Closed tube standing wave

[exaramco]

Standing waves have a fundamental frequency equal to 4x the length of the pipe if the pipe is closed at one end and open at the other end.

So, blowing across the top of a 33.2 cm bottle should produce a fundamental frequency of v/4L or about 340/1.2= 283 hz. When I record the sound produced by this bottle and then run a spectral analysis (I have done this several times) sampling at both 1000 hz and 44khz I consistently get a fundamental frequency of 96 hz with harmonics at multiples of 96 hz. A closed end tube should produce only odd harmonics.

What is going on?

 

[maimonides]

A bottle is not a pipe.
A bottle often works as a Helmholtz resonator.
This is probably what happened in your experiment.

 

[exaramco]

Right you are! I changed to a pipe and the spectrum came right on target. Thank you.

 

[exaramco]

In fact, when I plugged in the equation for the resonant Helmholts frequency, it came at about 100 hz--just what I measured. Thanks again.

 

[pmacias]

I would first like to commend you on your observations and experimentation. Your understanding of closed tube standing waves is correct in that it produces a fundamental frequency equal to 4 times the length of the pipe. However, there are a few factors that could be contributing to the discrepancy in the frequency you are recording.

Firstly, it is important to note that the fundamental frequency of a closed tube standing wave is not always exactly 4 times the length of the pipe. This is because the speed of sound can vary depending on the temperature, humidity, and composition of the air inside the pipe. So, while theoretically the fundamental frequency should be 283 Hz in your 33.2 cm bottle, in reality it may be slightly different due to these variables.

Secondly, the shape and size of the bottle can also affect the frequency produced. A perfectly cylindrical bottle with smooth edges will produce a more consistent frequency, but if the bottle has any irregularities or is not completely sealed at the closed end, it can affect the standing wave and therefore the frequency produced.

Lastly, it is possible that your recording and spectral analysis equipment may not be accurately capturing the true frequency. There could be background noise or interference that is affecting the results, or the equipment itself may have limitations in accurately measuring high frequencies.

In conclusion, while the fundamental frequency of a closed tube standing wave should be 4 times the length of the pipe, there are various factors that can affect the actual frequency produced. It is important to consider these variables and to use precise equipment and techniques when conducting experiments to accurately measure and analyze the frequency.