Question

A guitar string is 110 cm long and has a mass of 2.80 g. From the bridge to the support post (L) is 65 cm, and the string is under a tension of 430 N. What is the frequency of the first overtone?

Answer 1

Given Data

mass , m = 2.80 g = 2.8x10^-3 kg

Length, l = 110 cm = 110 x 10^-2 m

support post (L) = 65 cm = 65 x 10^-2 m = 0.65 m

tension, T = 430 N

Solution : -

linear mass density, μ = m/l

                                 = 2.8x10^-3/110 x 10^-2

                                 = 2.545 x 10^-3kg/m

v = √(T/μ)

   =√(430 / 2.545x10^-3 )

   = 411 m/s

v₀ = v/2L

    = 411 / (2 x 0.65)

    = 316.2 Hz fundamental overtone

first overtone is

v₁ = 2 v₀= 632 Hz