For a stringed instrument, the tension on each string must be roughly the same t

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 80 N and is 64 cm long. The steel core of the string has a density of 7860 kg/m3.
If the wavelength on a string is twice its length, then what is the linear density for the high E string (f = 329.6 Hz)?

Correct, computer gets: 4.49e-04 kg/m

20. [1pt]
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:

Explanation / Answer

Lambda=1.28m

v=f*lambda=329.6*1.28=421.9m/s

v=sqrt(T/mu)

mu=T/v^2=80/421.9^2

=4.49x10^-4 kg/m

b)mu=rho*A=7860*pi*r^2

r=sqrt(mu/pi/7860)

=1.35*10^-4m

D=2r=2.70*10^-4m

=1.06*10^-2 inches

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