Answer
(a) $7.60Hz$
(b) $15.2Hz$
(c) increase
Work Step by Step
(a) We can calculate the fundamental frequency as
$v=\sqrt{\frac{F}{u}}$
$\implies v=\sqrt{\frac{22.1}{0.0125/7.66}}=116.4\frac{m}{s}$
Now $f_1=\frac{nv}{2L}$
We plug in the known values to obtain:
$f_1=\frac{1(116.4)}{2(7.66)}=7.60Hz$
(b) The second harmonic frequency can be calculated as
$f_2=\frac{nv}{2L}$
We plug in the known values to obtain:
$f_2=\frac{2(116.4)}{2(7.66)}=15.2Hz$
(c) We know that the wavelength is directly proportional to the square root of the tension and similarly the frequency is directly proportional to the wave speed. Thus, if the tension is increased, the frequencies in part (a) and (b) increase as well.
