When do two pulses begin to meet?

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SUMMARY

The discussion centers on calculating the meeting point of two pulses traveling along a wire under tension. The wire has a mass of 140 g and is under a tension of 200 N, leading to a wave speed determined by the formula v = sqrt(T/DENSITY). Pulse 1 is emitted from x = 7.0 m at t = 0, while Pulse 2 is emitted from x = 0 at t = 30.0 ms. The solution involves setting the equations of motion for both pulses equal to find the position x where they meet.

PREREQUISITES
  • Understanding of wave mechanics and pulse propagation
  • Familiarity with kinematic equations
  • Knowledge of tension and density in physical systems
  • Ability to manipulate equations to solve for unknowns
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  • Calculate wave speed using the formula v = sqrt(T/DENSITY) with given values
  • Formulate the equations of motion for both pulses
  • Explore relative motion concepts to simplify the problem
  • Practice similar problems involving wave interactions in different mediums
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Homework Statement


A 140 g wire is held under a tension of 200 N with one end at x = 0 and the other at x = 7.0 m. At time t = 0, pulse 1 is sent along the wire from the end at x = 7.0 m. At time t = 30.0 ms, pulse 2 is sent along the wire from the end at x = 0. At what position x do the pulses begin to meet?


Homework Equations


v=sqrt(T/DENSITY)



The Attempt at a Solution



I assume you set two equations equal, but am unsure how to use the information given to find where they meet
 
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Well, they have the same velocity that you give, but in the opposite direction. Try not to think about them as pulses but as two objects (like cars or something similar) moving towards each other with that velocity and see if you can find some kinematic equation to solve for where the two objects meet. See also if you need to use 7-x instead of x in one of the equations (so you get the distance from the origin for the first object).
 
You could also find the relative velocity of Pulse 2 with respect to Pulse 1 and put the situation in the perspective of Pulse 1. The question then becomes "When does Pulse 2 arrive at x=0 m? (Then you'd have to convert back to the original reference frame.)
 

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