Pendulum Pipes

Comparing frequencies

Introduction

The frequency of a pendulum is inversely proportional to the square root of its length, while the frequency of a pipe is inversely proportional to its length.

Math Root

The frequency of a pendulum, f, depends on its length, L, and on the acceleration of gravity,g.

f = (1/2p) (g/L)0.5

If the length of the pendulum is cut to 1/4 of its original length the frequency of its swing will double.

The frequency of a tube open at both ends depends on the speed of sound, v.

f = v/2L

If the length of the tube is cut to 1/4 of its original length the frequency quadruples.

If you have two pendulums with lengths PL1 and PL2 and frequencies Pf1 and Pf2 with a ratio Pf2/Pf1

and you want to make two tubes with lengths TL1 and TL2 and the same frequency ratio Tf2/Tf1

Then Pf2/Pf1 = (PL1/PL2)^0.5 = Tf2/Tf1 = TL1/TL2

and TL1/TL2 = (PL1/PL2)^0.5

The ratio of the lengths of the tubes is the square root of the ratio of the lengths of the pendulums.

 Scientific Explorations with Paul Doherty © 2006 21 October 2006