What is the fundamental frequency of the string?

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SUMMARY

The fundamental frequency of a string measuring 1.4 meters in length is calculated to be 5.5 Hz, based on the difference between successive harmonic frequencies of 18.4 Hz and 23.9 Hz. The wave speed on the string can be determined using the equation v = hf, where h is the harmonic frequency. The relationship between wave speed, frequency, and wavelength is critical, with the wavelength being the distance required to complete one full cycle of the wave.

PREREQUISITES
  • Understanding of harmonic frequencies and their relationships
  • Familiarity with wave speed calculations
  • Knowledge of the formula v = hf
  • Basic concepts of wavelength in wave mechanics
NEXT STEPS
  • Study the relationship between frequency and wavelength in wave mechanics
  • Learn how to apply the formula ω = nπv/L for wave calculations
  • Explore the concept of harmonics in string theory
  • Investigate the effects of string length on wave speed and frequency
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Physics students, educators, and anyone interested in understanding wave mechanics and harmonic frequencies in strings.

mattmannmf
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One of the harmonics on a string 1.4 meters long has a frequency of 18.4 Hz. The next higher harmonic frequency is 23.9 Hz.

(a) What is the fundamental frequency of the string?
f1 = Hz *
5.5 OK

(b) What is the speed of the waves on the string?
v = m/sec

the URL:https://wug-s.physics.uiuc.edu/cgi/cc/shell/DuPage/Phys1201/spring/tma.pl?Ch-14-Waves/wt_fundamental#pr

I found the frequency, but I am just a little confused on how to find the speed. i know i have to use the equation: v=hf. but I am just confused on how to find wavelength... wavelength is the distance it takes to complete a full cycle correct? i don't know where I am going wrong in my calculations
 
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You know the difference between the frequencies of successive harmonics is 5.5 Hz. This difference is a function of v and L, and you already know L.

(Hint: Use ω = nπv/L, you have to convert the angular frequency here to Hertz)
 
Last edited:

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