August 13, 2022

# How to make a sound wave spin? Hit it with a pipe

It’s a question I’m sure was keeping you up at night: can you make an object spin with a sound wave? The answer, generally speaking, used to be no. Now, though, mechanical engineers have taken a look at what their colleagues who play with lasers can do, and having seen the light, they copied it. And with that, spinning objects with sound waves has been achieved… but only in simulations.

## Is it really that hard to make things spin?

To get an idea of why making things spin with sound waves is difficult, picture a tube that holds a turbine. Normally, to make the turbine spin, a fluid would flow past the blades of the turbine. The force of the fluid on the blades imparts a torque, which sets the turbine spinning. If we replace that flow with a pressure wave (like a sound wave), the fluid moves back and forth. So the local motion will first impart a torque that is clockwise and then one that is counterclockwise. The result is a rocking motion.

More fundamentally, the wave carries linear momentum but not angular momentum (specifically, it’s orbital angular momentum, but we’ll drop the “orbital”). Something that spins has angular momentum. In the turbine example, the total angular momentum cannot change. If the wave has no angular momentum and the turbine has no angular momentum, nothing will change.

(Flowing fluid doesn’t have angular momentum, either, but it can set the turbine spinning. This works because the fluid will form vortices after it has passed the turbine. The vortices carry angular momentum with the opposite spin to the turbine so that the total angular momentum remains zero.)

This is all well-trodden ground. But until recently, no one was sure that sound waves could carry this type of angular momentum. Even assuming they could, we had no idea how to generate a sound wave with angular momentum. So the first step the researchers took was to show that sound waves could carry angular momentum. Having done that (the bulk of the thinking work), it was time to figure out how to generate the waves.

## First, make a phonon dizzy…

The trick is to make mechanical waves spin. To visualize this idea, you need to understand the idea of a wavefront. For example, let’s take a sound wave traveling in the air. A sound wave consists of high-pressure and low-pressure regions that move through space. If we could freeze time, we could look down on the frozen sound wave and draw a line where the pressure is highest. This line (which is usually a curve) is at right angles to the direction that the wave is traveling. If we unfreeze time for an instant and then refreeze it, we’ll find that the line has advanced at the speed of sound to a new position.

Our picture of wavefronts can be expanded to three dimensions. Here, the line of high pressure becomes a plane of high pressure that advances through space at the speed of sound.

This wavefront describes the wave’s momentum and angular momentum. For a wave with angular momentum, the wavefront is no longer a line (or a plane). Instead, the surface is a helix (like an Archimedes screw). The wave still travels at right angles to the wavefront surface, but it is now a spiral that circles a central axis. If you were to take a single bit of wavefront and track it, you would find that it corkscrews along that axis.

What happens at the center of the corkscrew? At that location, the wavefront has no single value. The center has to be a location of simultaneously high and low pressure. The Universe doesn’t like self-contradiction, so it takes the average, and the sound wave at the center has no amplitude.