How to Calculate Wave Velocity in a Tuned Violin String

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SUMMARY

The discussion focuses on calculating the wave velocity in a tuned violin string, specifically one measuring 31.6 cm in length. The string vibrates at frequencies of 880 Hz and 1320 Hz, indicating that the fundamental frequency (f_0) is 440 Hz. Using the formula v = fλ, the calculated wave velocity is approximately 278.08 m/s, which differs slightly from the key's answer of 275 m/s, likely due to rounding discrepancies.

PREREQUISITES
  • Understanding of wave equations, specifically v = fλ
  • Knowledge of fundamental frequency and overtones
  • Familiarity with string length and its impact on wave velocity
  • Basic skills in rounding and significant figures in calculations
NEXT STEPS
  • Research the relationship between frequency and wavelength in string instruments
  • Explore the concept of harmonics and overtones in musical acoustics
  • Learn about the effects of string tension and length on wave velocity
  • Investigate rounding techniques and their implications in scientific calculations
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Musicians, physics students, and educators interested in the acoustics of string instruments and wave mechanics.

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Homework Statement


A tuned violin, with strings of 31.6 cm each, is placed in front of a speaker. When varying the speakers frequency between 500 and 1500 Hz, it was discovered that a certain string only vibrated at 880 Hz and 1320 Hz. Determine the velocity of the wave in this string.


Homework Equations


v=fλ


The Attempt at a Solution


The frequencies has to be overtones or the fundamental tone f_0. That gives nf_0=880 Hz and (n+1)f_0=1320 Hz, so n=2 and f_0=440 Hz. When f=f_0 the string has two nodes so v=f_0*2l (l=0.316m). v=278.08. But the key says 275 m/s, did I do something wrong or have they rounded it weirdly? Thanks
 
Last edited:
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I don't see anything wrong in your solution. It most probably is a case of rounding off weirdly.
 
Last edited:
Adithyan said:
I don't see anything wrong in your solution. It most probably is a case of rounding off weirdly.
Yes, has to be so. Thanks :)
 

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