Reflection and Transmission (Waves in strings)

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SUMMARY

The discussion focuses on calculating the mass of a block suspended from two copper wires of different diameters and lengths, which are joined end-to-end. The transverse pulse travels the combined length of 3 meters in 50 milliseconds. The linear mass densities (Mu) for the wires were calculated as 7.0e-3 kg/m for the 1.0 mm diameter wire and 2.8e-2 kg/m for the 2.0 mm diameter wire. The relationship between pulse time, wire length, and wave speed is crucial for determining the tension and ultimately the mass of the block.

PREREQUISITES
  • Understanding of wave mechanics, specifically wave speed and tension in strings
  • Familiarity with linear mass density calculations
  • Knowledge of basic physics equations, including Newton's laws
  • Experience with cylindrical volume calculations and density concepts
NEXT STEPS
  • Calculate wave speed using the formula v = L/T, where L is the length and T is the time
  • Explore the relationship between tension and mass using T = Mu * v^2
  • Investigate the application of sine functions in wave mechanics
  • Review the derivation of linear mass density from volume and density of materials
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics and tension in strings, as well as educators looking for practical examples of these concepts in action.

trusean
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Homework Statement



Two copper wires, one 1.0 mm in diameter and 1.0 m long, the other 2.0 mm in diameter
and 2.0 m long, are joined together end-to-end and hung vertically. In order to tension
this compound wire, a block is suspended from it. It is found that a transverse pulse takes
50 ms to travel the length of the joined wires. What is the mass of the block? The density
of copper is 8920 kg/m3. (Hint: Given the volume mass density and diameters of the
wires, how can we find their linear mass densities?)

Homework Equations



v=square root (T/Mu)
Sum of All Forces=0
V=Pir^2h
d=m/V
Where:
v=wave speed
T=Tension of string/wire
Mu=mass/length of string in units kg/m
V=volume of cylinder
d=density

The Attempt at a Solution



We started by finding Mu with the above equations to be 7.0e-3 kg/m for wire one and 2.8e-2 kg/m for wire two, respectably. What we do not understand is the relationship between the pulse time (50 milli-seconds), length of wire (3m) and the wavespeed. We think that after finding the wavespeed of the pulse we can use Newtons law to find the mass attached to the tensile forces. Any suggestions?
 
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Perhaps using the a sine function and v(wavespeed)=lambda/T(period) we could determine the wavespeed by inputing Pi/2 for T and 50ms for lambda?
 

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