Frequency of The Wave
Once the speed of propagation is known, the frequency of the sound produced by the string can be calculated. The speed of propagation of a wave is equal to the wavelength divided by the period, or multiplied by the frequency :
If the length of the string is, the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so is half of the wavelength of the fundamental harmonic. Hence:
where is the tension, is the linear density, and is the length of the vibrating part of the string. Therefore:
- the shorter the string, the higher the frequency of the fundamental
- the higher the tension, the higher the frequency of the fundamental
- the lighter the string, the higher the frequency of the fundamental
Moreover, if we take the nth harmonic as having a wavelength given by, then we easily get an expression for the frequency of the nth harmonic:
And for a string under a tension T with density, then
Read more about this topic: Vibrating String
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