Exercise involving acoustics physics engineering

In summary, to reject a disturbance signal propagating in a ventilation duct with a fundamental frequency of 250Hz and odd harmonics in its spectrum, the appropriate filter option is to use an expansion chamber with dimensions that will attenuate the signal by 20dB. This is possible because the expansion chamber has been proven to attenuate each odd harmonic by the same amount as the fundamental frequency. Another option, using a helmotz band stop resonator, would allow for complete attenuation of the 250Hz frequency, but this is not necessary for the given problem.
  • #1
louisnach
15
0

Homework Statement


A disturbance signal propagates in a ventilation duct with cross-sectional area A=0,04m2. The fundamental frequency of the disturbance signal is 250Hz and its spectrum consists of odd harmonics only.

Choose the appropriate filter options for rejecting this particular disturbance.
Justify your choice (advantages)
Choose the dimension of your filter in order to attenuate by 20 dB

Homework Equations



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The Attempt at a Solution


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I hesitate between two approachs: using a expansion chamber with transmitted power formula
= 4 / ( 4cos²(kl)+ (A1/A2 +A2/A1)²sin²(kl) ) where A area of the duct and A2 area of the chamber and l length of the chamber, and getting a transmitted value in order to attenuate 20dB, in the lectures the expansion chamber was not presented as a filter so maybe it is completely stupid thie approach

the other idea is using a helmotz band stop resonnator but then it become possible to attenuate completely 250Hz by designing a helmotz resonnator with resonnance frequency equal to 250Hz, so i don't understand why it is asked to attenuate 20dB

In both case i don't know what means "its spectrum consists of odd harmonics only" and how to use this.

Happy end of year for everybody (sorry for my english i am not a native english speacker)
 
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  • #2
Sorry I can't quite make the leap to acoustics just now, but if it were a problem in electrical engineering, involving a transmission line, we might use a stub of transmission line shunted across the main line. By choosing a suitable length, the fundamental and odd harmonics can be reduced greatly.
 
  • #3
It's okay i solved it by using expansion chamber, when it attenuates a frequency f0 (at maximum attenuation) it is possible to show that it attenuates the same each odd harmonics (2n+1)*f0, so the expansion chamber is the good filter
 

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