Sinusoidal wave traveling along a composite string

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SUMMARY

A sinusoidal wave traveling along a composite string with differing mass/length densities was analyzed. The incident wave is defined by the equation y_i(x,t)=A_i*sin(wt-k1x). It was concluded that while the frequency of the wave remains constant during transmission and reflection at the junction, the wave number may differ due to the change in medium properties. The entire string is under tension F, which influences wave behavior at the interface.

PREREQUISITES
  • Understanding of wave mechanics, particularly sinusoidal waves
  • Knowledge of mass/length density and its effect on wave propagation
  • Familiarity with wave equations and boundary conditions
  • Concept of tension in strings and its impact on wave speed
NEXT STEPS
  • Study the effects of tension on wave speed in strings
  • Learn about wave reflection and transmission at boundaries
  • Explore the relationship between frequency and wave number in different media
  • Investigate composite materials and their mechanical properties affecting wave behavior
USEFUL FOR

Physics students, mechanical engineers, and anyone studying wave dynamics in composite materials will benefit from this discussion.

golnat
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I've been working on this one for quite some time...

Consider a sinusoidal wave traveling along a string composed of two sections, one with a lighter mass/length density than the other. A pulse is traveling in the light region and about to hit the junction. If the incident wave is given by y_i(x,t)=A_i*sin(wt-k1x), will the transmitted and reflected waves have the same wave number or frequency?
 
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forgot to mention the fact that the whole string is under tension F
 
golnat said:
will the transmitted and reflected waves have the same wave number or frequency?
The frequency remains the same.
 

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