Micro Sound Waves: Can 1 Hear What Only Another Can?

[LightningInAJar]

TL;DR Summary

Are there sound waves small enough that they can be focused like a laser?

Are there soundwaves so tightly packed that you could have two people standing next to one another and fire sound at a distance directly into one person's ear as that only that person hears it?

 

[tech99]

To take some ballpark figures, a dish 1m in diameter using a frequency of 30kHz will, by my rough mental arithmetic, produce a 1 degree beamwidth. This would separate two people 1m apart at a distance of 100m. The wavelength will be about 1cm. Notice however that such high frequencies do not propagate very well in air.

 

[jasonRF]

The calculation by tech99 is of course correct for linear waves, which is what we normally think about. These kinds of calculations also apply to electromagnetic waves and dish antennas.

However, I have been to museums that use the 'audio spotlight', so a person standing in front of an exhibit hears the audio track, and a person a few feet away doesn't hear it at all. It really confused me the first time I experienced it, and I couldn't figure out how it worked. I later learned that this technology is based on nonlinear acoustics. I believe it transmits an ultrasonic signal that has been amplitude-modulated by the audio track, and through nonlinearities in the air a fraction of the energy is converted to audio frequencies. Here is an abstract that gives the basic idea
https://asa.scitation.org/doi/pdf/10.1121/1.389414

jason

 

[DaveE]

The calculation by tech99 is of course correct for linear waves, which is what we normally think about. These kinds of calculations also apply to electromagnetic waves and dish antennas.

However, I have been to museums that use the 'audio spotlight', so a person standing in front of an exhibit hears the audio track, and a person a few feet away doesn't hear it at all. It really confused me the first time I experienced it, and I couldn't figure out how it worked. I later learned that this technology is based on nonlinear acoustics. I believe it transmits an ultrasonic signal that has been amplitude-modulated by the audio track, and through nonlinearities in the air a fraction of the energy is converted to audio frequencies. Here is an abstract that gives the basic idea
https://asa.scitation.org/doi/pdf/10.1121/1.389414

jason

From that abstract: "A finite amplitude ultrasound wave that can be amplitude modulated..."

That's smart, the infinite amplitude waves are problematic in practice, LOL.

 

[jasonRF]

From that abstract: "A finite amplitude ultrasound wave that can be amplitude modulated..."

That's smart, the infinite amplitude waves are problematic in practice, LOL.

Love this comment!

But I feel like I should add some context for the OP given this is an Intermediate level (as opposed to advanced level) post

LightningInAJar:
in case you aren't aware, the fundamental equations for propagation of sound through a fluid are nonlinear. When we linearize the equations about some configuration we obtain the typical wave equation you have probably seen in a few contexts. The physics described by this linearized model doesn't formally depend at at all on the wave amplitude, but it is only valid if the amplitude is very small (small enough that the nonlinear terms can be neglected). Some authors may even write 'infinitesimal', although that is not a rigorous term. The 'finite amplitude' label mentioned to in the abstract refers to the case where the amplitude is large enough that the linearization is not valid, and a nonlinear model is required that predicts amplitude-dependent physics. I have seen other authors use this same jargon, but I don't know how standard it is.

By the way, if you aren't familiar with linearizing systems of partial differential equations (as is done for the problem at hand), notionally it not so different than using a linear approximation of a function as learned in freshman calculus. The linear approximation near a point is a line tangent to the function at that point. It is valid near the tangent point, and the further a point on the line is from the tangent point, the worse the approximation is. For large enough deviations the linear approximation my be inadequate and you may need a nonlinear model (such as a quadratic) to obtain the desired accuracy.

jason

 

[LightningInAJar]

What device can do this spotlight type audio? And can one send this audio straight up until it disburses enough that it can be heard in all directions, but maybe the source of the audio would be tough to track down?

 

[sophiecentaur]

What device can do this spotlight type audio?

I had a pair of 1.4m (iirc) microwave comms dishes fixed to my lab walls. They were very effective in producing the sort of effect that the OP is describing. Not a distant 'spotlight' effect but nonetheless, a strongly localised sound.

Putting a quiet sound source (a transistor radio played quietly) at the focus of one dish produced a very localised region around the focus of the other dish where it could be heard. (+/- the width of your head) You get similar set-ups in Science parks but usually over a longer path. My demo was very 'near field' and seemed to work better in that respect than I have heard on bigger equipment.
Note - this was with audio wavelengths and I think one reason it was so good was the audio bandwidth involved (a couple of octaves and some very squeaky sounds.
I sometimes used to hear kids whispering things way across the room which I was not meant to hear!