# Under what tension must the string be placed?

1. Nov 18, 2008

### itryphysics

1. The problem statement, all variables and given/known data

The A string on a violin has a fundamental frequency of 440 Hz . The length of the vibrating portion is 32 cm , and it has a mass of 0.38 g . Under what tension must the string be placed?

2. Relevant equations

v = sqrt [T / u]

3. The attempt at a solution

(343 m/s ) ^2 = T / (.32m/.00038kg)

T= 99072800 N

Not sure if this is the right approach

2. Nov 18, 2008

### mgb_phys

Re: violin

Right approach - a bit of confusion in the sums.
If the string is vibrating at it's fundemental the length of the string is half the wavelength. If you draw it, the ends are fixed and there is half a wave between them.

u is mass / length - you have put the units in the answer but not checked that they balance.

Your answer has a force of 100tons on the violin strings, unlikley for a little wooden instrument.

3. Nov 18, 2008

### natives

Re: violin

..I dont know,I kinda got the answer as 94.16 N! Taking the formula for wave in strings {because violin is a string instrument,not an organ pipe instrument so you cant use v as velocity of sound in air as when it would be with organ pipe instruments but with strings v=fk=2fl where k=lambda(wavelength)}.. f(n)=sqrt(T/û)/2nl..in which case n=1 and û=mass per unit length...I checked several times and result is 94.16 T!

4. Nov 18, 2008

### natives

Re: violin

Meant N (newtons) not T whateva that might cause its not the Tesla!

5. Nov 18, 2008

### natives

Re: violin

Meant N (newtons) not T whateva that might be because its not the Tesla!

6. Nov 18, 2008

### itryphysics

Re: violin

so u worked out the problem I listed and the answer u got was 94.16 N?

When i calculated i got 279 N

someone else, please do a quick run trough so we can determine the error

7. Nov 18, 2008

### mgb_phys

Re: violin

94.16N is correct. Are you sure you converted everything into m , kg ?

8. Nov 18, 2008

### itryphysics

Re: violin

yes...I did it following the approach u suggested ...not the equation that was given by natives... can you please explain why that equation works

Thank you

9. Nov 18, 2008

### mgb_phys

Re: violin

The equation natives wrote is correct.
The speed of sound in a string is sqrt( tension / mass_per_unit length)
Speed of a wave is also wavelenght * frequency.
If you put these together with knowing that the length of the string is half a wavelength you get frequency = (1/2L) * sqrt(T/u)
A bit of rearranging gives you Tension.

The equation is derived here http://en.wikipedia.org/wiki/Vibrating_string

10. Nov 18, 2008

### itryphysics

Re: violin

Thank you very much mgb phys and natives!