amplitude

Examples of amplitude in the following topics:

• Energy, Intensity, Frequency, and Amplitude

  • The amount of energy in a wave is related to its amplitude.
  • Large-amplitude earthquakes produce large ground displacements, as seen in .
  • Loud sounds have higher pressure amplitudes and come from larger-amplitude source vibrations than soft sounds.
  • In fact, a wave's energy is directly proportional to its amplitude squared because:
  • The energy effects of a wave depend on time as well as amplitude.

• Interference

  • Interference occurs when multiple waves interact with each other, and is a change in amplitude caused by several waves meeting.
  • In physics, interference is a phenomenon in which two waves (passing through the same point) superimpose to form a resultant wave of greater or lower amplitude.
  • When the waves have opposite amplitudes at the point they meet they can destructively interfere, resulting in no amplitude at that point.
  • By playing a sound with the opposite amplitude as the incoming sound, the two sound waves destructively interfere and this cancel each other out.
  • Pure constructive interference of two identical waves produces one with twice the amplitude, but the same wavelength.

• Radio Waves

  • The abbreviation AM stands for amplitude modulation—the method for placing information on these waves.
  • The resulting wave has a constant frequency, but a varying amplitude.
  • Thus, since noise produces a variation in amplitude, it is easier to reject noise from FM.
  • (c) The frequency of the carrier is modulated by the audio signal without changing its amplitude.
  • Amplitude modulation for AM radio.

• Superposition

  • Superposition occurs when two waves occupy the same point (the wave at this point is found by adding the two amplitudes of the waves).
  • The value of this parameter is called the amplitude of the wave; the wave itself is a function specifying the amplitude at each point.
  • Each disturbance corresponds to a force, or amplitude (and the forces add).
  • That is, their amplitudes add.
  • Constructive interference occurs when two waves add together in superposition, creating a wave with cumulatively higher amplitude, as shown in .

• Forced Vibrations and Resonance

  • As the frequency at which the finger is moved up and down increases, the ball will respond by oscillating with increasing amplitude.
  • Conversely, for small-amplitude oscillations, such as in a car's suspension system, there needs to be heavy damping.
  • Heavy damping reduces the amplitude, but the tradeoff is that the system responds at more frequencies.
  • A child on a swing is driven by a parent at the swing's natural frequency to achieve maximum amplitude.
  • The amplitude of a harmonic oscillator is a function of the frequency of the driving force.

• Driven Oscillations and Resonance

  • The amplitude A and phase φ determine the behavior needed to match the initial conditions.
  • F_0$ is the driving amplitude and $\!
  • \omega_r = \omega_0\sqrt{1-2\zeta^2}$, the amplitude (for a given $\!
  • For strongly underdamped systems the value of the amplitude can become quite large near the resonance frequency (see ).
  • Steady state variation of amplitude with frequency and damping of a driven simple harmonic oscillator.

• Impedance

  • where V is the amplitude of the AC voltage, j is the imaginary unit (j2=-1), and $\omega$ is the angular frequency of the AC source.
  • Thus the resistor's voltage is a complex, as is the current with an amplitude $I = \frac{V}{R}$.
  • The amplitude of this complex exponential is $I = j \omega CV$.
  • The magnitude of the complex impedance is the ratio of the voltage amplitude to the current amplitude.
  • We see that the amplitude of the current will be $V/Z = \frac{V}{\sqrt{R^2+(\frac{1}{\omega C})^2}}$.

• Wavelength, Freqency in Relation to Speed

  • Waves are defined by its frequency, wavelength, and amplitude among others.
  • The first property to note is the amplitude.
  • The amplitude is half of the distance measured from crest to trough.
  • Finally, the group velocity of a wave is the velocity with which the overall shape of the waves' amplitudes — known as the modulation or envelope of the wave — propagates through space.

• Resonance in RLC Circuits

  • Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies—in an RLC series circuit, it occurs at $\nu_0 = \frac{1}{2\pi\sqrt{LC}}$.
  • Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others.
  • Frequencies at which the response amplitude is a relative maximum are known as the system's resonance frequencies.
  • The driving AC voltage source has a fixed amplitude V0.

• The Simple Pendulum

  • A simple pendulum acts like a harmonic oscillator with a period dependent only on L and g for sufficiently small amplitudes.
  • Using this equation, we can find the period of a pendulum for amplitudes less than about 15º.
  • If θ is less than about 15º, the period T for a pendulum is nearly independent of amplitude, as with simple harmonic oscillators.
  • For amplitudes larger than 15º, the period increases gradually with amplitude so it is longer than given by the simple equation for T above.
  • For example, at an amplitude of θ0 = 23° it is 1% larger.