Natural Frequency and wavelength

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SUMMARY

The discussion focuses on the natural frequency and wavelength of a piano string, specifically analyzing a string length of 0.50 meters that produces a fundamental frequency of 440 Hz. To play a C note at 528 Hz, the violinist must place their finger 0.083 meters from the bridge, resulting in a new effective length of 0.416 meters. Additionally, it is confirmed that playing a D note at 294 Hz is not possible without returning to the original string length, as the required length exceeds the physical constraints of the string.

PREREQUISITES
  • Understanding of wave mechanics
  • Knowledge of harmonic frequencies
  • Familiarity with the equation V(n)/2L=f
  • Basic principles of string instruments
NEXT STEPS
  • Study the relationship between frequency and wavelength in string instruments
  • Learn about harmonic series in musical acoustics
  • Explore the effects of string tension on pitch
  • Investigate the physics of sound waves in different mediums
USEFUL FOR

Musicians, music educators, physics students, and anyone interested in the acoustics of string instruments will benefit from this discussion.

viciousp
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Homework Statement


The portion of a piano string between the bridge and upper end of the finger board is 0.50 meters long. The string when plucked sounds a note of 440Hz- the first harmonic.

a. where must the violinist put a finder to pay a C note- 528Hz
b Without returning, is it possible to play a D note- 294 Hz


Homework Equations


V(n)/2L=f


The Attempt at a Solution


a.
V(1)/(2)(.5)=440 Hz
V=440 m/s

528=440(1)/2L
L=.416, so the violinist must put his finger up .083 meters

b. 440(1)/2L=294
L=.748 meters, so no he can not.

Does my work make sense?
 
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