Wavelength & Frequency: Thin to Dense Rope

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When a wave transitions from a thin rope to a denser one, its speed decreases, but the frequency remains constant as it is determined by the wave source. The wavelength, however, decreases in this scenario. Conversely, when a wave moves from a denser rope to a lighter one, the speed increases, leading to an increase in wavelength while frequency stays the same. In a test scenario where a second wave with double the frequency is sent through the same rope, the speed remains unchanged because it depends solely on the rope's properties, such as tension and mass per unit length. Therefore, understanding the relationship between wave speed, frequency, and wavelength is crucial for accurate predictions in wave behavior.
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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)?
 
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Hint: What happens to the speed of the wave?
 
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.
 
The frequency, which is a property of the source of the wave, remains constant as the wave encounters different densities.
 
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?
 
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.
 
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