Lowest Resonant Frequency Issues

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SUMMARY

The discussion focuses on calculating the lowest resonant frequency of a string with a length of 138 cm, mass of 4.98 g, and tension of 6.35 N. The wave speed for this string is confirmed to be 41.9 m/s. The user consistently arrives at a frequency of 30.4 Hz using the formula ƒ = v / λ, but this result is incorrect. The issue lies in the misunderstanding of the relationship between wavelength, frequency, and tension in the context of standing waves on a string.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with the formula for wave speed: v = √(T / μ)
  • Knowledge of frequency and wavelength relationships in wave physics
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Review the derivation of the wave speed formula: v = √(T / μ)
  • Study the concept of fundamental frequency and harmonics in stringed instruments
  • Learn about the relationship between tension, mass per unit length, and frequency in vibrating strings
  • Explore practical examples of calculating resonant frequencies for different string lengths and tensions
USEFUL FOR

Students studying physics, particularly those focused on wave mechanics, as well as musicians and string instrument enthusiasts seeking to understand the physics behind sound production.

Hypnos_16
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Homework Statement



A 138 cm length of string has a mass of 4.98 g. It is stretched with a tension of 6.35 N between fixed supports. What is the wave speed for this string?

What is the lowest resonant frequency of that wave?

(wavelength) = 138cm = 1.38m
M = 4.98g = 0.00498kg
Ft = 6.35N
v = 41.9m/s
(It's a two part question, i already know the speed is right, it's the second half I'm having trouble with)

Homework Equations



I've tried all the equations i can think of that have ƒ in them
(Wavelength) = (1 / ƒ) * ( √(T / µ))

V = (Wavelength) / T
ƒ = 1 / T


The Attempt at a Solution



(Wavelength) = (1 / ƒ) * (√ T / µ)
(Wavelength) = (1 / ƒ) * (v)
(Wavelength) = (1 / ƒ) * (41.9)
(1.38)(41.9) = (1 / ƒ)
(0.0329) = (1 / ƒ)
ƒ = 30.4Hz

that's always the answer i get no matter what i try, and it's always wrong.
What's going on?
 
Physics news on Phys.org
do you play a string instrument such as guitar or violin?
 
No, no i do not.
 

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