# If a sound has a fundamental frequency of 100Hz. What is the frequency of the first 5 harmonics of this tone?

Jun 10, 2014

It will depend on which type of pipe (or air column) the standing wave of sound is produced in.

There are two types of pipe / air column:
1. Open Pipes (open at both ends, e.g. flutes)
2. Closed Pipes (closed at one end, e.g clarinets and saxophones)

The conditions for pipes are: antinodes occur at open ends and nodes occur at closed ends. As the harmonic is increased by one the number of nodes increases by one and the number of antinodes increases by one.

Open Pipes (or strings fixed at both ends)
Fundamental occurs at ${f}_{0}$ (the fundamental is the first harmonic). Harmonics occur at integer multiples of ${f}_{0}$, i.e. $2 {f}_{0} , 3 {f}_{0} , 4 {f}_{0} , 5 {f}_{0}$ etc.

Closed Pipes
Fundamental occurs at ${f}_{0}$. Harmonics occur at odd integer multiples of ${f}_{0}$, i.e. $3 {f}_{0} , 5 {f}_{0} , 7 {f}_{0} , 9 {f}_{0}$ etc.

Practically speaking, the difference between open and closed pipes means that flutes overblow at the octave, while clarinets overblow at the 12th.

If you investigate this further you will see that the wavelength (which you can calculate for a given length of pipe and the location of antinodes and nodes) multiplied by the frequency is equal to a constant. The constant is the speed of the progressive waves that formed the standing wave.