The **fundamental frequency**, often referred to simply as the **fundamental**, is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids (e.g. Fourier series), the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts, the fundamental is usually abbreviated as ** f_{0}** (or

**FF**), indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as

**, the first harmonic. (The second harmonic is then f**

*f*_{1}_{2}= 2⋅f

_{1}, etc. In this context, the zeroth harmonic would be 0 Hz.)

All sinusoidal and many non-sinusoidal waveforms are periodic, which is to say they repeat exactly over time. A single period is thus the smallest repeating unit of a signal, and one period describes the signal completely. We can show a waveform is periodic by finding some period *T* for which the following equation is true:

Where *x*(*t*) is the function of the waveform.

This means that for multiples of some period T the value of the signal is always the same. The least possible value of T for which this is true is called the fundamental period and the fundamental frequency (*f*_{0}) is:

Where *f*_{0} is the fundamental frequency and *T* is the fundamental period.

The fundamental frequency of a sound wave in a tube with a single **CLOSED** end can be found using the following equation:

*L* can be found using the following equation:

λ (lambda) can be found using the following equation:

The fundamental frequency of a sound wave in a tube with either **BOTH** ends **OPEN** or **CLOSED** can be found using the following equation:

*L* can be found using the following equation:

The wavelength, which is the distance in the medium between the beginning and end of a cycle, is found using the following equation:

Where:

*f*_{0}= fundamental frequency*L*= length of the tube*v*= wave velocity of the sound wave- λ = wavelength

At 20 °C (68 °F) the speed of sound in air is 343 m/s (1129 ft/s). This speed is temperature dependent and does increase at a rate of 0.6 m/s for each degree Celsius increase in temperature (1.1 ft/s for every increase of 1 °F).

The velocity of a sound wave at different temperatures:-

- v = 343.2 m/s at 20 °C
- v = 331.3 m/s at 0 °C

Read more about Fundamental Frequency: Mechanical Systems

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