Frequency and wavelength of a wave on a vertical rope

In summary, as a wave travels up a rope with constant frequency f, the tension and phase velocity increase. This means that either the frequency or wavelength must increase to balance the equation C = fλ. Since the frequency is stated to be constant, it must be the wavelength that increases. This is supported by considering a series of pulses sent up the rope with a separation of 1 s. If the frequency doubles, the period decreases to 0.5 s, resulting in pulses that are 0.5 seconds apart at the top of the rope.
  • #1
Helloworld
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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


C=√(T/p), C = fλ
f=ω/2π, λ=2π/k

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?
 
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  • #2
Can you perhaps think of any obviously absurd consequences that would result if the frequency was not constant?
 
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  • #3
Orodruin said:
Can you perhaps think of any obviously absurd consequences that would result if the frequency was not constant?

Then maybe the frequency will increase because the period decrease(amplitude of the wave decrease as well)?
 
  • #4
I feel as if you are just guessing rather than thinking it through.

Consider a series of pulses from the bottom to the top sent with a separation of 1 s. How far apart would those pulses be at the top of the rope if frequency increased by a factor of 2?
 
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  • #5
Orodruin said:
I feel as if you are just guessing rather than thinking it through.

Sorry about this. To be honest, I have no clue after the C. I will do more research to answer the question about the pulses
Orodruin said:
Consider a series of pulses from the bottom to the top sent with a separation of 1 s. How far apart would those pulses be at the top of the rope if frequency increased by a factor of 2?
So T = 1/f and if frequency doubled, T would be 0.5s thus 0.5 seconds apart
 
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Related to Frequency and wavelength of a wave on a vertical rope

1. What is the relationship between frequency and wavelength?

The frequency and wavelength of a wave are inversely proportional to each other. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: wavelength = speed of the wave / frequency.

2. How do you measure the frequency and wavelength of a wave on a vertical rope?

The frequency and wavelength of a wave on a vertical rope can be measured using a stopwatch and a ruler. To measure frequency, count the number of complete waves that pass a point in one second. To measure wavelength, measure the distance between two consecutive points on a wave (e.g. from crest to crest).

3. What factors affect the frequency and wavelength of a wave on a vertical rope?

The frequency and wavelength of a wave on a vertical rope are affected by the tension, length, and mass of the rope. Higher tension and shorter length result in higher frequency and shorter wavelength, while higher mass results in lower frequency and longer wavelength.

4. Can the frequency and wavelength of a wave on a vertical rope be changed?

Yes, the frequency and wavelength of a wave on a vertical rope can be changed by altering the tension, length, or mass of the rope. Additionally, the medium through which the wave travels can also affect its frequency and wavelength.

5. How are frequency and wavelength related to the speed of a wave on a vertical rope?

The frequency and wavelength of a wave on a vertical rope are directly proportional to the speed of the wave. This means that as the frequency or wavelength increases, the speed of the wave also increases. This relationship is described by the equation: speed of the wave = frequency x wavelength.

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