The Nature of Waves
Summary
- Properties
- A wave is a disturbance that propagates through a medium.
- Propagation describes the spreading of a disturbance
- Waves transfer energy, momentum, and information, but not mass.
- Classifying Waves by Medium
- Mechanical Waves: matter is the medium
- Sound is a mechanical wave
- Electromagnetic Waves: electric and magnetic fields are the media
- Light is an electromagnetic wave
- Gravitational Waves: the gravitational field is the medium.
(The existence of gravitational waves has not yet been confirmed.)
- Classifying Waves by Orientation
- Transverse Waves: disturbance is perpendicular to the direction of propagation
- All electromagnetic waves are transverse. This includes light.
- Crest: a point of maximal displacement in the positive direction
- Trough: a point of maximal displacement in the negative direction
- Longitudinal Waves: disturbance is parallel to the direction of propagation
- Sound is a longitudinal wave
- Compression or Condensation: a region where the medium is under compression
- Rarefaction or Dilation: a region where the medium is under tension
- Surface Waves or Complex Waves: a combination transverse-longitudinal wave, forms near the surface of some media
- Torsional Waves: disturbance causes the medium to twist
- Classifying Waves by Duration
- adj. episodic; noun pulse: disturbance is momentary and sudden
- adj. periodic, harmonic; noun wave train: disturbance repeats at regular intervals
- Classifying Waves by Appearance
- Traveling Waves: appear to move
- Standing Waves: do not appear to move
- Characteristics
- Amplitude (A) is the maximum absolute value of a periodically varying quantity.
- Amplitude has the unit of the quantity that is changing (ex. displacement, pressure, field strength, etc.)
- Period (T) is the time between successive cycles of a repeating sequence of events.
- T = t/n (time per number of cycles)
- The SI unit of period is the second [s].
- Frequency (ƒ) is the number of cycles of a repeating sequence of events in a unit interval of time.
- ƒ = n/t (number of cycles per time)
- Frequency and period are reciprocals (or inverses) of one another: ƒ = 1/T.
- The SI unit of frequency is the hertz [Hz = 1/s = s−1].
- Phase (ϕ) is the stage of development of a periodic process.
- Two points on a wave with the same phase have the same …
- quantity of disturbance (ex. displacement) and
- rate of change of disturbance (ex. velocity).
- Phase is an angular quantity.
- Adjacent points in phase are separated by one complete cycle.
- Adjacent points out of phase are separated by half a cycle.
- The SI unit of phase is the radian, which is itself a unitless ratio [rad = m/m = Pa/Pa = (V/m)/(V/m) = etc.].
- Wavelength (λ) is the distance between any point on a periodic wave and the next point corresponding to the same portion of the wave measured along the path of propagation.
- Wavelength is measured between adjacent points in phase.
- The SI unit of wavelength is the meter [m].
- Speed (v) is …
- Waves propagate with a finite speed (sometimes called the wave speed) that depends upon …
- the type of wave,
- the composition of the medium, and
- the state of the medium
- v = Δs/Δt the rate of change of distance with time by definition and
- v = ƒλ the product of frequency and wavelength for periodic waves.
- Frequency and wavelength are inversely proportional.
- Lower frequency waves have longer wavelengths.
- Higher frequency waves have shorter wavelengths.
- The speed of a wave is sometimes known as its wave speed
- The SI unit of speed is the meter per second [m/s].
- One-Dimensional Wave Equation
- ƒ (x, t) = A sin (2π (ft − x/λ) + ϕ)
- A, amplitude
- ƒ, frequency
- λ, wavelength
- ϕ, phase
- ƒ (x, t) = A sin (ωt − kx + ϕ)
- A, amplitude
- ω, angular frequency, ω = 2πƒ
- k, wave number k = 2π/λ
- ϕ, phase
