From speed to tension

Problem

You want a string with $\mu = 1\cdot 10^{-3}\;\mathrm{kg/m}$ to have wave speed $v = 200\;\mathrm{m/s}$. Calculate the required tension.

Solution

Setup. From the wave speed on a string $v = \sqrt{T/\mu}$, the tension is found by squaring:

$T = \mu\,v^2$

Substitution.

$T = (1\cdot 10^{-3})\cdot (200)^2 = 10^{-3}\cdot 4\cdot 10^{4}\;\mathrm{N}$

$\ev{T = 40\;\mathrm{N}}$

To double the speed you would need four times the tension: speed grows only as the square root of tension.

Linked atoms

Topics: Onde Concepts: Onda armonica Skills: Analisi dimensionale