A guitar string is 90cm long and has a mass of 3.8g . The distance from the bridge to the support post is L=62cm , and the string is under a tension of 540N . What are the frequencies of the fundamental and first two overtones?

Question

A guitar string is 90cm  long and has a mass of 3.8g . The distance from the bridge to the support post is L=62cm , and the string is under a tension of 540N . What are the frequencies of the fundamental and first two overtones?

Elena · Accepted Answer

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=576.8 Hz f2=v/λ₂=v/(2L/3)=3 v/2L=865.2 Hz