Speed on a violin string

Problem

A violin string has linear density $\mu = 5\cdot 10^{-4}\;\mathrm{kg/m}$ and is under tension $T = 80\;\mathrm{N}$. Calculate the speed of transverse waves and compare it with the speed of sound in air.

Solution

Setup. Speed of transverse waves on a string:

$v = \sqrt{\frac{T}{\mu}}$

Substitution.

$v = \sqrt{\frac{80}{5\cdot 10^{-4}}} = \sqrt{1{,}6\cdot 10^{5}}\;\mathrm{m/s}$

$\ev{v \approx 400\;\mathrm{m/s}}$

Comparison. Sound in air travels at $\approx 343\;\mathrm{m/s}$: the wave on the string is slightly faster. Note that $v$ depends only on tension and linear density, not on the frequency at which the string is played.

Links

Topics: Onde Concepts: Onda armonica Skills: Analisi dimensionale