# Fundamental frequency

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.

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:

To find L you will use:

To find λ (lambda) you will use:

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

To find L you will use:

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

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, or 0.6 m/s for every increase of 1 °C.

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

## Mechanical systems

Consider a beam, fixed at one end and having a mass attached to the other, this would be a single degree of freedom (SDoF) oscillator. Once set into motion it will oscillate at its natural frequency. For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties; mass and stiffness. The circular natural frequency, *ω*_{n}, can be found using the following equation:

where:

*k* = stiffness of the beam

*m* = mass of weight

*ω*_{n} = circular natural frequency (radians per second)

*f*_{n} = natural frequency in hertz (1/seconds)

From the circular frequency, the natural frequency, *f*_{n}, can be found by simply dividing *ω*_{n} by 2*π*. Without first finding the circular natural frequency, the natural frequency can be found directly using:

## See also

de:Grundfrequenz et:Põhivõnkesagedus nl:Grondtoon (natuurkunde) sv:Grundfrekvens