A Helmholtz resonator is a rigid container which has an opening to the air surrounding it. A common example of a Helmholtz resonator is a bottle because it has a set volume as well as having an opening which is open to the surrounding air. By considering the Helmholtz resonator as having a neck, such as the neck of a wine bottle, the dynamics of the system may be described. When energy is introduced near the opening of the bottle, for example blowing across it, some of the energy will vibrate the cylindrical plug of air inside the neck of the bottle. This plug of air is assumed to move as a unit. This movement is due to the driving force of blowing across the bottle, the elastic force on the inner end of the plug, and the dissipation force.
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These results can be seen in Figure 1. The frequency results were plotted against the volume of the bottles that was changed by adding water. The results showed that when using the wine bottle, the theoretical calculations were very similar to the experimental results. Since the results agreed, there was a noticeable trend that the smaller the volume, the greater the difference between the theoretical and experimental frequencies. This is due to the indentation at the bottom of the bottle that could make the volume seem …show more content…
For another comparison, another bottle of a different shape was used to compare the theoretical and experimental results. These results are shown in Figure 2 and both results have a similar trend. The theoretical and experimental results had a much larger difference for the jug than the wine bottle, but the results stayed consistently off. Having such a large difference between the two results, showed that the results do agree since trends are similar. This led us to believe that some of the measurements could have been slightly off due to difficulty in measuring the dimensions of the jug.
After testing two different bottles, it was apparent that the Helmholtz resonant frequency equation is an accurate tool when estimating the resonant frequency of Helmholtz resonators. Figure 2: Plot of the frequency vs volume of a jug for theoretical and experimental results.
These results can be seen in Figure 1. The frequency results were plotted against the volume of the bottles that was changed by adding water. The results showed that when using the wine bottle, the theoretical calculations were very similar to the experimental results. Since the results agreed, there was a noticeable trend that the smaller the volume, the greater the difference between the theoretical and experimental frequencies. This is due to the indentation at the bottom of the bottle that could make the volume seem …show more content…
For another comparison, another bottle of a different shape was used to compare the theoretical and experimental results. These results are shown in Figure 2 and both results have a similar trend. The theoretical and experimental results had a much larger difference for the jug than the wine bottle, but the results stayed consistently off. Having such a large difference between the two results, showed that the results do agree since trends are similar. This led us to believe that some of the measurements could have been slightly off due to difficulty in measuring the dimensions of the jug.
After testing two different bottles, it was apparent that the Helmholtz resonant frequency equation is an accurate tool when estimating the resonant frequency of Helmholtz resonators. Figure 2: Plot of the frequency vs volume of a jug for theoretical and experimental results.