Tension and frequency relationship on a violin

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SUMMARY

The discussion centers on the relationship between tension and frequency in violin strings, articulated through the equation T = v²(μ), where T represents tension, v is wave velocity, and μ is mass per unit length. Increasing the tension in a string results in a higher frequency, as demonstrated by the relationship v = fλ, where an increase in frequency (f) leads to an increase in wave velocity (v) and, consequently, tension (T). This principle is fundamental for tuning violin strings by adjusting their tension.

PREREQUISITES
  • Understanding of wave mechanics, specifically wave velocity and frequency.
  • Familiarity with the equation T = v²(μ) and its components.
  • Basic knowledge of string instruments and their tuning methods.
  • Concept of standing waves and their formation on strings.
NEXT STEPS
  • Research the impact of mass per unit length (μ) on string vibration and frequency.
  • Explore the principles of wave mechanics in string instruments.
  • Learn about different methods for tuning string instruments, focusing on tension adjustments.
  • Investigate the relationship between string length and frequency in stringed instruments.
USEFUL FOR

Musicians, particularly string instrument players, physics students studying wave mechanics, and instrument makers interested in the acoustics of stringed instruments.

CAF123
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There is an equation relating the tension in a string fixed between two nodes and the velocity of the traveling waves which form the allowed standing waves. It is T = v^2 (μ) where μ is the mass per unit length.

Am I correct in saying that if the tension in the string increases then frequency also increases? I say ths because v= fλ and if f increases then so does v and subsequently, by the above formula, T.

Thanks.
 
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You are correct. This is how you tune the strings: by adjusting their tension.
 

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