What is the Tension of a Cello String with Given Frequency and Linear Density?

[RaPiD]

Homework Statement

On a cello, the string has (linear density) m/L = 1.56 x 10^-2 kg/m, and produces frequency of 65.4 Hz and has length of .800 m between the fixed ends. Find the tension.

Homework Equations

v= sqrt(F/(m/L))

v= f (lambda)

The Attempt at a Solution

I first thought to find the velocity first, then plug in the velocity into the first equation and then find the tension. But, then I figured that the length given was the length of the string and not the wavelength so that eliminates using the second equation. Is there another equation to use, that's not occurring to me to find the velocity?

 

[dx]

Your equatoins are correct, but the length of the string is half the wavelength for the fundamental mode, so λ = 2L.

 

[RaPiD]

thanks dx that clears up a lot

 

[dx]

No problem. Welcome to PF.