natural frequency

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.