What if overtone is not achieved?

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?

Rap

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.

jedishrfu

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.

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?

Rap

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.

Mr Checkmate

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

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

Rap

I think willem2 is right.

sophiecentaur

When the string is at or near resonance, energy will build up in the string. When it is away from resonance, the source of energy is mis-matched and little energy actually gets into the vibrations. In the end, the string will just go up and down by the amount of the drive mechanism and there will be no resonance. If the frequency of excitation coincides with one of the overtones then the source has a good match into the string and the standing wave energy will build up. At precisely the right frequency (ies) the matching is best and more energy gets into the standing wave, on either side of that frequency, the standing wave is not 'perfect' and less energy feeds into it.