Wavelength of A4

Problem

A sound in air at $20\;^\circ\mathrm{C}$ ($v \approx 343\;\mathrm{m/s}$) has frequency $440\;\mathrm{Hz}$ (A$_4$). Calculate the wavelength and compare it with the dimensions of a person.

Solution

Setup. Fundamental wave relation:

$\lambda = \frac{v}{f}$

Substitution.

$\lambda = \frac{343}{440}\;\mathrm{m}$

$\ev{\lambda \approx 0{,}78\;\mathrm{m}}$

Comparison. The wavelength of A$_4$ is about $78\;\mathrm{cm}$, of the same order of magnitude as a person’s height (roughly half). This is why sound, with waves on a “human” scale, easily bends around obstacles such as the body or furniture (diffraction).

Links

Topics: Onde Concepts: Periodo e frequenza Skills: Analisi dimensionale