The frequency (f) of the note produced by striking a pipe of length (L) and radius (r) is given by f = 2r + c over 2L where c is
the speed of sound, which is mately 13,500 in./sec. The following table shows some frequencies and related pipe lengths for PVC pipe with a radius of 1 in. What length pipe should be used in order to create the lowest note on an 88-key piano (an A), which has a frequency of 27.5 hertz?
Now the aim of the above discussion is to internalize the mathematical relationships for open-end air columns in order to perform calculations predicting the length of air column required to produce a given natural frequency. And conversely, calculations can be performed to predict the natural frequencies produced by a known length of air column. Each of these calculations requires knowledge of the speed of a wave in air (which is approximately 340 m/s at room temperatures). The graphic below depicts the relationships between the key variables in such calculations. These relationships will be used to assist in the solution to problems involving standing waves in musical instruments.
