Acoustic Resonators for Noise Control
Introduction to Resonators
Acoustic resonators are used to amplify or absorb sound in very specific frequency ranges. Car mufflers and bass traps absorb unwanted noise, while the body of a guitar or a violin amplifies certain frequencies.
While there are many types of acoustic resonators, the two most common are the Helmholtz resonator and the quarter-wave tube. A Helmholtz resonator consists of a neck that leads into a larger volume. One example of this type of resonator is a glass bottle. When blown into, the bottle resonates at a very specific frequency. The fundamental frequency depends on the cross-sectional area and length of the neck, as well as the volume of the cavity.
The response of a Helmholtz resonator can be modeled as a mass-spring system. The plug of air in the neck acts as a mass that moves as you blow into it. The volume of air in the cavity is stretched and compressed like a spring.
A quarter-wave tube is a simple pipe that is open on one end and closed at the other. The fundamental frequency depends on the length of the tube.
When either of these resonators are implemented as a side branch, they absorb sounds at their resonance frequencies.
BYU Resonator Research
Currently, the design of most acoustic resonators is done by trial and error. Our research at BYU is focused on modeling the response of acoustic resonators and arrays of resonators in different applications so little to no tuning needs to be done after fabrication.
We are using higher order approximations for the response of the resonators instead of modeling them as simple mass spring systems. We are also trying to find more accurate representations for end corrections in the neck of the resonator.
Measurement of Transmission Loss
In order to check the accuracy of our model, we measure the transmission loss of the resonators in different configurations using an impedance tube. The impedance tube we use has a loudspeaker on one end and an anechoic termination on the other. We can then place different resonators in parallel with the impedance tube to see how they respond.
Using the two microphone method, the incoming and reflected waves inside the tube can be analyzed separately. The frequencies that do not reach the second pair of microphones were absorbed by the resonators.
As seen below, the preliminary results showed fairly good agreement between the model and measurements, though further improvements are ongoing.
- Fundamentals of Acoustics – Kinsler and Frey Chapter 10
- Engineering Noise Control – Bies and Hansen Chapter 9
- Ingard, K.U. On the theory and design of acoustic resonators
Two Microphone Method:
- Chung, J.Y. Transfer function method of measuring in-duct acousics properties (1980)