Fix the mistake: Wave Phenomena

Fundamentals of Waves and the Principle of Superposition

A wave is “a phenomenon in which vibrations of a medium are transmitted.” After learning the relationships among wavelength, frequency, and wave speed, as well as the principle of superposition, we will move on to interference and standing waves.

Basic Knowledge

Basic quantities of waves and their relationships:
・Wavelength λ [m]: The length of one crest of a wave (the distance between adjacent points in the same phase)
・Frequency f [Hz]: The number of vibrations per second
・Period T [s]: The time for one vibration T = 1/f
・Wave speed v [m/s]: v = fλ = λ/T
・Amplitude A: The maximum value of displacement

Principle of superposition: When multiple waves pass through the same place, the resultant displacement becomes the sum of the displacements of the individual waves (even when waves collide, they pass through one another without affecting one another).
Independence of waves: Even after superposition, each wave continues to propagate unchanged.

Important Terms
Longitudinal wave（The direction of vibration of the medium is parallel to the direction of propagation. Example: sound waves）
Transverse wave（The direction of vibration of the medium is perpendicular to the direction of propagation. Examples: light and waves on a string）
Phase（The angle representing “which stage” of the periodic change of a wave）
In phase・Out of phase（In phase: displacements are in the same direction; out of phase: displacements are in opposite directions）
Principle of superposition（Resultant displacement = sum of the displacements of the individual waves. Valid in a linear medium）

Further Study (Background・Significance)

v = fλ is a universal relationship for waves. The speed of sound (approximately ~340 m/s in air) varies with the medium (temperature and density), whereas the speed of light is constant in a vacuum at c = 3.0×10⁸ m/s (the basis of the theory of relativity).
Sound, which is a longitudinal wave, travels through liquids and solids, whereas transverse waves travel only through solids. Earthquake P waves (longitudinal) and S waves (transverse) provide evidence of the liquid core inside Earth because of this difference.
The principle of superposition holds only in a linear medium. In nonlinear media (large-amplitude waves, plasmas, and so on), it breaks down precisely, but in ordinary physics problems it is treated as valid.

Key Points
  • v = fλ = λ/T（Required formula）
  • Longitudinal wave = sound; transverse wave = light and waves on a string
  • Superposition: resultant displacement = sum of the individual displacements
  • Independence of waves: waves remain unchanged after passing through one another
  • Waves reinforce in phase and weaken out of phase

Points to Note (Easily Confused)

① Wave speed v is determined by the properties of the medium and does not change with frequency (within the same medium). ② Distinguishing longitudinal and transverse waves: the relationship between the direction of vibration and the direction of propagation. ③ “Amplitude” is the maximum value of displacement and is unrelated to wave speed or frequency. ④ Period T and frequency f are reciprocals: T = 1/f. Pay attention to the units.

Practice

  1. Find the wavelength of a sound wave with a frequency of 440 Hz (speed of sound 340 m/s).
  2. Find the period and frequency of a wave with a wavelength of 2.0 m and a wave speed of 10 m/s.
  3. Explain the difference between longitudinal and transverse waves in terms of the two points “direction of vibration of the medium” and “media through which they can propagate.”

Physics (High School Advanced): related lessons