Fundamental frequency

Encyclopedia

The

. In terms of a superposition of sinusoids (e.g. Fourier series

), the fundamental frequency is the lowest frequency sinusoidal in the sum.

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 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 lowest value of T for which this is true is called the fundamental period (T

Where is the fundamental frequency and is the fundamental period.

The fundamental frequency of a sound wave in a tube with a single

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

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:

= fundamental frequency

= length of the tube

= velocity of the sound wave

= 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:-

Where:

of the beam

From the radian frequency, the natural frequency,

Where:

while doing the modal analysis of structures and mechanical equipments, the frequency of 1st mode is called fundamental frequency.

**fundamental frequency**, often referred to simply as the**fundamental**and abbreviated**f**, is defined as the lowest frequency of a periodic waveform_{0}Waveform

Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...

. In terms of a superposition of sinusoids (e.g. Fourier series

Fourier series

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a set of simple oscillating functions, namely sines and cosines...

), the fundamental frequency is the lowest frequency sinusoidal in the sum.

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 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 lowest value of T for which this is true is called the fundamental period (T

_{1}) and thus the fundamental frequency (F_{0}) is given by the following equation:Where is the fundamental frequency and 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

Lambda

Lambda is the 11th letter of the Greek alphabet. In the system of Greek numerals lambda has a value of 30. Lambda is related to the Phoenician letter Lamed . Letters in other alphabets that stemmed from lambda include the Roman L and the Cyrillic letter El...

) can be found using the following equation:

The fundamental frequency of a sound wave in a tube with either both ends

**OPEN**or both ends**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:

= fundamental frequency

= length of the tube

= velocity of the sound wave

= wavelength

At 20 °C (68 °F) the speed of sound

Speed of sound

The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....

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

## 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 radian frequency,*ω*_{n}, can be found using the following equation:Where:

*k*= stiffnessStiffness

Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...

of the beam

*m*= mass of weight*ω*_{n}= radian frequency (radians per second)From the radian frequency, the natural frequency,

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

*f*_{n}= natural frequency in hertz (cycles/second)*k*= stiffness of the beam (Newtons/Meter or N/m)*m*= mass at the end (kg)while doing the modal analysis of structures and mechanical equipments, the frequency of 1st mode is called fundamental frequency.

## See also

- Missing fundamentalMissing fundamentalA sound is said to have a missing fundamental, suppressed fundamental, or phantom fundamental when its overtones suggest a fundamental frequency but the sound lacks a component at the fundamental frequency itself....
- Natural frequency
- OscillationOscillationOscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
- HertzHertzThe hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
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- Pitch detection algorithmPitch detection algorithmA pitch detection algorithm is an algorithm designed to estimate the pitch or fundamental frequency of a quasiperiodic or virtually periodic signal, usually a digital recording of speech or a musical note or tone. This can be done in the time domain or the frequency domain.PDAs are used in various...