A guitar string is 90 cm long and has a mass of 3.6 g . The distance from the bridge to the support post is L=62cm, and the string is under a tension of 530 N . What are the frequencies of the fundamental and first two overtones?
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v = sqrt(TL₀/m)
=sqrt(540•0.9/0.0038)
=357.6 m/s.
Fundamental frequency f: λ=v/f=2L
f=v/ λ=v/2L
=357.6/2*0.62 = 288.4 Hz.
f1=v/λ₁=v/L=357.6/0.62=576
The fundamental frequency is v/2L
where v = sqrt(T/μ) = sqrt(T*L/m)
= sqrt(520*0.90/0.0038) = 351m/s
So f = 351/(2*0.90) = 195Hz
The next two overtones are 195*2 = 390Hz and 195*3 = 585Hz
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