# How to find the tension in a guitar string?

JustinLiang

## Homework Statement

The B-string of a guitar is made of steel (density 7800 kg/m^3), is 63.5 cm long, and has diameter 0.406mm. The fundamental frequency is f = 247.0 Hz. Find the string tension.

F/A = YΔL/L

## The Attempt at a Solution

So I know we have the A, the Young's modulus, and the length. But there is no change in length! So there should be no tension/stress. I have no clue where to start, need some hints!
Also how does frequency have anything to do with the tension? Is it just there to throw you off?

Thanks.

Gold Member
Frequency has a lot to do with tension. The length from the nut to the bridge does not change, but the tension does. You have to adjust the tension in the string using the tuning machine. Higher tension = higher pitch.

Darth Frodo
You should be supplied with the formula..

f = $\frac{1}{2l}$$\sqrt{\frac{T}{\mu}}$

f = frequency
l = length
T = tension
$\mu$ = mass per unit length

JustinLiang
You should be supplied with the formula..

f = $\frac{1}{2l}$$\sqrt{\frac{T}{\mu}}$

f = frequency
l = length
T = tension
$\mu$ = mass per unit length

Wow, never seen that before, I think our prof assigned the wrong question. I talked to a lot of my friends and they have no clue what to do with this question either.

Thanks though, now I know :P

for simple harmonic motion, $F=k x$, where x is the displacement from equilibrium...
Into Newton's Second Law, $m\frac{d^2x}{dt^2}=kx$, you get a differential equation whose solution $x=A\cos(\omega t+\theta_0)$ tells you what
the angular frequency $\omega$ is (and what it depends and doesn't depend on).