Tension in an oscillating string

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SUMMARY

The discussion focuses on calculating the tension in a 120-cm-long string oscillating in its n = 4 mode at a frequency of 150 Hz. The correct formula to use is derived from the wave velocity equations, specifically v = f * λ and v = sqrt(T/(m/L)). The initial attempt yielded a tension of 324 N, which was incorrect due to an assumption of wave velocity. The correct approach requires calculating the wave speed based on the tension and mass per unit length of the string.

PREREQUISITES
  • Understanding of wave mechanics and oscillation modes
  • Familiarity with the formula for wave speed: v = f * λ
  • Knowledge of tension calculation in strings: T = m * v^2 / L
  • Basic algebra for solving equations
NEXT STEPS
  • Study the relationship between frequency, wavelength, and tension in strings
  • Learn about different harmonic modes in oscillating strings
  • Explore the concept of wave speed in various media
  • Review the principles of wave mechanics and their applications in physics problems
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Students studying physics, particularly those focusing on wave mechanics and oscillations, as well as educators looking for examples of tension calculations in strings.

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Homework Statement


A 120-cm-long, 3.0 g string oscillates in its n = 4 mode with a frequency of 150 Hz and a maximum amplitude of 5.5 mm. Wavelength is 0.6 m.

What is the tension in the string?

Homework Equations


f = sqrt(TL/m)/2L


The Attempt at a Solution



150 = sqrt(1.2T/.003)/2.4

Solving for T gives me
T = 324
Which, according to the program(Mastering Physics), is wrong. I'm not sure if this is the right equation, but its the only found I could find that uses all of the information I have, excluding amplitude.
 
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The 2L only works if the string is at the fundamental harmonic. More generally, the velocity of a wave is v = f*l (in which f is frequency and l is wavelength) and v = Sqr(T/(m/L)), in which T is tension, m is mass, and L is string length.
 
Ah, thank you! I got it now. I was assuming 343 m/s for the velocity. Should I not assume, unless the problem explicitly says "through air"?
 

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