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

  • damping

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.
  • Forced motion

    • Notice that if you tap it at just the natural frequency $\omega_0$ , your taps are synchronized with the motion, so the energy you apply goes directly into increasing the amplitude of the oscillation.
    • If you swing your legs back and forth with the natural frequency of the swing, you'll get a big amplification of your motion.
    • The forcing function doesn't know anything about the natural frequency of the system and there is no reason why the forced oscillation of the mass will occur at $\omega_0$ .
    • Notice especially what happens if we force the system at the natural frequency: $\omega = \omega_0$ and the amplitude blows up.
    • If we apply a force to a system at its characteristic frequency we should expect a big effect.
  • 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 $\nu_0 = f_0$.
  • Standing Waves and Resonance

    • Standing waves on strings have a frequency that is related to the propagation speed vw of the disturbance on the string.
    • The lowest frequency, called the fundamental frequency, is thus for the longest wavelength, twice the length of the string.
    • The overtones or harmonics are multiples of the fundamental frequency. shows the fundamental mode along with six overtones.
    • A building may be vibrated for several seconds with a driving frequency matching that of the natural frequency of the vibration of the building—producing a resonance resulting in one building collapsing while neighboring buildings do not.
  • Wave Nature of Matter Causes Quantization

    • The wave nature of matter is responsible for the quantization of energy levels in bound systems.
    • If a string was free and not attached to anything, we know that it could oscillate at any driven frequency.
    • Once the string becomes a "bound system" with specific boundary restrictions, it allows waves with only a discrete set of frequencies.
    • The wave nature of matter is responsible for the quantization of energy levels in bound systems.
    • Explain relationship between the wave nature of matter and the quantization of energy levels in bound systems
  • 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.
  • The Photoelectric Effect

    • Study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave-particle duality.
    • Since energy carried by a wave should only depend on its amplitude (and not on the frequency of the wave), the frequency dependence of the emitted electrons' energies didn't make sense.
    • A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect.
    • As the frequency of the incoming light increases, each photon carries more energy, hence increasing the energy of each outgoing photoelectron.
    • The work function satisfies $\phi = h f_0$, where $f_0$ is the threshold frequency for the metal for the onset of the photoelectric effect.
  • Gamma Rays

    • Gamma rays are very high frequency electromagnetic waves usually emitted from radioactive decay with frequencies greater than 1019 Hz.
    • Natural sources of gamma rays on Earth include gamma decay from naturally occurring radioisotopes such as potassium-40, and also as a secondary radiation from various atmospheric interactions with cosmic ray particles.
    • Some rare terrestrial natural sources that produce gamma rays that are not of a nuclear origin, are lightning strikes and terrestrial gamma-ray flashes, which produce high energy emissions from natural high-energy voltages.
    • Gamma rays have characteristics identical to X-rays of the same frequency—they differ only in source.
    • At higher frequencies, γ rays are more penetrating and more damaging to living tissue.
  • Frequency of Sound Waves

    • The perception of frequency is called pitch.
    • The perception of frequency is called pitch.
    • The SI unit of frequency is called a Hertz, denoted Hz.
    • Different species can hear different frequency ranges.
    • Three flashing lights, from lowest frequency (top) to highest frequency (bottom). f is the frequency in hertz (Hz); or the number of cycles per second.
  • Standing Waves in Air Columns

    • This is considered to be a natural vibration of the air column independently of how it is induced.
    • The lowest resonant frequency is called the fundamental, while all higher resonant frequencies are called overtones.
    • Now let us look for a pattern in the resonant frequencies for a simple tube that is closed at one end.
    • The resonant frequencies of a tube closed at one end are:
    • It is interesting that the resonant frequencies depend on the speed of sound and, hence, on temperature.
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