A wave is a phenomenon that transmits energy. The substance itself does not move; vibrations are transmitted. Let us understand the basic properties and types of waves.
Basic Knowledge
Basic elements of waves:
・Amplitude (A): Maximum displacement of a wave. Proportional to the amount of energy
・Wavelength (λ, lambda): Length of one wave [m]
・Period (T): Time required for one wave to pass [s]
・Frequency (f): Number of waves passing per second [Hz]. f = 1/T
・Wave speed (v): v = fλ = λ/T [m/s]
Types of waves:
・Transverse wave: The direction of vibration is perpendicular to the direction of travel. Light, surface water waves, and seismic S-waves
・Longitudinal wave: The direction of vibration is parallel to the direction of travel. Sound waves and seismic P-waves
Longitudinal waves are also called compressional waves because the medium repeatedly becomes rarefied (less dense) and compressed (more dense).
Amplitude (amplitude)（Maximum displacement from the center line of a wave. Unit: m）
Wavelength (wavelength, λ)（Distance between adjacent points in the same phase. Unit: m）
Frequency (frequency, f)（Number of vibrations per second. Unit: Hz）
Period (period, T)（Time required for one vibration. Unit: s）
Transverse and longitudinal waves（Classified according to whether the vibration direction is perpendicular or parallel to the direction of travel）
Compressional wave（Another name for a longitudinal wave. Rarefied and compressed regions alternate）
Further Study (Background and Significance)
The wave-speed formula v = fλ is a very important basic formula. For example, the wavelength of a 440 Hz sound, assuming a sound speed of 340 m/s, is λ = v/f = 340/440 ≒ 0.77 m.
It is easier to understand longitudinal waves when they are shown as transverse-wave diagrams. If compressed regions are marked + and rarefied regions −, a displacement graph can be drawn as the same sine curve as a transverse wave.
Without a medium, waves cannot travel. However, electromagnetic waves (such as light) can travel through a vacuum. In this sense, they are special because they are neither longitudinal nor transverse waves. The speed of light in a vacuum is c = 3.0 × 10⁸ m/s.
Earthquakes produce both P-waves (longitudinal, fast) and S-waves (transverse, slow). P-waves arrive first and cause the “initial tremor,” while S-waves arrive later and cause the “principal motion.” The distance to the focus can be calculated from this time difference.
- Wave speed: v = fλ = λ/T
- Frequency and period: f = 1/T
- Transverse wave: vibration direction ⊥ direction of travel (light, S-waves)
- Longitudinal wave: vibration direction ∥ direction of travel (sound, P-waves)
- Longitudinal wave = compressional wave
- Amplitude determines the amount of energy
- Light travels through a vacuum (electromagnetic wave)
Important Notes (Common Confusions)
① Wavelength λ is the “spatial length” of one wave, while period T is the “time length” of one wave. ② Frequency f and period T are reciprocals (f = 1/T). ③ Wave speed is determined by the properties of the medium and is unrelated to amplitude or frequency. ④ Be careful because graphs of longitudinal waves can cause confusion, such as thinking that “a compressed point has zero displacement.”
Practice
- Find the speed of a wave with a frequency of 200 Hz and a wavelength of 1.7 m.
- Find the frequency of a wave with a period of 0.01 s.
- Is a sound wave transverse or longitudinal?