## What if overtone is not achieved?

Lets say there is a experiment to set a stationary wave on a stretched string. If the length of the string is not integer times larger than half of the lengthwave of the propogating wave set up. In other words there is no overtone, would there still be a stationary wave set up?

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 Quote by Mr Checkmate Lets say there is a experiment to set a stationary wave on a stretched string. If the length of the string is not integer times larger than half of the lengthwave of the propogating wave set up. In other words there is no overtone, would there still be a stationary wave set up?
Every possible state of the string is given by a sum of the fundamental and the overtones (the harmonics) at various amplitudes (Fourier series). That means that a wave that cannot be expressed as a sum over the harmonics cannot exist on the string. A wave that was not a sum over the harmonics would not go to zero at each end of the string, and I believe you are referring to a string where its endpoints are held fixed. Once you hold the endpoints fixed, you are limited to only a sum over the standing-wave harmonics.

 this is the operating principle of stringed instruments. Strings can be of varying lengths and they will produce the base tone and harmonics as well depending on where they are plucked.

## What if overtone is not achieved?

i mean what if you force the string to oscillate at a frequency where harmonics is not reached, will a stationary wave be still set up?

 Quote by Mr Checkmate i mean what if you force the string to oscillate at a frequency where harmonics is not reached, will a stationary wave be still set up?
You cannot "force the string to oscillate at a frequency where harmonics is not reached". You cannot do it, its impossible. As long as both ends are fixed, it cannot be done.

 i mean on one end there is a oscillator, meaning one end is not fixed.

 Quote by Mr Checkmate i mean on one end there is a oscillator, meaning one end is not fixed.
If there is some damping, you will eventually get a standing wave with the frequency of the forced oscillations. The closer you are to a resonance frequency, the bigger the amplitude of the wave.

see"
http://physics.nyu.edu/~physlab/GenP...01-26-2010.pdf

 Quote by willem2 If there is some damping, you will eventually get a standing wave with the frequency of the forced oscillations. The closer you are to a resonance frequency, the bigger the amplitude of the wave. see" http://physics.nyu.edu/~physlab/GenP...01-26-2010.pdf
I think willem2 is right.

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