A long, heavy rope hangs straight down from a high balcony on an apartment building. The lower end of the rope hangs about 1.0 m above the ground. If you grab onto the lower end and waggle it back and forth with constant frequency f, a wave travels up the rope. What would happen to the frequency and wavelength of the wave as it travels up the rope? For each property, state whether it would increase, decrease or remain the same, and explain briefly.
C=√(T/p), C = fλ
The Attempt at a Solution
The tension increases as we go up the rope since the force at the top is exerted to counteract the weight force of the remaining rope. So the phase velocity C increases meaning that either the frequency or the wavelength must increase to balance the equation C = fλ. The question is, which one will increase? It is stated in the question that the frequency is constant but will it be constant as it travels up the rope?