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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 anti-nodes. Thus, unlike a closed pipe, the fundamental frequency and the subsequent overtones increase by one-half of a wavelength. This concept is very hard to understand without looking at the image below. Open_Pipe.png

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

     l=(n/2)wavelength

Where:

      l=length of pipe
      n=nodes

This equation can easily be rearranged to solve for wavelength:

     wavelength=2l/n

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: wavelength=2l/n

= 2(.5m)/1 = 1m 

Then, use substitute the 1m for lambda in the equation f=v/\lambda

f=v/\lambda

= (330m/s)/1m = 330Hz, our final answer.  Great job!

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