Sound & Music - Tension of a string

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SUMMARY

The tension required for the A string of a violin, with a fundamental frequency of 440Hz, a vibrating length of 32.4cm, and a mass of 0.340g, is calculated to be 85.277N. The velocity of the wave on the string was determined to be 285.12 m/s after correcting the wavelength calculation. The mass per unit length (μ) was confirmed to be 0.001049 kg/m, which is essential for accurate tension calculations. Proper unit conversion and significant figures are critical in achieving the correct result.

PREREQUISITES
  • Understanding of wave mechanics, specifically wave velocity and tension equations.
  • Familiarity with the concepts of mass per unit length (μ) in string physics.
  • Knowledge of unit conversions, particularly between grams and kilograms.
  • Ability to apply fundamental frequency concepts in string instruments.
NEXT STEPS
  • Learn about wave velocity calculations in strings and their relationship to tension.
  • Study the impact of mass per unit length on string tension and frequency.
  • Explore the significance of significant figures in scientific calculations.
  • Investigate the physics of string instruments and how tension affects sound quality.
USEFUL FOR

Musicians, physics students, and string instrument makers who are interested in understanding the relationship between tension, frequency, and sound production in stringed instruments.

Torrie
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Homework Statement



  1. The A string on a violin has a fundamental frequency of 440Hz. The length of the vibrating portion is 32.4cm and has a mass of 0.340g. Under what tension must the string be placed?

Homework Equations


V = Fλ
Vs = √t/μ

The Attempt at a Solution


I plugged in my info to determine V = 142.604
then I attempted the second equation as:
T = .340(142.604^2)
This gave me the wrong answer
I also tried:
T = 1.049(142.604^2) - (.340g/.324m = 1.049g/m)
This also gave me the wrong answer. I am not sure what to do
 
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Now I realize that v = 285.12. I forgot to multiple length by 2 to get the wavelength.
But I still can't figure out the second equation
 
Torrie said:
Now I realize that v = 285.12. I forgot to multiple length by 2 to get the wavelength.
But I still can't figure out the second equation
Make sure that your units all match (pay attention to your units for μ).
 
Should μ be kg/m?
So... 0.00034/.324m = .001049kg/m?
 
Torrie said:
Should μ be kg/m?
So... 0.00034/.324m = .001049kg/m?
Yes.
 
Okay so then I have

.001049(285.12^2) = 85.277

So the tension would need to be 85.277N?
 
Looks right to me. Be sure to round to the required number of significant figures.
 
Thank you so much!
 

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