trough

Examples of trough in the following topics:

• The Speed of a Wave on a String

  • Transverse waves have what are called peaks and troughs.
  • The peak is the crest, or top point of the wave and the trough is the valley or bottom point of the wave.
  • Refer to Figure 2 for a visual representation of these terms.The amplitude is the maximum displacement of a particle from its equilibrium position.Wavelength, usually denoted with a lambda (λ) and measured in meters, is the distance from either one peak to the next peak, or one trough to the next trough.Period, usually denoted as T and measured in seconds, is the time it takes for two successive peaks, or one wavelength, to pass through a fixed point.Frequency, f, is the number of wavelengths that pass through a given point in 1 second.
  • Peaks are the top most points of the waves and troughs are the bottom, or valleys of the waves.

• Reflections

  • Transverse waves have what are called peaks and troughs.
  • The peak is the crest, or top point of the wave and the trough is the valley or bottom point of the wave.
  • Wavelength, usually denoted with a lambda (λ) and measured in meters, is the distance from either one peak to the next peak, or one trough to the next trough.
  • This swaps the peaks with the troughs and the troughs with the peaks.

• Conditions for Wave Interference: Reflection due to Phase Change

  • Destructive interference occurs when the crest of one wave meets a trough of another wave.
  • When light is reflected off a medium with a higher index of refraction, crests get reflected as troughs and troughs get reflected as crests.

• Wavelength, Freqency in Relation to Speed

  • The amplitude is half of the distance measured from crest to trough.
  • We also observe the wavelength, which is the spatial period of the wave (e.g. from crest to crest or trough to trough).

• Superposition and Interference

  • When two identical waves arrive at the same point exactly in phase the crests of the two waves are precisely aligned, as are the troughs .
  • If two identical waves that arrive exactly out of phase—that is, precisely aligned crest to trough—they may produce pure destructive interference.

• Transverse Waves

  • The wavelength spans crest to crest while the amplitude is 1/2 the total distance from crest to trough.
  • The amplitude is the 1/2 the distance from crest to trough.

• Aliasing

  • The extrema (peaks and troughs) of a sinusoid of frequency $f_s$ will lie exactly $1/2f_s$ apart.

• Young's Double Slit Experiment

  • Constructive wave interference occurs when waves interfere with each other crest-to-crest (peak-to-peak) or trough-to-trough (valley-to-valley) and the waves are exactly in phase with each other.
  • Destructive wave interference occurs when waves interfere with each other crest-to-trough (peak-to-valley) and are exactly out of phase with each other.

• Standing Waves on a String

  • This swaps the peaks with the troughs and the troughs with the peaks. diagrams a transverse wave on a string that meets a free end.