Wavelength & Frequency: Thin to Dense Rope

[student85]

When you have a wave traveling through a thin rope and then passing to a denser one, what happens to its wavelength and frequency? What about the opposite process (from heavier to light rope)?

 

[Doc Al]

Hint: What happens to the speed of the wave?

 

[student85]

The speed goes down in the heavier rope. But still, speed equals wavelength times frequency so I don't know which one increases and which one decreases.

 

[Doc Al]

The frequency, which is a property of the source of the wave, remains constant as the wave encounters different densities.

 

[student85]

Thanks Doc.
I had a test last week, which had a question that said a wave traveled through a rope and that afterwards, a second experiment was done on the same rope, now passing a wave with double the frequency as in the first experiment. The question was: What is the speed of the second wave as compared to the first?
At first I chose the answer that said it was doubled up but then I thought about it and remembered the formula v = sq.root(tension/u)
So I thought those variables remained constant as it was the same rope, so I finally chose the option that said the speed didn't change.
But I'm not sure if I got it right.
Did I get it right?

 

[Doc Al]

You got it right: the speed of the wave depends only on the properties of the rope (tension and mass/length). So if those properties don't change, the speed of the wave doesn't change. Good thinking.