Notes on Wave Characteristics and Calculations

Understanding Waves and Their Characteristics

• Definition of Amplitude:

  • Amplitude is defined as the maximum displacement of the medium from its equilibrium position.
  • On the given wave diagram, the equilibrium is represented by a dashed line, and amplitude is half the total height of the wave oscillation.

• Example Calculation of Amplitude:

  • Total height of wave = 1.2 meters.
  • Therefore, Amplitude = (\frac{1.2}{2} = 0.6) meters.
  • The correct answer for the amplitude of the given wave is 0.6 meters (Option A).

• Wave Characteristics:

  • The provided diagram shows two and a half waves with a total length of 8 meters.
  • Wavelength (not requested in this problem) is calculated by dividing the total length by the number of waves, which will be different from both amplitude and total height.

Understanding Standing Waves

• Standing Wave Concept:

  • A standing wave is formed by the interference of two waves traveling in opposite directions.
  • In the case of the standing wave created by two children with a rope, the displayed wave represents only half of a full wave cycle, known as the fundamental frequency or first harmonic.

• Calculating Wavelength from a Standing Wave:

  • The relevant measurement in this problem is given as 4.3 meters, which represents only half the wave length.
  • To find the wavelength, this value must be doubled:
  • Wavelength = (4.3 imes 2 = 8.6) meters (Correct answer is Option D).
  • Approximately 65% of participants answered this correctly.

Transverse Wave Wavelength Determination

• Understanding Wavelength in Transverse Waves:

  • A wave's wavelength is defined as the distance between two corresponding points that are in phase (e.g., crest to crest or trough to trough).
  • An example with points A and G shows that these two points are actually 1.5 waves apart and therefore not a valid measurement for one wavelength.

• Criteria for Identifying Wavelength:

  • For correct identification of the wavelength, two points must complete one full wave cycle.

• Conclusion for Problem Three:

  • Reiterate the necessity of identifying points that are in phase to determine the wavelength accurately.