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The most important thing to remember when working with open pipes (what is here referred to as a pipe is any cylindrical solid, i.e. a tube, and "open" is defined as having no obstruction at either end) is that at the two ends are antinodes. Thus, unlike a closed pipe, the fundamental frequency and the subsequent overtones increase by onehalf of a wavelength. This concept is very hard to understand without looking at the image below.
The most simple possibility is the "fundamental frequency" where there is one node in the center of the pipe. The wavelength is 1/2 lambda (λ). The next possibility is the "first overtone". Here, there are two nodes (therefore n=2) and the wavelength is 2/2, or 1λ. Then comes the second overtone, with three nodes, which is 3/2λ.
The equation for finding the length of an open pipe is
Where:
l=length of pipe n=nodes
This equation can easily be rearranged to solve for wavelength:
PracticeEdit
Let's use this equation with a practice problem: Find the fundamental frequency of an open pipe that is .5m long.
To solve this, we need to use two equations. First, solve for lambda:
= 2(.5m)/1 = 1m
Then, use substitute the 1m for lambda in the equation
= (330m/s)/1m = 330Hz, our final answer. Great job!