Question

For a stringed instrument, the tension on each string must be roughly the same to avoid warping. Suppose each string on an acoustic guitar has a tension of 79 N and is 64 cm long. The steel core of the string has a density of 7970 kg/m3.

If the wavelength on a string is twice its length, then what is the linear density for the low E string (f = 82.4 Hz)?

Answer=7.10e-03 kg/m

What is the string's diameter? Traditionally, the diameter is given in inches (1 inch = 2.54 cm). Give your answer in inches; don't enter units ?

Answer 1

Wavelength is given by, λ = 2 x 0.64 = 1.28 m velocity is (v)-hf-128x824-105.47 m/s Again, we have, (where, μ = linear density of the string) Vー 79 v(105.47) 1-7. 1 x 10-3 kg/m Therefore, the required linear density of the string is |μ-7.1x10-3 kg/m Now, we have the relation, ρπ ρπ 7.1x10 7970× π d = 5.32×10-4 m d -0.021inch Therefore, the diameter of the string is d 0.021 inch