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(Index, Outline)

The **fundamental tone**, often referred to simply as the **fundamental** and abbreviated **f _{o}**, is the lowest frequency in a harmonic series.

The **fundamental frequency** (also called a **natural frequency**) of a periodic signal is the inverse of the pitch period length. The pitch period is, in turn, the smallest repeating unit of a signal. One pitch period thus describes the periodic signal completely. The significance of defining the pitch period as the *smallest* repeating unit can be appreciated by noting that two or more concatenated pitch periods form a repeating pattern in the signal. However, the concatenated signal unit obviously contains redundant information.

A 'fundamental bass' is the root note, or lowest note or pitch in a chord or sonority when that chord is in root position or normal form.

In terms of a superposition of sinusoids (for example, fourier series), the fundamental frequency is the lowest frequency sinusoidal in the sum.

To find the fundamental frequency of a sound wave in a tube that has a closed end you will use the equation:

$ F=\frac{V}{4L} $

To find L you will use:

$ L=\frac{\lambda}{4} $

To find λ (lambda) you will use:

$ \lambda = \frac{V}{F} $

To find the fundamental frequency of a sound wave in a tube that has open ends you will use the equation:

$ F=\frac{V}{2L} $

To find L you will use:

$ L=\frac{\lambda}{2} $

To find Wavelength which is the distance in the medium between the beginning and end of a cycle and is found using the following equation: - WAVELENGTH = Velocity/Frequency or

$ -\lambda=\frac{V}{F} $

At 70 °F the speed of sound in air is approximately 1130 ft/s or 340 m/s. This speed is temperature dependent and does increase at a rate of 1.1 ft/s for each degree Fahrenheit increase in temperature.

The velocity of a sound wave at different temperatures:

- V = 343.7 m/s at 20 °C
- V = 331.5 m/s at 0 °C

WHERE:

F = fundamental Frequency

L = length of the tube

V = velocity of the sound wave

λ = wavelength

## See also Edit

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