Frequency and wavelength of vertical string wave

[ming]

Homework Statement

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.

Homework Equations

v=fλ

The Attempt at a Solution

Due to gravity the velocity of the wave should be constantly decreasing as it travels upwards. However, I am not sure whether f decreases, λ decreases or something I have never thought of.

 

[TSny]

Welcome to PF!

Due to gravity the velocity of the wave should be constantly decreasing as it travels upwards.

A ball projected vertically upward will slow down due to gravity. But a wave traveling up the rope might not act like the ball. So, you need to reconsider this.

What properties of the rope determine the speed of a wave on the rope?

 

[ming]

Welcome to PF!
A ball projected vertically upward will slow down due to gravity. But a wave traveling up the rope might not act like the ball. So, you need to reconsider this.

What properties of the rope determine the speed of a wave on the rope?

So the velocity of the wave stays constant. It also seems the tension of the particles on the string increases as you go up as well. I'm guessing wavelength would increase because of this?

 

[TSny]

So the velocity of the wave stays constant.

Why do you say the velocity will remain constant? Did you try to answer the question I posed in post #2?

It also seems the tension of the particles on the string increases as you go up as well.

Yes, the tension increases as you move up the string.