Transmission of mechanical wave on two different ropes

In summary, two infinite ropes, rope 1 and rope 2, with the same linear density and tension are connected at the origin. A harmonic wave with given amplitude and frequency is traveling towards the origin on one branch of rope 1. The velocities and wavelengths of the transmitted and reflected waves will be the same due to the identical properties of the ropes. However, the amplitudes and average powers of these waves cannot be determined without considering the boundary conditions at the node. The reflection coefficient will not be zero due to the influence of the additional ropes on the transversal force balance. Further analysis is needed to find the amplitudes and powers of the transmitted and reflected waves.
  • #1
Soren4
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Homework Statement


Two infinite ropes, rope 1 and rope 2, of same linear density ##\mu=0.1 kg/m## have the same tension ##T=100N## and lie on the same plane, one perpendicular to the other. The two ropes are connected in the origin. On one of the two branches of rope 1 an harmonic wave is traveling towards the origin. The oscillation are perpendicular to the plane of the ropes with amplitude ##A=3cm## and frequency ##f=5 Hz##. Determine
a) wavelenghts, frequencies and velocities of transmitted and reflected waves
b) amplitudes of transmitted and reflected waves
c) average power of transmitted and reflected waves

Homework Equations


Reflection and transmission coefficients for mechanical waves, see here https://cnx.org/contents/IEH5M2Ue@2/Reflection-and-Transmission-of

The Attempt at a Solution


a) Since ##\mu## and ##T## are the same for all rope, the velocities and wavelenghts are all the same for all the waves (frequency would be the same in any case)

The problem is that I cannot really figure out what happens for points b) and c).

What I'm quite sure about is that there is no reflected wave on the branch where the wave is coming from, because the coefficient of reflection is zero, since ##\mu## is the same in all the rope 1. I'm also quite sure that there is a transmitted wave.

But are waves generated on rope 2? If so, how to find aplitudes and powers?
 
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  • #2
Soren4 said:
What I'm quite sure about is that there is no reflected wave on the branch where the wave is coming from, because the coefficient of reflection is zero, since μμ\mu is the same in all the rope 1. I'm also quite sure that there is a transmitted wave.
The reflection coefficient is not going to be zero because the additional ropes are going to affect the transversal force balance in the node. You need to find the proper boundary conditions at the node and use them to determine what is going on.
 

Related to Transmission of mechanical wave on two different ropes

1. How does a mechanical wave travel on two different ropes?

The transmission of a mechanical wave on two different ropes occurs when one rope is disturbed or set into motion, causing a disturbance in the rope that is connected to it. This disturbance travels through the ropes as a wave, transferring energy from one rope to the other.

2. What factors affect the transmission of a mechanical wave on two different ropes?

The transmission of a mechanical wave on two different ropes can be affected by several factors, including the tension of the ropes, the density and material of the ropes, and the frequency of the wave.

3. Can a mechanical wave travel on two different ropes with different properties?

Yes, a mechanical wave can travel on two different ropes with different properties. However, the speed and amplitude of the wave may be affected by the differences in the properties of the ropes.

4. How does the medium of the ropes affect the transmission of the mechanical wave?

The medium of the ropes plays a crucial role in the transmission of a mechanical wave. The properties of the medium, such as density and elasticity, determine the speed and behavior of the wave as it travels through the ropes.

5. What happens to the mechanical wave when it reaches the end of the ropes?

When a mechanical wave reaches the end of the ropes, it can either be reflected back or transmitted into another medium. The behavior of the wave at the end of the ropes depends on factors such as the tension and density of the ropes, as well as the properties of the medium it is entering.

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