If you very lightly touch a guitar string at its midpoint, you can hear a tone that is one octave above the fundamental for that string. explain?

Change, increase in note frequency of the sound that comes as a result of the reduction in the vibrating length (wavelength) when the string movement is slightly restricted at its midpoint

Explanation:

When the midpoint of a vibrating guitar string is lightly touched it reduces the wavelength of the guitar string sound, halving it and such increases the the frequency inversely by a factor of 2

The relationship

f = vw/λ, for sound wave where vw is the speed of sound, frequency, f and λ is the wavelength

Frequency varies inversely with wavelength

An Octave

is the frequency vibration of sound-wave twice that of its lower note

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