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.

I'm saying that frequency increase because as the wave travel upward there is more tension, with more tension there is higher velocity. Can someone help me if its right or not and I'm not sure about the wavelength.

result is right

will stay the same

The frequency will remain the same and the wavelength will increase.

You're partially correct in your reasoning. As the wave travels up the rope, the frequency of the wave would indeed remain the same. The frequency of a wave is determined by the source that is producing it (in this case, you waggling the rope with a constant frequency), and it does not change as the wave propagates through the medium.

However, the wavelength of the wave would change as it travels up the rope. The wavelength is determined by the speed of the wave and the frequency. As you mentioned, there is more tension in the rope as you move up, which means there is a higher velocity of the wave traveling through the rope. With a higher velocity and a constant frequency, the wavelength of the wave would increase.

To summarize:
- Frequency: remains the same because it is determined by the source.
- Wavelength: increases as the wave travels up the rope, due to the higher velocity caused by increased tension.

Note: This explanation assumes there are no other factors, such as the rope's mass or any damping effects, that could influence the behavior of the wave.

the tension is constant through out the string, so your explanation is not valid.