Answer
$f_1=7.91Hz$
Work Step by Step
We know that,
$f=\frac{v}{\lambda}$
For possible wavelengths,, the formula is:
$\lambda=\frac{2L}{n}$
This can be rearranged as:
$f=\frac{nv}{2L}$
As $v=\sqrt\frac{T}{\mu}=\sqrt\frac{TL}{M}$,
so $f_n=\frac{n}{2L}\sqrt\frac{TL}{M}=\frac{n}{2}\sqrt\frac{T}{LM}$
We plug in the known values to obtain:
$f_n=\frac{n}{2}\sqrt\frac{250}{(10)(0.1)}=n(7.91)Hz$
The first lowest frequency is:
$f_1=1(7.91)=7.91Hz$
