Answer:
[tex]T=245.76N[/tex]
Explanation:
We know that the frequency of the nth harmonic is given by [tex]f_n=nf[/tex], where [tex]f[/tex] is the fundamental harmonic. Since we have the values of two consecutive frequencies, we can do:
[tex]f_{n+1}-f_n=(n+1)f-nf=nf+f-nf=f[/tex]
Which for our values means (we do not need the value of n, that is, which harmonics are the frequencies given):
[tex]f=f_{n+1}-f_n=480Hz-400Hz=80Hz[/tex]
Now we turn to the formula for the vibration frequency of a string (for the fundamental harmonic):
[tex]f=\frac{1}{2L} \sqrt{\frac{T}{\mu}}[/tex]
So the tension is:
[tex]T=\mu(2Lf)^2[/tex]
Which for our values is:
[tex]T=(0.0006kg/m)(2(4m)(80Hz))^2=245.76N[/tex]
