Tension In a string Second Harmonic

AI Thread Summary
The discussion revolves around calculating the tension required for a musical instrument string to achieve a specific frequency in its second overtone. Given a string length of 79 cm and a mass of 8.74 g, the calculated tension of approximately 710,977.38 N appears excessively high, raising concerns about the accuracy of the input data. Participants noted that the high frequency and mass could lead to unrealistic tension values, suggesting that the parameters may not align with typical string specifications. A more reasonable frequency of 435.44 Hz was proposed, but even then, the resulting tension of 19,698 N was still deemed too high. The conversation highlights the importance of accurate data when calculating string tension for musical applications.
Punkyc7
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One string of a certian musical intrument is 79 cm long and it has a mass of 8.74 g. It is being played in a room where the speed of sound is 344m/s
To what tension must you adjust the string so that when vibrating in its second overtone it produces a wavelenght of 3.39 cm

v=sqrt(T/mu)
f=nv/2l
v=lambda f

f=344/.0339=10147.49 hertz

10147.49=v/l=sqrt(T/m/l)/l

which gives me a tension of 710977.38 N which seems to large for a string on an instrument. Is that right?
 
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It is correct. Remember, the tension is force/m2 and the diameter of a string is in the mm range. Multiplying the tension with the cross section area of the string results in a small force.

ehild
 
ehild said:
Multiplying the tension with the cross section area of the string results in a small force.

ehild

But isn't the force really big?
 
Yes, you are right, it is a very big force, I was mistaken. Are you sure that the data are correct?

ehild
 
thats what i was given but it seems to large to be reasonable
 
I think the frequency is very high, that is why the tension is so impossibly great.

ehild
 
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So you can't use the speed of sound as v in this problem?
 
how about a f of 435.44 does that sound more reasonable

that gives me 19698 N which still seems to high
 
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Your solution was correct. The force corresponds to the numerical data given. The given wavelength in air corresponds to a very high frequency.
The mass is also too high. If the string is made of steel, the diameter can be of 1.3 mm.
In case of a guitar string, for example, a typical diameter is of 0.5 mm and the tension of 100 N. But the mass would be about 1 g then.

ehild
 

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