How Does Changing a Hole in a Pipe Affect Its Resonant Frequency?

[jmason52]

This is more a clarification concerning harmonics, I think. :)

The problem is thus: If a hole in a pipe changes the resonant frequency of the pipe by a factor of 2, what is the new frequency.

My confusion: I think this is a simple harmonics question, but I am confused by the term "factor of 2". Does this mean: f2 = 2*f1 indicating it is the Second Harmonic, or does it mean an increase of 2 harmonics, making it f2 = 3*f1? I guess then, my question is: does 1 level of factor = 1 harmonic?

Thanks for the help/opinions!

 

[jbsteele]

No, one level of factor does not equal one harmonic. A factor of two would imply that the new frequency is twice the original frequency, or two times the fundamental frequency. This means that the new frequency is the second harmonic (2f1).