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

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To find the tension of a cello string with a linear density of 1.56 x 10^-2 kg/m, a frequency of 65.4 Hz, and a length of 0.800 m, the relationship between wave speed, tension, and linear density is crucial. The velocity of the wave on the string can be calculated using the equation v = sqrt(F/(m/L)), where F is the tension. The length of the string corresponds to half the wavelength for the fundamental frequency, leading to the equation λ = 2L. By substituting the known values into the equations, the tension can be determined. Understanding these relationships is essential for solving the problem accurately.
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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?
 
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Your equatoins are correct, but the length of the string is half the wavelength for the fundamental mode, so λ = 2L.
 
thanks dx that clears up a lot
 
No problem. Welcome to PF.
 

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