How Does Tension Affect the Mass and Velocity of a Guitar String?

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SUMMARY

The discussion focuses on the relationship between tension, mass, and wave velocity in a guitar string, specifically a steel B-string resonating at 240 Hertz with a length of 0.620 m. The wave velocity is calculated using the formula V = F(2)L, resulting in a velocity of 297.6 m/s. The tension in the string is given as 84.0 N, which allows for the calculation of mass per unit length, leading to the total mass of a 3 m long piece of the string. The key takeaway is the direct correlation between tension, mass per unit length, and wave speed in stringed instruments.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with the formula V = F(2)L
  • Knowledge of tension in strings
  • Basic principles of mass per unit length
NEXT STEPS
  • Research the derivation of wave velocity formulas in strings
  • Learn about the effects of tension on string vibration frequencies
  • Explore the concept of mass per unit length in different materials
  • Study the harmonic frequencies of guitar strings
USEFUL FOR

Musicians, physics students, and anyone interested in the mechanics of stringed instruments will benefit from this discussion, particularly those looking to understand the physics behind sound production in guitars.

jamielees
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Homework Statement



A typical steel B-string in a guitar resonates at its fundamental frequency at 240 Hertz. The length of the string is 0.620 m. What is the wave velocity along the string? Find your answer in m/s.
V=F(2)L
240(2)(.620)= 297.6

so THEN the question asks;

The tension in the above string is 84.0 N. Calculate the mass of a 3 m long piece of the steel string. Find your answer in kilograms.


we know that ; From the velocity of the wave and the tension we can find the mass per unit length. The total mass is the mass per unit length times length.
I think my formulas are confused. or I'm not sure what formula to use?
 
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jamielees said:
we know that ; From the velocity of the wave and the tension we can find the mass per unit length. The total mass is the mass per unit length times length.
I think my formulas are confused. or I'm not sure what formula to use?

What did you learn is the relation between speed, tension and mass of unit length?

ehild
 

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