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| January 11, 2016

• Introduction and Objective:

The objective of the project is to allow students to study and understand the concepts of Helmholtz Resonator Theory. It allows building up students’ skills in manufacturing and vibration analysis field. The students construct two Helmholtz Resonators which made of steel and aluminum in MTSU workshop. Also, another purpose of this project is to help students to figure out and compare between theoretical frequency (calculated) and experimental frequency (tested). Using spectrum analysis and wavelength feature of Audacity software to measure frequency.

• Helmholtz Resonator Theory:

The Helmholtz Resonator design is unique is that it provides as way to construct a physical system that almost completely ignores the effects of damping present in most real-world spring-mass-damper system. In this design, the air mass in the (narrower) neck of the resonator acts as the mass, and the air in the (larger) body provides the spring force for the system, deriving the equation for the frequency of this system gives:

• Design and Fabrication:

The resonator design was devised by prior students and Dr. Sridhara and a set of plans were provided to current students (figure 1).  Students construct two resonators in MTSU machine shop to match these dimensions in figure 1. The two resonators made of 6061 T- Aluminum and Mid Steel. Each of the resonators was produced to the specification provides as accurately as possible. Student use lathe machine to fabricate these resonator. Also, we try to have smooth surface finish inside and outside resonator. The resonator s consists of two parts which upper part (body) and lower pat (cover).  Also, press machine is used to join the upper and lower parts together.

• Design Calculation:

This calculation shows the theoretical calculation of our resonator dimensions and the values of expected frequency:

 Figure 1

• Testing:

Once the resonators were completed and finish all manufacturing process, the resonators were tested by Audacity software. Before testing, we set up program and microphone in proper place to read correctly. For each resonator, the students blew across the open top hole of the resonator and make sure to do not blowing directly into the microphone.  We record two reading for two resonator and check the spectrum for each resonator.

• Discussion of results:

The students are successful in capturing and analyzing data for each of two resonators. The peak frequency for each resonator is shown in Table 1 below. The result shows the steelresonator performed closest to the theoretical frequency (965 Hz). The steel was the furthest from the theoretical at only. During the testing, the pitch of the steel and aluminum resonators was clearly a lower tone.

 Classification of Resonators Frequency Result  in Hz Steel Resonator 891 Aluminum Resonator 818

• Conclusion:

This project proves that changing area of any system provides more damping characteristics due to change in the air mass. Also, the ability of air to compress allows air to have damping properties.  The theoretical frequency of two resonators based on the Helmholtz Equation is 1000 Hz which our frequency results are similar. Also, the most likely cause for this is that the material is in fact having some damping effect on the system due to softness of material. This conclusion supports by the fact that aluminum resonator, which is softer material than steel resonator, had lower frequency than steel resonator.

• Bibliography:

Nudehi, Shahin S. ” Modeling and Experimental Investigation of a Helmholtz Resonator With a Flexible Plate.”  American Society of Mechanical Engineers, January 27, 2013. Web.

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