What Does Speed Mean in the Context of Standing Waves?

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SUMMARY

The discussion centers on the concept of speed in the context of standing waves, specifically addressing the formula v = √(F_T/(m/L)). The key point is that standing waves are formed by the superposition of two traveling waves moving in opposite directions, exemplified by the equations cos(x - vt) and cos(x + vt). The resulting standing wave can be expressed as 2cos(x)cos(vt), illustrating that while the wave's position does not change, the speed refers to the oscillation of the wave's amplitude over time.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with the formula for wave speed v = √(F_T/(m/L))
  • Knowledge of trigonometric functions and their properties
  • Concept of superposition in wave theory
NEXT STEPS
  • Study the principles of wave superposition in greater detail
  • Explore the derivation and implications of the wave speed formula v = √(F_T/(m/L))
  • Investigate the behavior of traveling waves and their interaction
  • Learn about the applications of standing waves in various physical systems
USEFUL FOR

Students of physics, educators teaching wave mechanics, and anyone interested in the mathematical modeling of waves and their properties.

ahaanomegas
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My Friend and I were discussing standing waves and I made problem about speed, inspired off a concept taught in my Physics book: [itex]v = \sqrt {\frac {F_T}{m/L}}[/itex]. My Friend asked a very valid question: "How in the whole can you defined speed of a standing wave when it's not changing position?" - He understands the formula but not what velocity in a standing wave means. And he stumped me on it. I couldn't find an answer to that question.

Can you?
 
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You can think of a standing wave as the superposition of two traveling waves moving in opposite directions.

For example ##\cos(x - vt)## and ##\cos (x + vt)## are two traveling waves, and their sum is ##\cos(x - vt) + \cos(x + vt) = 2\cos x \cos(vt)## which is a standiing wave.
 

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