And now for a bit of research that is suddenly highly relevant in today’s locked-up and closed-in world: noise reduction. Does air-conditioning drive you mad? The constant hiss of sterile air?

The average building designer doesn’t seem to give a damn about it. As long as water doesn’t drip out of the vents and the dust is kinda-sorta filtered out… well, you’ve got headphones don’t you?

Don’t stop the hiss

It is actually surprisingly difficult to get rid of ventilation noises. Fans and airflow are noisy, and the very ducting that allows the air to flow into your office space also allows the sound in. Therefore, the easiest way to get rid of ventilation noises is to just close the air duct. More realistically, you need a baffle that damps the sound waves over a wide range of frequencies but doesn’t restrict air flow.

Baffles work in two ways: first the sound waves impinge upon the solid structure and are scattered and absorbed by the solid. This reduces the transmission of sound. But the second aspect is that the airflow is split and recombined. The sound waves follow both paths, but those paths are different lengths. The wave gets split into two and recombined. As a result, the phase of the two waves is different, which can result in destructive interference, which reduces the sound volume. But for any particular path, the phase difference will only be destructive for a few frequencies.

A poetic aside

My wife challenged me to write my next article in iambic pentameter. She now has another reason to regret her life choices. It is, she tells me, best read with very dark sunglasses so that the reader can make up the words rather than make out the words. In a world of endless cacophony,

Silence comes as a blessed rarity,

Cars and trucks, airco, and more,

"Shut up," yell I, adding to the litany.

Those pesky waves flow with alacrity,

To stop them takes cork at the core;

Sealed in, no flow, the air is insanitary. Engineers reflect: waves taketh and give,

A sound in two parts, delay and mixed,

Is it louder or gain we silence?

The frequency tells all: one too massive,

The other, inaudible and vanquished,

The delay is just right, phase in essence.

But noise is white: waves un-sequenced. Ev’ry frequency needs its own delay,

A hollow corkscrewing spiral saves us.

Waves, un-delayed, go through the center,

Waves round the spiral go slow in disarray.

For the waves is entirely disastrous,

White cacophony reduced all over.

Grill of inglorious corkscrews, hooray! My wife challenged me to write my next article in iambic pentameter. She now has another reason to regret her life choices. It is, she tells me, best read with very dark sunglasses so that the reader can make up the words rather than make out the words.

That's the problem. The hiss of air-conditioning covers a wide range of frequencies, yet the interference effect only blocks a few frequencies.

Interfering with my hiss

This is where metamaterials and metasurfaces can play a role. Metamaterials and metasurfaces reverse the problem. Rather than starting with a material and figuring out what you can do with it, metamaterials allow researchers to start with a mathematical formulation of the engineering goal. That gets translated into a virtual material that has the right acoustic properties. Finally, the virtual material is deconstructed into real materials that consist of elements that are all smaller than the sound waves of interest.

This process also involves a bit of intuition, since the design process from a virtual material to real material elements requires a lot of insight—it's not a process we've automated.

The researchers recognized that a spiraled, horn-like structure produces a broadband acoustic structure that provides a kind of consistent phase delay, independent of wavelength. With the right number of spirals, the phase delay could be made just right for destructive interference. This is achieved by hollowing out the center of the spiral, so half the sound wave goes through the spiral and half goes though a central tube. By calculating the performance, the researchers were able to optimize the number of spirals, the aspect ratio, and the pitch to get noise suppression over a wide frequency range.

You can’t hear it, but it’s got a beat

Of course, wavelength independence does not go on forever. In the researchers' design, the predicted transmission loss is maximized between 800 and 1500Hz, though the actual frequency range can be adjusted by changing the pitch(es) of the spiral horn.

The researchers' calculations showed that they should get about 20dB of noise suppression (about 100 times less noise power), which is pretty good. Amazingly enough, their experiments on a single spiral in a duct showed similar performance.

Will this research turn up in buildings? I think it will, but it will take some time to work out the details. For instance, I’m not sure that the bandwidth is broad enough yet, and it has a couple of very sharp peaks (exceptionally high transmission loss). Those gaps may well be perceived as sharp tones due to the interference of the sound waves with each other on either side of the gap (the beating sound you hear when two piano strings are detuned is an example of this).

Nevertheless, I think the problems can be hammered out, and new baffles will make their way into our buildings to (quiet) applause.

Physical Review Applied, 2020, DOI: 10.1103/PhysRevApplied.13.044028 (About DOIs)