Tension In a string Second Harmonic

[Punkyc7]

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?

 

[ehild]

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

 

[Punkyc7]

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

ehild

But isn't the force really big?

 

[ehild]

Yes, you are right, it is a very big force, I was mistaken. Are you sure that the data are correct?

ehild

 

[Punkyc7]

thats what i was given but it seems to large to be reasonable

 

[ehild]

I think the frequency is very high, that is why the tension is so impossibly great.

ehild

 

[Punkyc7]

So you can't use the speed of sound as v in this problem?

 

[Punkyc7]

how about a f of 435.44 does that sound more reasonable

that gives me 19698 N which still seems to high

 

[ehild]

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