natural frequency

(noun)

The frequency at which a system vibrates on its own. For a spring (spring constant k) with an object of mass m attached, the natural frequency is given as $f_\mathrm{n} = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$.

Related Terms

Examples of natural frequency in the following topics:

  • Forced Vibrations and Resonance

    • The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance.
    • The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance.
    • A child on a swing is driven by a parent at the swing's natural frequency to achieve maximum amplitude.
    • Unfortunately, heavy winds happened to drive the bridge at its natural frequency, leading to the collapse.
    • Resonance occurs when the driving frequency equals the natural frequency, and the greatest response is for the least amount of damping.

  • Resonance in RLC Circuits

    • Frequencies at which the response amplitude is a relative maximum are known as the system's resonance frequencies.
    • The reactances vary with frequency $\nu$, with XL large at high frequencies and XC large at low frequencies given as:
    • This is also the natural frequency at which the circuit would oscillate if not driven by the voltage source.
    • Resonance in AC circuits is analogous to mechanical resonance, where resonance is defined as a forced oscillation (in this case, forced by the voltage source) at the natural frequency of the system.
    • A variable capacitor is often used to adjust the resonance frequency to receive a desired frequency and to reject others. is a graph of current as a function of frequency, illustrating a resonant peak in Irms at $\nu_0 = f_0$.

  • Population Genetics

    • The allele frequency (or gene frequency) is the rate at which a specific allele appears within a population.
    • If we also know that the frequency of the IB allele in this population is 0.14, then the frequency of the i allele is 0.6, which we obtain by subtracting all the known allele frequencies from 1 (thus: 1 - 0.26 - 0.14 = 0.6).
    • Genetic drift and natural selection usually occur simultaneously in populations, but the cause of the frequency change is often impossible to determine.
    • Natural selection also affects allele frequency.
    • Together, the forces of natural selection, genetic drift, and founder effect can lead to significant changes in the gene pool of a population.

  • Frequency-Dependent Selection

    • In frequency-dependent selection, phenotypes that are either common or rare are favored through natural selection.
    • Another type of selection, called frequency-dependent selection, favors phenotypes that are either common (positive frequency-dependent selection) or rare (negative frequency-dependent selection).
    • In this scenario, orange males will be favored by natural selection when the population is dominated by blue males, blue males will thrive when the population is mostly yellow males, and yellow males will be selected for when orange males are the most populous.
    • In one generation, orange might be predominant and then yellow males will begin to rise in frequency.
    • Frequency-dependent selection allows for both common and rare phenotypes of the population to appear in a frequency-aided cycle.

  • One-Way Tables (Testing Goodness of Fit)

    • Naturally, we do not expect the sample frequencies of the six possible outcomes to be the same since chance differences will occur.
    • This hypothesis is tested by computing the probability of obtaining frequencies as discrepant or more discrepant from a uniform distribution of frequencies as obtained in the sample.
    • We do not really "expect" the observed frequencies to match the "expected frequencies" exactly.
    • Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome, compute
    • It is clear that the observed frequencies vary greatly from the expected frequencies.

  • Genetic Drift

    • Genetic drift is the change in allele frequencies of a population due to random chance events, such as natural disasters.
    • Genetic drift is the converse of natural selection.
    • Unlike natural selection, genetic drift describes the effect of chance on populations in the absence of positive or negative selection pressure.
    • Genetic drift can also be magnified by natural events, such as a natural disaster that kills a large portion of the population at random.
    • When an allele reaches a frequency of 1 (100%) it is said to be "fixed" in the population and when an allele reaches a frequency of 0 (0%) it is lost.

  • Radio Waves

    • Naturally occurring radio waves are made by lightning or by astronomical objects.
    • The lowest commonly encountered radio frequencies are produced by high-voltage AC power transmission lines at frequencies of 50 or 60 Hz.
    • In this case, a carrier wave having the basic frequency of the radio station (perhaps 105.1 MHz) is modulated in frequency by the audio signal, producing a wave of constant amplitude but varying frequency.
    • Other channels called UHF (ultra high frequency) utilize an even higher frequency range of 470 to 1000 MHz.
    • Frequency modulation for FM radio.

  • Hardy-Weinberg Principle of Equilibrium

    • We can also write this as p + q = 1.If the frequency of the Y allele in the population is 0.6, then we know that the frequency of the y allele is 0.4.
    • From the Hardy-Weinberg principle and the known allele frequencies, we can also infer the frequencies of the genotypes.
    • The frequency of homozygous pp individuals is p2; the frequency of hereozygous pq individuals is 2pq; and the frequency of homozygous qq individuals is q2.
    • The frequency of heterozygous plants (2pq) is 2(0.6)(0.4) = 0.48.
    • The genetic variation of natural populations is constantly changing from genetic drift, mutation, migration, and natural and sexual selection.

  • Where Octaves Come From

    • The higher the frequency of a note, the higher it sounds.
    • But to see where octaves come from, let's talk about frequencies a little more.
    • Any note that is twice the frequency of another note is one octave higher.
    • A note that is an octave higher or lower than a note named "C natural" will also be named "C natural".
    • A sound that has a shorter wavelength has a higher frequency and a higher pitch.

  • Cumulative Frequency Distributions

    • A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.
    • A cumulative frequency distribution is the sum of the class and all classes below it in a frequency distribution.
    • Rather than displaying the frequencies from each class, a cumulative frequency distribution displays a running total of all the preceding frequencies.
    • Constructing a cumulative frequency distribution is not that much different than constructing a regular frequency distribution.
    • The second column should be labeled Frequency.