Wavespeed in a Vibrating String

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SUMMARY

The discussion centers on calculating the number of wavelengths in a vibrating string when the mass is increased from m to 4m. The initial setup includes a tuning fork with a frequency of 388Hz and a string length of 2m, resulting in a wavespeed of 600m/s. The user calculated the tension as 1800N for mass m and 7200N for mass 4m, leading to a velocity of 60m/s and an approximate wavelength of 0.15m. The user incorrectly concluded that 13 wavelengths occupy the string, indicating a misunderstanding in the calculation process.

PREREQUISITES
  • Understanding of wave mechanics, specifically in vibrating strings.
  • Familiarity with the equations for wavelength and wavespeed.
  • Basic knowledge of tension and mass relationships in physics.
  • Ability to manipulate algebraic equations for problem-solving.
NEXT STEPS
  • Review the derivation of the wavelength formula: wavelength = velocity/frequency.
  • Study the impact of tension on wavespeed in a vibrating string.
  • Learn about the relationship between mass, tension, and frequency in wave mechanics.
  • Practice similar problems involving changes in mass and their effects on wave properties.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in wave mechanics, particularly in the context of vibrating strings and tension effects.

k3vination
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Homework Statement


A tuning fork, frequency 388Hz, is mounted vertically on a ring stand. A string of length 2m is attached to the tuning fork, and a mass m is hung at the end of the string. The tuning fork is activated, and a wave passes through the string (wavespeed 600m/s.) Assume the tension does not affect the frequency.

If mass m is replaced with mass 4m, how many wavelengths, or fractions of a wavelength, occupy the string?

Homework Equations


wavelength= velocity/frequency
wavespeed= sqrt[tension/(mass/length)] in a vibrating string


The Attempt at a Solution


Ok, so I used the second equation to isolate T before more mass was added, assuming m=1kg. I found the tension, and it was 1800N. Then I found the wavespeed after the mass was added. Since the mass increased by a factor of 4, I used 7200N as the tension and 4kg as the mass. I found the velocity to be 60m/s. Then I used the first equation to find the wavelength, 0.15m approx. Then I divided 2 by that to find how many whole waves would occupy the string, which was 13, and apparently that is wrong.

I am not sure what I am doing wrong, thanks for helping.
 
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