The
fundamental frequency, often referred to simply as the
fundamental and abbreviated
f0, is defined as the lowest frequency of a periodic
waveformWaveform 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 seriesIn 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 (
lambdaLambda 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 soundThe 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,
ωn, can be found using the following equation:
Where:
k =
stiffnessStiffness 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
ωn = radian frequency (radians per second)
From the radian frequency, the natural frequency,
fn, can be found by simply dividing
ωn by 2
π. Without first finding the radian frequency, the natural frequency can be found directly using:
Where:
fn = 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 fundamental
A 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
- Oscillation
Oscillation 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...
- Hertz
The 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....
- Electronic tuner
The term electronic tuner can refer to a number of different things, depending which discipline you wish to study.In the Discipline of radio frequency electronics an electronic tuner is a device which tunes across a part of the radio frequency spectrum by the application of a voltage or appropriate...
- Scale of harmonics
The scale of harmonics is a musical scale based on the noded positions of the natural harmonics existing on a string. This musical scale is present on the guqin, regarded as one of the first string instruments with a musical scale . Most fret positions appearing on Non-Western string instruments ...
- Pitch detection algorithm
A 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...