Answer
(a) The tension should be 9.53 N
(b) $v = 20.8~m/s$
Work Step by Step
(a) We can find the required tension.
$\sqrt{\frac{F_T}{\mu}} = \lambda~f$
$F_T = (\lambda~f)^2~\mu$
$F_T = (\lambda~f)^2~(\frac{m}{L})$
$F_T = (0.0333~m)^2(625~Hz)^2~(\frac{0.0165~kg}{0.750~m})$
$F_T = 9.53~N$
The tension should be 9.53 N
(b) We can find the speed of the wave.
$v = \lambda~f$
$v = (0.0333~m)(625~Hz)$
$v = 20.8~m/s$