How Is the Length of a String Determined from Wave Properties?

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SUMMARY

The length of a string under tension can be determined using wave properties and the relationship between velocity, frequency, and wavelength. In this discussion, the mass of the string is 9.00 x 10-3 kg, the tension is 120 N, the frequency is 260 Hz, and the wavelength is 0.60 m. The calculated wave velocity is 156 m/s, which is derived from the equation velocity = frequency * wavelength. To find the length of the string, the formula velocity = sqrt(F/(m/L)) must be applied correctly.

PREREQUISITES
  • Understanding of wave properties, including frequency and wavelength
  • Familiarity with tension in strings and its effect on wave propagation
  • Knowledge of basic physics equations related to wave velocity
  • Ability to manipulate algebraic equations to solve for unknowns
NEXT STEPS
  • Review the derivation of wave velocity from tension and mass per unit length
  • Learn how to apply the wave equation in different scenarios
  • Explore the effects of varying tension and mass on wave speed
  • Investigate real-world applications of wave properties in musical instruments
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to explain the relationship between wave properties and string length.

sheri1987
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Homework Statement



The mass of a string is 9.00 10-3 kg, and it is stretched so the tension in it is 120 N. A transverse wave traveling on this string has a frequency of 260 Hz and a wavelength of 0.60 m. What is the length of the string?

Homework Equations


1)velocity = frequency*wavelength
2)velocity = sqroot(F/(m/L))

The Attempt at a Solution



I thought i needed to calculate the velocity first, so I used the frequency of 260 * wavelength of .6 and got 156 m/s...then I plugged that in for v into the second equation and also 9.00E-3 as the mass and F is equal to the 120 ...what am I doing wrong, I tried solving for L?
 
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Looks like you are correct so far... why do think you are wrong?
Just solve for L, being careful to treat the velocity correctly...
 

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