Finding Mass for a Standing Wave in a Horizontal String

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SUMMARY

The discussion focuses on calculating the mass required to produce standing waves on a horizontal string with a linear density of 4.7 x 10-4 kg/m, attached to a 58 Hz mechanical vibrator. The problem specifies finding the mass for one, two, and five loops of standing waves. Key equations involve wave velocity, wavelength, and frequency, utilizing the linear density provided to derive the necessary mass for each scenario.

PREREQUISITES
  • Understanding of wave mechanics, specifically standing waves
  • Familiarity with the relationship between frequency, wavelength, and wave speed
  • Knowledge of linear density in the context of string physics
  • Basic algebra for solving equations related to mass and wave properties
NEXT STEPS
  • Study the wave equation and its application to standing waves
  • Learn how to calculate wave speed using linear density and tension
  • Explore the relationship between frequency, wavelength, and the number of loops in standing waves
  • Practice problems involving mass calculations for different wave configurations
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to enhance their understanding of standing wave phenomena in strings.

MK7_Ironman
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Homework Statement


One end of a horizontal string of linear density 4.7 multiplied by 10-4 kg/m is attached to a small-amplitude mechanical 58 Hz vibrator. The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11-48. Assume the string at the vibrator is a node, which is nearly true.

11_48.gif


What mass must be hung from this end of the string to produce a standing wave with the following number of loops?

a). one loop: ?
b). two loops: ?
c). five loops: ?

Homework Equations


I don't know how to do this problem that is why I'm asking.


The Attempt at a Solution


I really don't know where to start that is why I need help please!
 
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Welcome to PF :smile:

You'll have to come up with something before receiving help here. How about finding what equations have something to do with wave velocity, wavelength, and frequency?

Also, they gave you the linear density of the string in the problem statement. There's probably an equation that uses that, which will be useful here.
 

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