Answer
(a) $v = 17.5~m/s$
(b) $\lambda = 0.146~m$
(c) $v = 24.7~m/s$
$\lambda = 0.206~m$
Work Step by Step
(a) We can find the speed of a transverse wave.
$v= \sqrt{\frac{F_T}{\mu}}$
$v= \sqrt{\frac{mg}{\mu}}$
$v= \sqrt{\frac{(1.50~kg)(9.80~m/s^2)}{0.0480~kg/m}}$
$v = 17.5~m/s$
(b) We can find the wavelength.
$\lambda = \frac{v}{f}$
$\lambda = \frac{17.5~m/s}{120~Hz}$
$\lambda = 0.146~m$
(c) We can find the speed of a transverse wave.
$v= \sqrt{\frac{F_T}{\mu}}$
$v= \sqrt{\frac{mg}{\mu}}$
$v= \sqrt{\frac{(3.00~kg)(9.80~m/s^2)}{0.0480~kg/m}}$
$v = 24.7~m/s$
We can find the wavelength.
$\lambda = \frac{v}{f}$
$\lambda = \frac{24.7~m/s}{120~Hz}$
$\lambda = 0.206~m$
Note that the speed and the wavelength increased by a factor of $\sqrt{2}$ after the mass increased by a factor of 2.
