The wavelength of the note is [tex]\lambda = 39.1 cm = 0.391 m[/tex]. Since the speed of the wave is the speed of sound, [tex]c=344 m/s[/tex], the frequency of the note is
[tex]f= \frac{c}{\lambda}=879.8 Hz [/tex]
Then, we know that the frequency of a vibrating string is related to the tension T of the string and its length L by
[tex]f= \frac{1}{2L} \sqrt{ \frac{T}{\mu} } [/tex]
where [tex]\mu=0.550 g/m = 0.550 \cdot 10^{-3} kg/m[/tex] is the linear mass density of our string.
Using the value of the tension, T=160 N, and the frequency we just found, we can calculate the length of the string, L:
[tex]L= \frac{1}{2f} \sqrt{ \frac{T}{\mu} } =0.31 m [/tex]
