Sound

The Speed of Sound

v = f x wavelength

Sound obeys the same wave relation; a clean 170 Hz at 2 m gives 340 m/s, about the real speed of sound in air.

Example

Sound obeys the same wave relation; a clean 170 Hz at 2 m gives 340 m/s, about the real speed of sound in air. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Sound obeys the same wave relation

A sound wave travels at speed equals frequency times wavelength, just like any wave. Its speed is set by the air it moves through, not by how loud or high the note is.

v=f λv = f\,\lambda
A sound wave: pressure against positionA pressure-versus-position curve representing the sound wave in the air.pressure

A worked value near the real speed of sound

A 170 hertz note with a 2 metre wavelength travels at 170 times 2, or 340 metres per second — about the real speed of sound in air, which depends on the air's temperature.

v=f λ=170 Hz ⋅ 2 m=340 m/sv = f\,\lambda = 170\ \text{Hz} \,\cdot\, 2\ \text{m} = \hl{340}\ \text{m}/\text{s}

Same wavelength, higher frequency, faster sound

Hold wavelength fixed. More pressure cycles passing each second means more metres of wave pass each second.

fλv100 Hz2 m200 m/s170 Hz2 m340 m/s200 Hz2 m400 m/s\begin{array}{c|c|c}f & \lambda & v \\ \hline 100\ \text{Hz} & 2\ \text{m} & 200\ \text{m}/\text{s} \\ 170\ \text{Hz} & 2\ \text{m} & 340\ \text{m}/\text{s} \\ 200\ \text{Hz} & 2\ \text{m} & 400\ \text{m}/\text{s}\end{array}

Same frequency, longer wavelength, faster sound

Hold frequency fixed. A longer repeated pressure pattern covers more metres per cycle, so the wave speed is larger.

fλv170 Hz1 m170 m/s170 Hz2 m340 m/s170 Hz3 m510 m/s\begin{array}{c|c|c}f & \lambda & v \\ \hline 170\ \text{Hz} & 1\ \text{m} & 170\ \text{m}/\text{s} \\ 170\ \text{Hz} & 2\ \text{m} & 340\ \text{m}/\text{s} \\ 170\ \text{Hz} & 3\ \text{m} & 510\ \text{m}/\text{s}\end{array}
waves 170 Hz times 2 m is a clean 340 m/s, near the real speed of sound.