Tension, Linear Mass Density, and transverse waves

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SUMMARY

The discussion focuses on a physics problem involving transverse waves on two strings with different linear mass densities, specifically a heavy string with density u1 and a lighter string with density u2. The key conclusion is that when a wave transitions from a medium of higher mass density to one of lower mass density, the wave speed changes while frequency and amplitude remain constant. The solution requires applying continuity conditions at the junction of the two strings, specifically the continuity of displacement and the continuity of the positional derivative of displacement.

PREREQUISITES
  • Understanding of transverse waves and wave properties
  • Familiarity with linear mass density concepts
  • Knowledge of wave speed and its dependence on medium properties
  • Ability to apply continuity conditions in wave mechanics
NEXT STEPS
  • Study the relationship between wave speed and linear mass density in strings
  • Learn about continuity conditions in wave mechanics
  • Explore 1-D wave scattering problems in physics
  • Review mathematical derivations of wave behavior at material junctions
USEFUL FOR

Students in physics courses, particularly those studying wave mechanics, as well as educators and tutors looking to clarify concepts related to wave behavior in different media.

SpaceTrekkie
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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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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:

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