Seemingly simple Physics 2 wave question (third harmonic frequency)

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SUMMARY

The discussion centers on calculating the third harmonic frequency in a physics problem involving wave mechanics. The correct approach requires determining the values of the argument ##\theta## for which ##\sin(\theta) = 1/2##, leading to the calculation of the wave number ##k = 2\pi/\lambda##. The relationship between the wavelength ##\lambda## and the length of the string is crucial for solving the problem. Additionally, clarity in calculations and units is emphasized to avoid confusion in the final answer.

PREREQUISITES
  • Understanding of wave mechanics and harmonic frequencies
  • Knowledge of trigonometric functions, specifically sine values
  • Familiarity with the wave equation and its components
  • Ability to perform unit conversions and dimensional analysis
NEXT STEPS
  • Study the relationship between wavelength and string length in wave mechanics
  • Learn how to derive wave numbers from given parameters
  • Explore the concept of harmonics in vibrating strings
  • Review trigonometric identities and their applications in physics problems
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Students of physics, educators teaching wave mechanics, and anyone involved in solving harmonic frequency problems in wave theory.

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Homework Statement
A string vibrates at its third-harmonic frequency. The amplitude at a point 35 cm from one end is half the maximum amplitude. How long is the string?
Relevant Equations
y=Acos(ωt)sin(kx)
I cannot find the correct answer anywhere online and the answer I keep getting is 5.4 (incorrect)

Please show me the process to get to the answer! Thank you
 
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1. For what values of the argument ##\theta## does ##\sin(\theta)## equal 1/2? 35 cm corresponds to ##kx## having that value. Since you know what ##x## is, that gives you possible values for ##k = 2\pi/\lambda## and therefore you can work out ##\lambda##.

2. For the third harmonic, what is the relationship between ##\lambda## and the length of the string?

3. If you want a comment on your calculations, show your calculations. Saying "I got 5.4" is pointless and carries no information. Also you didn't include any units. Was that 5.4 km? mm? miles? Light years?

It seems to me that as there are multiple answers for my first question, there are multiple answers to this problem.
 

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