acoustic length

[par1]

Can anyone tell me the difference between normal length & acoustic length measurement for straight pipe, Helmoltz Resonator to calculate attenuation?

I have heard there are some mathematical formula for acoustic length calculation for different intake & exhaust system but how to get those?

 

[sms]

In a straight run of pipe, acoustic length is equal to physical length. The acoustic length changes due to end conditions on open ended pipe, and also in fittings like tees, reducers, and elbows.

-The future's so bright I gotta wear shades!

 

[SomptingGuy]

For a flanged pipe, the end correction is 0.85r. For an open pipe, it's 0.6r. r is the radius of the pipe. Add the end correction to the physical length.

 

[par1]

There is a difference between simple length calculation & acoustic length.

How to define acoustic length for tees, reducers, & elbows..

what is the difference between acoustic length & simple length calculation?

 

[SomptingGuy]

This is the standard text on the subject. It is pretty expensive, but a good buy if you're spending someone else's money. My company's copy is almost worn out now.

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471847380.html

 

[par1]

Somptingguy:

I bought the book " Acoustic of Ducts & Mufflers" by M.L. Munjal & was reading the page 52 of End Correction where there is a analogy between Electrical impedence & Acoustic impedence. The text is as follow:

" If a small tube were exposed to the atmosphere or a large volume, the radiation reactance can be added to the lumped impedence of the tube & the combined reactance can be looked upon as impedence of extended tube; the hypothetical additional length is tghen termed the end correction"

Questions:

(1) Still couldn't get the physical meaning of acoustic length for Helmoltz resonator or any chamber?

(2) The book doesn't have any information on how to do length & diameter calculation for given helmoltz resonator or any quarter wave or chamber? do you have any other suggestion?

 

[GregLocock]

Well, leaving aside Helmholtz resonators do you understand how to work out the important length of a quarter wave tuner, for example, and its physical meaning?

Helmholtz resonators don't really have a tuned length. They have an important length (the length of the neck), but it does not bear the same relationship to frequency as the length of a quarter wave pipe. that is, I can design two Helmholtz systems with different neck lengths and the same resonant frequency.





Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[SomptingGuy]

My copy of The Book is currently on its holidays, touring Australia and New Zealand with one of my colleagues. But to answer (hopefully) your first question...

The physical meaning of an end correction is that pipes don't behave ideally. If you measure the first resonant frequency, you'll find that its corresponding (half) wavelength is a bit longer than the pipe. The actual standing wave protrudes from the ends of the pipe by a little bit - the end correction. Not really surprising, because some of the atmosphere at each end will be influenced by what's going on inside the pipe. And the degree of influence depends on the form of the ends of the pipe.

For a Helmholz resonator, the "length" of the neck should include the end corrections at each end, because it is the effective length of the column of air making the "mass" part of the equivalent spring-mass system.

In practice because this end correction is an imprecise amount, the acoustic length is also imprecisely defined and leads to a "squashing" of the TL curve of the resonator (lower, wider resonant peak). Reducing the length of the neck magnifies this effect, because it increases the uncertainty in the acoustic length. Long, thin necks give sharp, high peaks. Short, fat necks (of equal volume) give rounded, low peaks.

The same may be true for 1/4 wave resonators, for the same reasons.

I don't know the answer to your second question. You could try looking into "Noise and Vibration Control" by L.L.Beranek