Flow animations for higher harmonics

These animations show how pulses with higher frequencies can produce harmonics in an open pipe. Introductions are given in Open vs closed pipes (Flutes vs clarinets) or Flute acoustics. A pulse of high pressure reflects at the open end of a pipe and returns as a pulse of low pressure. A pulse of hlow pressure reflects as a pulse of high pressure. In a pipe open to the air at both ends, a complete cycle of vibration is the time taken for the pulse to travel twice the length L of the pipe (once in each direction). The pulse travels at the speed of sound v, so the cycle would repeat at a frequency of v/2L.

Note that this situation is not symmetric from right to left. A high density pulse moves from left to right, which is air flow to the right. Then a low density pulse moves from right to left, which is also flow to the right.

What happens if we send pulses with twice the frequency? In the next animation, we send a negative pulse half a period after the positive pulse. Because negative and positive pulses are different, this doesn't change the period. Unlike the animation above, it is symmetrical. A Fourier spectrum of the first animation would have a DC term, whereas this one does not.


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