Editing Fundamental frequency (section)

===Fundamental frequency of a pipe===

For a pipe of length <math>L</math> with one end closed and the other end open the wavelength of the fundamental harmonic is <math>4L</math>, as indicated by the first two animations. Hence,
{{block indent|1=<math>\lambda_0 = 4L</math>}}

Therefore, using the relation

{{block indent|1=<math> \lambda_0 = \frac{v}{f_0}</math>}}

where <math>v</math> is the speed of the wave, the fundamental frequency can be found in terms of the speed of the wave and the length of the pipe:

{{block indent|1=<math> f_0 = \frac{v}{4L}</math>}}

If the ends of the same pipe are now both closed or both opened, the wavelength of the fundamental harmonic becomes <math>2L</math> . By the same method as above, the fundamental frequency is found to be

{{block indent|1=<math> f_0 = \frac{v}{2L}</math>}}