Question

What id the equation for calculating the tension on a violin string (given length, frequency, and linear density)?

Answer 1

QUESTION:

What id the equation for calculating the tension on a violin string (given length, frequency, and linear density)?

ANSWER

We can calculate the tension on a string using Mersenne's law (for fundamental harmonic):

$$f = \frac {1}{2 L} \sqrt {\frac {F}{\mu}}$$

f is the frequency, L is the length of a string, F is a force (tension), and $\mu = \frac{m}{L}$ is linear density of a string (the mass per unit length)

Hence

$$f ^ {2} = \frac {1}{4 L ^ {2}} \frac {F}{\mu}$$ $$F = 4 \mu L ^ {2} f ^ {2}$$

ANSWER

$$F = 4 \mu L ^ {2} f ^ {2}$$