How Do You Calculate the Tension of a Cello String?

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SUMMARY

The tension of a cello string can be calculated using the formula T = (v^2) * μ, where v is the velocity of the string and μ is the linear mass density. In this discussion, the wavelength of the string is determined to be 1.4 meters, calculated from the length of the string (0.70 meters). The velocity is found to be 308 m/s using a frequency of 220 Hz. The resulting tension is calculated to be 186 Newtons, confirming the correctness of the calculations presented.

PREREQUISITES
  • Understanding of wave mechanics and string vibrations
  • Familiarity with the concepts of frequency and wavelength
  • Knowledge of linear mass density (μ) in physics
  • Basic algebra for manipulating formulas
NEXT STEPS
  • Research the relationship between frequency and tension in string instruments
  • Explore the effects of string length on pitch and tension
  • Learn about different materials used for cello strings and their impact on tension
  • Investigate advanced string vibration theories and their applications in acoustics
USEFUL FOR

Musicians, particularly string instrument players, physics students studying wave mechanics, and instrument makers interested in string tension calculations.

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Homework Statement
Compute the musical waves on a plucked cello string using:
frequency of note f = 220 Hz
length of string L = 0.70 m
mass density of string mu = 0.00196 kg/m

What is the tension in the string?
Relevant Equations
tension= (velocity of string)^2 * mu
wavelength of string= 2*L
wavelength of string=2*0.70m= 1.4m
velocity of string= frequency * wavelength
velocity of string= 220Hz * 1.4m= 308 m/s

tension= (308m/s)^2 * 0.00196 kg/m =186N
Is the tension correct?
 
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