Solved: What is the wavelength of a 340-Hz tone in air?

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We need the speed of sound in the air to solve this problem.

Consider the speed of sound in air as, \(\mathrm{v}_{\text {air }}=340 \mathrm{~m} / \mathrm{s}\)

Provided, the frequency of the sound, \(\mathbf{f}=\mathbf{3 4 0} \mathbf{H z}\).

We have to find out the wavelength of the sound wave in the air having a frequency \(340 \mathrm{~Hz}\).

The equation connecting the wavelength " \(\lambda\) ", frequency "f" and the speed of a wave "v" is,

\(\mathbf{v}=\mathbf{n}\)

Rearranging this equation to get the wavelength.

\(\lambda=\mathbf{v} / \mathbf{f}\)

Substituting the values of \(\mathrm{v}\) and \(\mathrm{f}\) in this equation we get,

\(\lambda=340 \mathrm{~m} / \mathrm{s} / 340 \mathrm{~Hz}=1 \mathrm{~m} / \mathrm{s} / \mathrm{Hz}\)

We know that the unit Hertz, \(\mathrm{Hz}=1 /\) second

Therefore, \(\lambda=1 \mathrm{~m} / \mathrm{s} /(1 / \mathrm{s})=1\) metre.