or outdoor sounds. Water also has the serious problem that there is no point when the noise is low.
You have a rapidly changing sound (in first and higher-order derivatives), a high minimum level of sound (ongoing sound), made of innumerable components. Good luck predicting anything even at the processing rate of two or three sound waves.
You may reply, as my friend did, that ambient noise cancellation can cancel even something bumping into the wall somewhat loudly, so it can react very quickly. First of all even bumping into the wall starts at a very low level and rises quickly, but there is an initial warning at very low volume and a convex rising in its volume. The system can track and predict several waves into the future. Also, considering the rate at which sounds are being processed, the system has to deal with this sound almost by itself, not the equivalent of 100,000 (or millions) of other bumps per minute like water. So it can recognize it very early.