Can Closed Pipes Produce Overtones from a Single Frequency Vibration?

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If you vibrate a tuning fork over a closed pipe (a pipe with one end closed and the other open) is it possible to get overtones in the pipe even thought the tuning fork only vibrates at one frequency
For example if you have a tuning fork of freq 300HZ and you allow it too vibrate above a closed pipe is it possible to get 3 times the frequency e.g. 900Hz?
 
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Because of end effects, the pressure wave is not purely sinusoidal, leading to some overtones. That is why the sound from the pipe has a different quality than the pure tuning fork.
 
Thanks for your reply. That is what I imagined. However wouldn't the overtones be very diminished? I mean would the fundamental frequency appear the loudest?
 
The strength of the overtones would depend on the length/radius of the pipe.
A narrower pipe would have a purer tone, but even a low level of overtones can affect the quality of the sound.