Frequency of a Plucked Guitar String

If a guitar string is plucked softly, owing to the lesser pressure that is applied the surrounding air particles are displaced by lesser distance. This means that the wavelength which is proportional to the length of this displacement is lesser in this case.However when the same guitar string is plucked hard , since the string is pulled little further the displacement of the air particles surrounding it should also be higher. Does this mean that the wavelength increases in this case because the compression + rarefaction cycle time is higher compared to the previous one ?
- Bharathram (age 34)
India

Bharathram,

To first order the frequency of a plucked string is not affected by the transverse amplitude.  It is dependent on the suspended length of the string.  The usual expression is given by: 

where T is the tension, μ is the mass per unit length and L is its suspended length.   The integer, n, is the mode number and gives rise to higher harmonics.

 

LeeH

(published on 12/17/2014)