The fundamental frequency (first harmonic) of a plucked string is given by
f=(1/2L)√(T/ρ)
where L=length, T= tension and ρ=mass/unit length
So we see that the frequency is inversely proportional to the length, and proportion to the square-root of the tension.
If both of them are doubled, then new frequency, f1 is can be obtained by :
f1=f*(1/2)*&radic(2)
=f/&radic(2)
=2048/1.414213562
=1448 Hz approximately
A guitar string is struck and found have a frequency of 2048Hz. If both tension and length are doubled, what is the new frequency of the string?
1 answer