Saturday, October 1, 2022
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Helmholtz resonator revisited

We completed a bottle of wine this night, and I blew throughout the highest as I usually do. (Don’t fear: I solely do that at house. If we’re ever in a restaurant collectively, I received’t embarrass you by blowing throughout the neck of an empty bottle.)

The pitch sounded decrease than I anticipated, so I revisited some calculations I did final 12 months.

As I wrote about right here, a wine bottle is roughly a Helmhotz resonator. The geometric approximation is just not superb, however the pitch prediction often is. A perfect Helmholtz resonator is a cylinder hooked up to a sphere, and a typical wine bottle is extra like a cylinder hooked up to a bigger cylinder. However the method predicting pitch is strong to departures from preferrred assumptions.

As famous earlier than, the method for the basic frequency of a Helmholtz resonator is

the place the variables are as follows:

  • f, frequency in Hz
  • v, velocity of sound
  • A, space of the opening
  • L, size of the neck
  • V, quantity

The opening diameter was 2 cm, the neck size 9 cm, and the amount 750 cm³. All these are typical. The expected frequency is f = 118 Hz. The measured frequency was 106 Hz, measured by the Sonic Instruments telephone app.

The precise frequency was about 10% decrease than predicted. That is about a complete step decrease in musical phrases. I may definitely hear an interval that enormous if I heard the 2 pitches sequentially. However I don’t have excellent pitch, and so I’m skeptical whether or not I may really discover a pitch distinction of that measurement from reminiscence.



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