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Resonance In A Rotating Tube

I must admit I am not sure how this works. In the video I propose that it is the speed of the air moving through the tube that changes the frequency but now I am not so sure. So let’s try and work it out step by step (logically).

What we know: The faster you spin the tube the higher the frequency it resonates at.

What we infer: The faster the tube spins the faster the air is flowing across the mouth of the spinning end of the tube. The end with the fast moving air will produce a zone of lower pressure compared to the more stationary end.

Predict: A pressure differential will cause air to move from the high pressure end of the tube to the low pressure end. This could be what is creating the resonance in the tube, sound wave velocity = frequency times twice the length of the tube (open at both ends). Changing the velocity of the air inside the tube should therefore change the sound wave velocity and therefore the frequency as the tube stays a constant length.

Check prediction: This cannot be the case because it would give a constantly changing frequency as the angular velocity of the pipe changed and this is not the case. The frequencies change in steps and the speed has to be just right to get resonance.

Infer: This therefore means we are dealing with harmonics that relate to the length of the tube and not the speed of the air in the tube. So perhaps it is the air passing the end of the tube that creates a noise at the end of the tube. When the frequency of the noise is such that it meets the resonance criteria that the speed of sound in air/ 2 times the length of the tube is a whole number then resonance happens. Spinning the tube faster changes the frequency of the noise at the spinning end of the tube and the tube resonates when that frequency is “just right” at whole number multiples of the lowest frequency.

Check prediction: This correlates with experience

Infer: The resonant frequencies should therefore change with the temperature of the air as this changes the speed of sound in air.

Check prediction: I have not done this but perhaps you could get your students to try it out. They could record the sound of the pipe as it is whirled on hot days and cold days and see if the resonant frequencies sound the same on both days.

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