Natural Frequency and wavelength

AI Thread Summary
The discussion revolves around calculating the positions on a piano string to produce specific musical notes based on their frequencies. For a string length of 0.50 meters vibrating at 440 Hz, the violinist must place a finger 0.083 meters from the bridge to play a C note at 528 Hz. However, to play a D note at 294 Hz, the required string length would need to be 0.748 meters, which is not possible with the given string length. The calculations confirm that the approach to finding the finger placement is correct. Overall, the mathematical reasoning and conclusions drawn from the equations are sound.
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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Yes, looks good.
 
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