Question

One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates at 125 Hz. The other end passes over a pulley and supports a 1.50 kg mass. The linear mass density of the rope is 5.50×10-2 kg/m .

a.What is the speed of a transverse wave on the rope?
b. What is the wavelength?
c. How would your answers to part (A) change if the mass were increased to 3.00 kg?
d. How would your answers to part (B) change if the mass were increased to 3.00 kg?

Answer 1

a) velocity = sqrt(tension/linear density) = sqrt((1.50 kg *9.8 m/s^2) / (0.0550 kg/m)) = 16.35 m/s
b) wavelength = velocity / frequency = 16.35 m/s / 125 Hz = 0.131 m
c) Since tension would double, it would increase by a factorof sqrt(2).
New velocity = sqrt(2) * 16.35 = 23.12 m/s
New Lambda = sqrt(2) * 0.131 = 0.185 m