Quarter wavelength 2

[doop4]

Can someone please tell me what the purpose of the quarter wavelength theory is? Why is it not 1/8 wavelength or even 1/9th . Why does it have to be 1/4? is there any justification/explanation. I understand it's for better acoustic matching but does ithave to be 1/4 for optimum matching?

Thanks

 

[btrueblood]

Um. I can tell you why 1/4-wave tubes are used as acoustic dampening elements. The 1/4-wave tube "fills" during a pressure peak in the main cavity, and empties 1/4 of a main wave oscillation later, when the velocity past the opening of the 1/4-wave tube is at a maximum. Thus, the jet formed by the 1/4-wave tube will create the maximum possible dissipation (generation of turbulence) and thus provide maximum dampening.

 

[johnab]

btrueblood:

I still kind of partially understand the quarter wave phenomena; but still wondering

consider the case when one straight pipe has side branch. (1)But is it true that all the time when the wave arrives at opening without of phase or one time after it strikes the end it would be out of phase & other time would be in phase.

(2) Also, we won't get any attenuation during the time duration when wave travels away from opening?

(3) Is any way, we can quick generate wave with straight pipe, quarter wave tube & see how much interference we get? like any software?

 

[btrueblood]

3) yes, there are a lot of acoustical software packages on the market, and I would assume that they would be capable of solving 1/4-wave absorber problems. You should also be able to find a nearly closed-form solution technique in a good acoustics book.

2) Mmm...usually not, but there is some attenuation as some of the main tube flow is diverted to fill the 1/4 wave tube.

1) a 1/4 wave located at one end of a pipe will have the poorest ability to dampen longitudinal waves. You want to locate the mouth of the 1/4 wave tube near a velocity anti-node for the wave in the main chamber you are trying to dampen (i.e. a location where velocity amplitude is at a maximum) to achieve the best dampening.

 

[SomptingGuy]

Sizing and locating resonators, be they 1/4 wave or helmholz is bread and butter to 1D performance/acoustic codes. Some of them provide features to locate the exact positions of antinodes under running conditions.

 

[doop4]

Thanks a for all the replies guys but I am still a bit confused.

For instance, if I were using a piezo crystal to generate ultrasound, I would have a contact material between the piezo and the pipe and this intermediate material will have thickness of 1/4 wavelength of the piezo material for maximum acoustic transfer. my question is why can't it be ,1/2, 1/3 1/5 . What's the speciality about 1/4?

Thanks once again for your replies and hope to have some more.

P.S: btrublood- you mentioned lots of acoustic software, can you/anyone recommend a good commercial software to model ultrasonic wave propogation?

 

[doop4]

or do you think my question shoul really be @What is quarter wavelength theory"? Could anyone recommend a good book on this? I have tried the acoustic books I use and have had no luck

 

[btrueblood]

doop4,

I was afraid I was answering the wrong question, looks like I was right. You are talking about "acoustic coupling" and "impedance matching" for ultrasound drivers. (Hint: plug those terms in varying groups into Google or other search engines and see what you come up with).

Still, the basic idea here is the same (I think). Just to make sure, you are being told that the transfer material (aka impedance matching layers) are to be sized such that a down-and-back time for an acoustic wave traversing the material is equal to 1/4 of the piezo drive wavelength. You have two surfaces, the drive surface (piezo face) and the driven surface (pipe). You want to transfer the energy from driver to driven at best efficiency.

Think about what's happening in a stepwise fashion: 1. the piezo head moves and pushes on the transfer material, generating a pressure wave. 2.) the wave travels until it hits the pipe wall; some of the wave energy is deposited into the pipe, but some of the energy is reflected back through the material. 3.)a.) If the reflected wave coming back through your material hits the piezo head when it is still in the "compression stroke" (to borrow an analogy from IC engines)(i.e. the transfer material response is much less than 1/4 wave), then the wave will reflect again, and you have a lot of "ringing" or spurious echoes going on. Similarly, if the wave hits the piezo head at bottom dead center. But, if the wave hits the piezo head at 1/4 wavelength later, it hits at a point when the head is moving backwards at its maximum velocity, and thus the echo (re-reflection from the head) is minimized; also, the energy in the reflected wave is tranferred at best efficiency back into the piezo head.

It's like trying to pump a swing - you can kick your legs, wiggle or whatver you want at either end of the swing, and not much happens. But if you shift your weight near the center of the swing, when the velocity is at a maximum, you can keep the swing moving.

Another really good experiment is to go grab a "slinky" spring toy, and tie down or have a friend hold one end. You drive the other end back and forth along the axis of the spring. Watch what happens as you vary the timing (phase angle) of your "compression stroke". Hint: start really slowly relative to the frequency of the spring's wave motion.

As far as acoustic wave propagation thru solid materials, you may want to look at FEA solvers. Although, simple 1-D analysis should take you a long ways. Get a good freshman physics textbook, if for no other reason than to refresh your memory and load up your head with the right terms and buzzwords; then go do a Google search for both software and recent technical papers. I'd sit here and rattle off a list of codes (both acoustics and FEA), but since it's been >10 years since I did anything along those lines, you'd probably have a hell of a time finding anything I could mention.

 

[WebWizz]

1/4 lambda resonators are used quite a lot for reactive mufflers, for example for compressor or combustion engine noise abatement.

A quarter wave length resonator is a way to 'filter out' a tone. The principle is that a wave (sinus) wave plus the same wave that is half a wavelength out of phase add up to zero. Superposition of the 'positive sinus part' and the 'negative part': adds up to zero.

To get this a side branch with a quarter of the wavelength is put on the pipe (exhaust or other application). As the wave travels in and out the total distance is half the wave length.

Regards, Wim

 

[doop4]

Thanks you guys. . .learning by hte minute!

So what you are saying is that the reflection in the 1/4 wavelength material will result in half a wavelength of the signal produced by the piezo, on its return to the piezo? But wouldn't this reduce the energy being transferred from the piezo, if the reflected signal cancels with the original one in the piezo?

Sorry guys for being so daft but I am still not very clear (MUCH clearer than before starting the thread but still have some dounts). Your very valuable contribution to the thread is MUCH appreciated! THANKS SO MUCH!!!!!!

Can anyone recommend a good text book on this?

 

[johnab]

Webwizz:

I tried to draw with pen & paper - one sine wave (tube) & other wave with half wavelength (quarter wave tube travel half wavelength) so get output as one time in a phase & other time out of phase-

Out of phase gives noise cancelation but wondering in phase gives superposition & hence, will increase sound. - Is it true or my method was incorrect - if anyone can explain?

 

[btrueblood]

"... But wouldn't this reduce the energy being transferred from the piezo, if the reflected signal cancels with the original one in the piezo?"

Yes, which is why I said you want the reflection to come back (to the piezo face) 1/4 wavelength (wavelength of the piezo driver) later, not a 1/2-wave later.

Somebody else claimed a 1/2-wave works for noise abatement, not me. Strongly suggest you review a freshman physics book, or an "intro to acoustics" text.

 

[WebWizz]

Johnab,

A wave can be shifted 1/2 a wave by using a 1/4 wavelength tube. The cancelation is correct for a 1/4 wavelength with a side tube which has the same diameter as the one you are connecting it to. This would be the filtered frequency.

For a frequency where the tube length equals half the wavelength the energy that goes into the tube gets added up with the next wave. For a steady state condition this would be the same, making this a 'passing frequency'.

All this can be calculated with flat wave front theory, the calculation are not easy though - complex numbers in T-matrices.

The principle can be found in most books about acoustics.

Cheers, Wim

 

[johnab]

webwizz,

I'm not certain after reading your reply,

So are you agree that at the opening of quarter wave tube attached to main tube having same dia- one time out of phase effect at opening so it will cancel the noise but next time one will get in phase effect & will increase the noise due to superposition.

If that's the case than why someone use for noise attenuation?

(definitely it requires to understand complex number wave equation addition)

 

[doop4]

btrueblood: so what it should be is to have the wave coming back at 1/4 wavelength at the piezo, the thickness of the material should be around 1/8 wavelength right ? That would make going back and forth 1/4 wavelength? Am I correct?

Thanks

 

[btrueblood]

doop,

Yes, that's what I wrote. Please check this with a good acoustics text, as other posters here seem to disagree with that statement.