Tension In a string Second Harmonic

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Homework Help Overview

The discussion revolves around calculating the tension required for a vibrating string on a musical instrument, specifically when it is in its second overtone. The string's length, mass, and the speed of sound in the environment are provided, along with a target wavelength.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between tension, mass per unit length, frequency, and wavelength. There are attempts to calculate the tension based on the provided data, with some questioning the reasonableness of the results. Others suggest that the frequency might be too high, leading to excessive tension values.

Discussion Status

Participants are actively discussing the calculations and assumptions involved in the problem. Some guidance has been offered regarding the implications of the frequency and the physical characteristics of the string. There is an ongoing examination of the data's validity and its impact on the results.

Contextual Notes

There are concerns about the accuracy of the provided mass and dimensions of the string, as well as the implications of using the speed of sound in the calculations. The discussion reflects uncertainty about the physical feasibility of the calculated tension values.

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 wavelength 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?
 
Last edited:
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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
 
Last edited:
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
 
Last edited:
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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