May 17, 2022

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How do you make a sound wave rotate? hit her with a pipe

I’m sure it’s a question that has been keeping you awake at night: Can you make an object spin with a sound wave? The answer, in general, was no. Now, though, the mechanical engineers have taken a look at what their colleagues are playing With laser you can doAnd when they saw the light copy it. In doing so, the rotation of objects with sound waves was achieved … but only in simulation.

Is it really hard to make things spin?

To get an idea of ​​why it’s hard to make things spin with sound waves, imagine a tube holding a turbine. Normally, to make the turbine spin, fluid flows through the turbine blades. The force of the fluid imparts torque to the blades, which determines the rotation of the turbine. If we replace this flow with a pressure wave (such as a sound wave), the fluid moves back and forth. So the local motion will transmit torque first clockwise and then counterclockwise. The result is a rocking motion.

Essentially, the wave has linear momentum but not angular momentum (specifically, it’s orbital angular momentum, but we’ll drop the “orbit”). An object that rotates 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, then nothing will change.

(The flowing fluid does not have angular momentum either, but it can adjust the rotation of the turbine. This works because the fluid will form vortices after the turbine has passed. The vortices carry angular momentum with the opposite rotation of the turbine so that the total angular momentum remains zero.)

This is all very well enclosed territory. But until recently, no one was sure that sound waves could carry this kind of angular momentum. Even assuming they could, we had no idea how to generate a sound wave with angular momentum. So the researchers’ first step was to show that sound waves can carry angular momentum. After doing that (the bulk of the thinking work), it’s time to figure out how to generate waves.

First, make the phone feel dizzy…

The trick is to make the mechanical waves rotate. To visualize this idea, you need to understand the idea of ​​a wavefront. For example, let’s take a sound wave traveling through the air. A sound wave consists of areas of high pressure and low pressure that move through space. If we can freeze time, we can look down on the frozen sound wave and draw a line where the pressure is higher. This line (usually a curve) is located at a right angle to the direction the wave is traveling. If we unfreeze time for a moment and then refreeze it, we will find that the line has advanced at the speed of sound to a new position.

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

Three beams of light with +1 (top), 0 and -1 (bottom) units of orbital angular momentum.  The left shows the wave fronts (steady phase lines).  The middle shows how the phase varies across the beam.  The right shows the beam intensity profile.

Three beams of light with +1 (top), 0 and -1 (bottom) units of orbital angular momentum. The left shows the wave fronts (steady phase lines). The middle shows how the phase varies across the beam. The right shows the beam intensity profile.

This wavefront describes the wave’s momentum and angular momentum. For a wave with angular momentum, the front of the wave is no longer a line (or plane). Instead, the surface is a helix (like an Archimedes screw). The wave is still moving at right angles to the wavefront surface, but is now helical and rotates about a central axis. If you were to take one part of the wavefront and trace it, you would find that they are helical keys along that axis.

What happens in the center of the key? At this site, the wavefront does not have a single value. The center should be a site of high and low pressure at the same time. The universe does not like self-contradiction, so it takes the mean, and the sound wave in the center has no amplitude.

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