Solve Homework: Sound Waves Lengths in Tube w/ 85cm Guitar String

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SUMMARY

The discussion centers on calculating the possible lengths of a closed tube that produces sound from a guitar string vibrating at its fundamental frequency of 350Hz. Given the string's length of 85cm and a wave speed of 1000m/s, the wavelength is determined to be 1.7m. The frequency of the sound wave in the tube is calculated to be 588.2Hz, indicating that the tube must resonate at this frequency to amplify the sound produced by the string.

PREREQUISITES
  • Understanding of wave mechanics, specifically the relationship between speed, wavelength, and frequency.
  • Knowledge of fundamental frequency and harmonic series in string instruments.
  • Familiarity with closed tube resonance and its implications on sound production.
  • Basic algebra for solving equations related to wave properties.
NEXT STEPS
  • Research the principles of wave propagation in different media, focusing on sound waves.
  • Learn about the harmonic series in closed tubes and how to calculate resonant frequencies.
  • Explore the effects of tension on the frequency of vibrating strings and its mathematical representation.
  • Study the relationship between wavelength and tube length for closed tube resonators.
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as musicians and sound engineers interested in the acoustics of string instruments and tube resonators.

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Homework Statement


A guitar string that is 85cm long is plucked. The fundamental frequency of the string is 350Hz. The string's tension is then increased and its wave speed is 1000m/s The string is vibrating at its fundamental frequency and a closed tube is next to it. A loud sound is produced by the tube. What are the possible lengths of the tube?

Homework Equations


speed = wavelength*frequency

The Attempt at a Solution



1000 = wavelength*frequency
wavelength = 0.85(2) = 1.7
1000 = 1.7*f
f = 588.2

I'm not sure what to do next. I know the speed of the wave inside the tube isn't going to be the same as its speed on the guitar string since they're different mediums, but I'm not sure what that speed would be.
 
Physics news on Phys.org
If the sound isoud, what does that tell you about the frequency of the sound wave in relation to the fundamental frequency of the tube?
 

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