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From frequency to wavelength
The relation between the frequency and wavelength is given by
![\[ \text{wavelength} = \frac{c}{\text{frequency}} \]](https://skippystudio.nl/wp-content/ql-cache/quicklatex.com-3b41a378fe09ac5a1d3adc8e6862d947_l3.png "Rendered by QuickLaTeX.com")
where 
is the speed of sound in air, which can be calculated by
![\[ c = 20 \sqrt{273 + T}. \]](https://skippystudio.nl/wp-content/ql-cache/quicklatex.com-1bfc5c6e6928bb35124af57af5805220_l3.png "Rendered by QuickLaTeX.com")
Here, T is the temperature in degrees celcius. For T=20, this results in a sound speed of approximately 342 m/s.
I have created an R script (below) to plot the relation between wavelength and frequency on a linear and double logarithmic scale.
Figure 1. Wavelength vs frequency on a linear scale
Figure 2. Wavelength vs frequency on a double logarithmic scale.
Some numbers
| Frequency (Hz) | Approximate wavelength |
| 20 | 17 m |
| 50 | 6.8 m |
| 100 | 3.4 m |
| 500 | 68 cm |
| 1000 | 34 cm |
| 4000 | 8.6 cm |
| 10000 | 3.4 cm |
| 20000 | 1.7 cm |
The lowest note on the standard guitar is E at about 83 Hz (wavelength ~4.1 meter)
The high E4 string =329.6Hz (wavelength ~1 meter)
Piano middle C = 256 Hz (wavelength ~1.3 meter)
Piano middle A = 440Hz (wavelength ~80cm)
See also the wavelength calculator.
Supplementary information
