Under what tension must the string be placed?

[itryphysics]

Homework Statement

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?

Homework Equations

v = sqrt [T / u]

The Attempt at a Solution

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

T= 99072800 N

Not sure if this is the right approach

 

[mgb_phys]

Right approach - a bit of confusion in the sums.
If the string is vibrating at it's fundamental 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.

 

[natives]

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

..I don't 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 can't 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!

 

[natives]

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

 

[natives]

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

 

[itryphysics]

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

 

[mgb_phys]

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

 

[itryphysics]

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

 

[mgb_phys]

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 wavelength * 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

 

[itryphysics]

Thank you very much mgb phys and natives!