What is the formula for sound refraction?

[WarVsFutility]

I know that electromagnetic waves travel slower in general through denser materials than through less dense materials. Sound waves, however, are the opposite. The formula for light refraction is the ratio of the sines of the incidence angles equals the respective speeds of light through the mediums. So sound waves should have their own formula for refraction, right?

 

[Stonebridge]

If a sound wave slows down when crossing from one medium to another, its path will be refracted towards the normal in exactly the same way, and with exactly the same formula, as any other wave.

 

[nasu]

The formula is the same as for EM waves. Only that for EM waves it is usually expressed in terms of the index of refraction whereas for sound waves the speeds are used.
v2 Sin(i) = v1 Sin(r)
v2 is the speed in the second medium, i is the angle of incidence, in the first medium.

 

[WarVsFutility]

So, a person could easily build a sound-focusing lense, right?

 

[nasu]

So, a person could easily build a sound-focusing lense, right?

"Easily" is a relative term. If you mean that it is possible, then yes.
Actually there are focused ultrasound generators which use a "lens" for this purpose.

 

[Redbelly98]

Sound is more easily focused using reflection rather than refraction:

[PLAIN]http://www.spyemporium.com/microphones_voice_booster/microphones_voice_booster_high_grade_broadcast_quality_parabolic_dgpm_2.jpg

(From http://www.spyemporium.com/microphones_voice_booster_high_grade_broadcast_quality_parabolic_dgpm.html )​

 

[WarVsFutility]

I was thinking more along the lines of a sonar eyeball, to get higher resolution imaging through the water or through the ground.

 

[nasu]

An alternative (used already in medical imaging) is to use phased arrays. It means an arrays of sources (and receivers) that can be addressed independently with signals. By choosing the appropriate phase pattern you can focus the resulting beam in a point of choice (within some limit). By changing the phase pattern you can change the position of the focal point so you can scan the target.

 

[sophiecentaur]

One effective form of lens uses an matrix of (hundreds of) small diameter tubes - shaped like a lens with tubes going from face to face - long ones in the centre and sort ones on the outside. The sound travels a bit slower through the tubes than through the air so you get a focussing effect just like with an optical lens. You can also use a very thin convex piece of very light, stiff foam.

 

[Blanketman]

I am currently busy with a project on sonar for an autonomous underwater vehicle, and am in a situation where some sort of acoustic lens would be a great help.
The sonar transducers I have emit a conical beam shape with a beam angle of about 6-7 degrees. I want to reduce that to about 1-2 degrees...

Any ideas?

 

[DragonPetter]

An alternative (used already in medical imaging) is to use phased arrays. It means an arrays of sources (and receivers) that can be addressed independently with signals. By choosing the appropriate phase pattern you can focus the resulting beam in a point of choice (within some limit). By changing the phase pattern you can change the position of the focal point so you can scan the target.

This is done in underwater sonar too.

I am currently busy with a project on sonar for an autonomous underwater vehicle, and am in a situation where some sort of acoustic lens would be a great help.
The sonar transducers I have emit a conical beam shape with a beam angle of about 6-7 degrees. I want to reduce that to about 1-2 degrees...

Any ideas?

See above. Use an array with phase/time delays on each element to perform beam shaping, it can greatly increase your SNR too. This works for transmitting and receiving. You can buy this already made, since the technique is pretty standard in sonar.

 

[Blanketman]

This is done in underwater sonar too.



See above. Use an array with phase/time delays on each element to perform beam shaping, it can greatly increase your SNR too. This works for transmitting and receiving. You can buy this already made, since the technique is pretty standard in sonar.

Yes, I did look into that, but it seems that would be a very expensive route to follow. I was hoping I could make use of what I already had. Thus I thought of using a lens of sorts.

 

[nasu]

You could try a lens, similar to the ones already mounted on the focused transducers.
One think to consider is that the shape of the lens (concave, convex) may be opposite to the optical case. Convergent lens is (or may be, depends on the material) concave.

 

[sophiecentaur]

You could try a lens, similar to the ones already mounted on the focused transducers.
One think to consider is that the shape of the lens (concave, convex) may be opposite to the optical case. Convergent lens is (or may be, depends on the material) concave.

Sound lenses are often made with tubes of different lengths - looking like a 2D array of organ pipes. The sound is slower down the pipes so, as with glass optical lenses, they are convex in that case to give a longer delay at the middle than at the sides.

 

[nasu]

I was talking about lenses made from a solid material. These are used on the focused, ultrasound transducers. I suppose they are easier to make than the pipe structure.
Is the pipe structure used to couple the transducer to air?

 

[sophiecentaur]

Well - slow structures will need fat middles and fast structures will need thin middles.

If you use a solid structure for the lens then isn't matching the impedance a bit of a problem? i.e. how do they cancel all the reflection? I thought that was why they use the honeycomb structure which has a similar speed of sound as in air - just a bit slower. I think that very light foam is also used (convex again I believe).

 

[nasu]

Well - slow structures will need fat middles and fast structures will need thin middles.

If you use a solid structure for the lens then isn't matching the impedance a bit of a problem? i.e. how do they cancel all the reflection? I thought that was why they use the honeycomb structure which has a similar speed of sound as in air - just a bit slower. I think that very light foam is also used (convex again I believe).

This is what I thought when I asked if they are used in air. Otherwise it won't make sense to have such a complicated structure.

On the other side, for ultrasound in water the impedance matching is not such a big problem so the immersion transducers have usually just a solid lens.
They may look like this:
http://www.ndtsystems.com/Transducers/Optima_Series/Immersion_Main/Immersion_Slim/Immersion_C_Type_200.jpg
Regarding the reflections due to various interfaces inside the transducer, they are present even for flat transducer. You can usually identify them easily by the time of flight and ignore them or use a delay line to move them (in time) farther from the interesting reflections. It depends on the application, of course.

 

[sophiecentaur]

This is what I thought when I asked if they are used in air. Otherwise it won't make sense to have such a complicated structure.

On the other side, for ultrasound in water the impedance matching is not such a big problem so the immersion transducers have usually just a solid lens.
They may look like this:
http://www.ndtsystems.com/Transducers/Optima_Series/Immersion_Main/Immersion_Slim/Immersion_C_Type_200.jpg
Regarding the reflections due to various interfaces inside the transducer, they are present even for flat transducer. You can usually identify them easily by the time of flight and ignore them or use a delay line to move them (in time) farther from the interesting reflections. It depends on the application, of course.

That makes totally good sense to me.

 

[Bobbywhy]

"The parametric array is a nonlinear transduction mechanism that generates narrow, nearly sidelobe free beams of low frequency sound, through the mixing and interaction of high frequency sound waves, effectively overcoming the diffraction limit (a kind of spatial 'uncertainty principle') associated with linear acoustics. Parametric arrays can be formed in water, air, and Earth materials/rock."

http://en.wikipedia.org/wiki/Parametric_array

 

[Blanketman]

awesome thanks guys, there's been some good inputs here. Will research parametric arrays for now. But I still like the idea of a lens. It seems they usually use some sort of plastic, like TPX plastic.

 

[Blanketman]

Alright, just to be sure, can the same laws of refraction in lenses be applied to acoustic waves?
For example, can I represent acoustic waves using "rays" as you would with light for the purpose of the design of the lens?

 

[sophiecentaur]

Alright, just to be sure, can the same laws of refraction in lenses be applied to acoustic waves?
For example, can I represent acoustic waves using "rays" as you would with light for the purpose of the design of the lens?

The only difference here is that the wavelengths are much longer than for light. Diffraction effects will need to be taken into account for much larger apertures and objects.

 

[nasu]

An example of a system of lenses used for sonar is shown in these papers:

http://www.apl.washington.edu/programs/z_DIDSON/Media/object_ident.pdf

http://traktoria.org/files/sonar/beamforming/acoustic_lens
/beamforming_and_imaging_with_acoustic_lenses_in_small_high-frequency_sonars.pdf

They use a system of compound plastic lenses on top of a transducer array (the lens system shown towards the bottom of the articles)

 

[Bobbywhy]

@nasu. Thank you for these references. Interesting, and exactly what the OP asked for!

 

[WarVsFutility]

One idea is to make a lens by taking a ring and stretching a balloon over it, and you could alter the focus of this lens by filling it or emptying it with a liquid that has less density than water. I haven't tried it, but it should work... I think.

 

[Blanketman]

Thanks nasu, that's helping a lot!
Cool beans.