Speed of a transverse on a pulley

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SUMMARY

The discussion centers on calculating the speed of a transverse wave on a rope attached to a tuning fork vibrating at 120Hz, with a mass of 1.50kg hanging over a pulley. The linear mass density of the rope is specified as 0.055kg/m, leading to a calculated wave speed of 16.3m/s as per the textbook answer. The key to solving the problem lies in understanding the relationship between tension in the rope and wave speed, which can be derived from the appropriate wave speed formula.

PREREQUISITES
  • Understanding of wave mechanics, specifically transverse waves
  • Knowledge of tension in ropes and its calculation
  • Familiarity with linear mass density concepts
  • Basic physics involving forces and mass
NEXT STEPS
  • Study the wave speed formula: \( v = \sqrt{\frac{T}{\mu}} \), where T is tension and μ is linear mass density
  • Learn about the effects of frequency on wave speed in different mediums
  • Explore the relationship between tension and mass in pulley systems
  • Review examples of transverse wave problems in physics textbooks
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics and pulley systems, as well as educators looking for problem-solving strategies in wave-related topics.

Andrew Jacobson
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Homework Statement


Hi, I encountered a problem whilst doing problems involving transverse waves. If somebody could give me a pointer I would appreciate it. The question is:

"One end of a horizontal rope is attached to a prong of an electrically driven tuning fork that vibrates the rope transversely at 120Hz. The other end passes over a pulley and supports a 1.50kg mass. The linear mass density of the rope is 0.055kg/m. What is the speed of a transverse wave on rope?"

The answer in the book is 16.3m/s.

Homework Equations

The Attempt at a Solution


If I'm honest I'm struggling to even start. I figure that you have to balance the forces, where the downward force would be 9.81*(1.5+0.055L)N where L is the length of the rope and perhaps you can relate that to the power of the tuning fork and work it out from there? A pointer would be lovely. Thanks.
 
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Nah, there is an expression for the speed of a wave as a function of the tension in a rope. Find it (in your textbook or in your notes, for instance) and you're done.

Tuning fork power would have been provided if that was needed for the exercise. Pulley and weight only serve to get the tension.
 

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