Question

A string with a mass per length of 2.00 g/m is stretched between two points that are 0.400 m apart. The second mode of frequency of the stretched string is 50.0 Hz lower than the third mode frequency. What is the tension in the string? Answer is 281 N, not sure of the equations to use.

Answer 1

Are you sure that the values you gave here are correct. Because these are my calculations and they don't match with your ans.
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\(f_\mathrm{n} = \frac{n}{2L} \sqrt{\frac{T}{\mu}}\)
n ==> nth mode
we know,
\(f_\mathrm{2}\) + 50 Hz = \(f_\mathrm{3}\)
or
2* \(f_\mathrm{1} + 50 Hz = 3 \(f_\mathrm{1}\)
==> \(f_\mathrm{1}\) = 50 Hz
==> T = 3.2 N