Exercise involving acoustics physics engineering

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SUMMARY

The discussion centers on selecting an appropriate filter to reject a disturbance signal in a ventilation duct with a cross-sectional area of 0.04 m² and a fundamental frequency of 250 Hz, which consists solely of odd harmonics. The user concludes that an expansion chamber is the most effective solution for achieving a 20 dB attenuation of the disturbance. The justification lies in the expansion chamber's ability to attenuate not only the fundamental frequency but also its odd harmonics, making it a suitable choice for this acoustics engineering problem.

PREREQUISITES
  • Understanding of acoustics principles, specifically sound propagation in ducts.
  • Familiarity with filter design, particularly expansion chambers and Helmholtz resonators.
  • Knowledge of dB attenuation and its significance in acoustics.
  • Basic grasp of harmonic frequencies and their implications in signal processing.
NEXT STEPS
  • Study the design and application of expansion chambers in acoustics engineering.
  • Learn about Helmholtz resonators and their role in frequency attenuation.
  • Research the mathematical modeling of sound propagation in ducts, focusing on odd harmonics.
  • Explore practical applications of dB attenuation in various engineering fields.
USEFUL FOR

Acoustics engineers, sound designers, and students studying physics or engineering disciplines focused on noise control and signal processing will benefit from this discussion.

louisnach
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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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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.
 
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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