Tension, Linear Mass Density, and transverse waves

In summary, the problem involves a long string under tension with a linear mass density u1 tied to a second string with a much smaller linear mass density u2. Transverse waves are incident on the junction and the goal is to determine what happens to them. The solution requires applying two continuity conditions at the junction, continuity of displacement and continuity of positional derivative of displacement. Alternatively, there may be a formula that can be used instead.
  • #1
SpaceTrekkie
24
0
Not 100% sure if this is supposed to be in Math or Physics...Admin please move if it is wrong...?

Homework Statement



A long string under tension t having linear mass density u1 is tied to a second string with linear mass density u2 << u1. Transverse waves on the heavey string are incident on the junction. Find what happens to them.


Homework Equations



I don't know :(



The Attempt at a Solution



I do know tht when a wave goes through something with a different mass density, it changes the wave speed, but the frequency and amplitude stay the same, but that is all I really understand (and I am not even 100% on that). I think I may just be over thinking the problem, so any direction to start would be awesome.


I know i have been asking a lot of questions, but I don't have a pre-req for this class, so I am trying to learn as I go...and sometimes and getting lost.
 
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  • #2
This is a 1-D wave scattering problem. You must apply two continuity conditions at the junction: continuity of displacement and continuity of positional derivative of displacement. Or, your book may have some formula that you simply plug into, which is a lot less work.

EDIT: sorry, I don't think that is the point of the problem question. Ignore the above.
 
Last edited:

Related to Tension, Linear Mass Density, and transverse waves

What is tension?

Tension is a force that is exerted on an object by pulling or stretching it. In the context of physics, it is often described as the force that resists the stretching of an object.

What is linear mass density?

Linear mass density, also known as linear density, is the measure of mass per unit length of an object. It is typically denoted by the symbol μ and is calculated by dividing the mass of the object by its length.

How are tension and linear mass density related?

Tension and linear mass density are related because the amount of tension in a string or rope is directly proportional to its linear mass density. This means that as the linear mass density increases, so does the tension in the string or rope.

What is a transverse wave?

A transverse wave is a type of wave where the particles of the medium move perpendicular to the direction of the wave's propagation. This means that the disturbance caused by the wave travels in a direction that is perpendicular to the direction of the wave's movement.

How does tension affect transverse waves?

Tension plays a crucial role in determining the speed of a transverse wave. The higher the tension in the medium, the faster the wave will travel. Additionally, tension also affects the frequency and wavelength of transverse waves.

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