Frequency

A pendulum making 25 complete oscillations in 60 s, a frequency of 0.41 Hertz
A pendulum with a period of 2.8 s and a frequency of 0.36 Hz
Diagram of the relationship between the different types of frequency and other wave properties.
Modern frequency counter
Complete spectrum of electromagnetic radiation with the visible portion highlighted
The sound wave spectrum, with rough guide of some applications

Number of occurrences of a repeating event per unit of time.

- Frequency

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Sound

Vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.

A drum produces sound via a vibrating membrane
Spherical compression (longitudinal) waves
A 'pressure over time' graph of a 20 ms recording of a clarinet tone demonstrates the two fundamental elements of sound: Pressure and Time.
Sounds can be represented as a mixture of their component Sinusoidal waves of different frequencies. The bottom waves have higher frequencies than those above. The horizontal axis represents time.
U.S. Navy F/A-18 approaching the speed of sound. The white halo is formed by condensed water droplets thought to result from a drop in air pressure around the aircraft (see Prandtl–Glauert singularity).
Figure 1. Pitch perception
Figure 2. Duration perception
Figure 3. Loudness perception
Figure 4. Timbre perception
Approximate frequency ranges corresponding to ultrasound, with rough guide of some applications

Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans.

Light

Electromagnetic radiation within the portion of the electromagnetic spectrum that is perceived by the human eye.

A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) are separated.
The electromagnetic spectrum, with the visible portion highlighted
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Beam of sun light inside the cavity of Rocca ill'Abissu at Fondachelli-Fantina, Sicily
Due to refraction, the straw dipped in water appears bent and the ruler scale compressed when viewed from a shallow angle.
Hong Kong illuminated by colourful artificial lighting.
Pierre Gassendi.
Christiaan Huygens.
Thomas Young's sketch of a double-slit experiment showing diffraction. Young's experiments supported the theory that light consists of waves.
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Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750-420 terahertz, between the infrared (with longer wavelengths) and the ultraviolet (with shorter wavelengths).

Wave

Propagating dynamic disturbance of one or more quantities.

Surface waves in water showing water ripples
Example of biological waves expanding over the brain cortex, an example of spreading depolarizations.
Wavelength λ, can be measured between any two corresponding points on a waveform
Animation of two waves, the green wave moves to the right while blue wave moves to the left, the net red wave amplitude at each point is the sum of the amplitudes of the individual waves. Note that f(x,t) + g(x,t) = u(x,t)
Sine, square, triangle and sawtooth waveforms.
Amplitude modulation can be achieved through f(x,t) = 1.00×sin(2π/0.10×(x−1.00×t)) and g(x,t) = 1.00×sin(2π/0.11×(x−1.00×t))only the resultant is visible to improve clarity of waveform.
Illustration of the envelope (the slowly varying red curve) of an amplitude-modulated wave. The fast varying blue curve is the carrier wave, which is being modulated.
The red square moves with the phase velocity, while the green circles propagate with the group velocity
A wave with the group and phase velocities going in different directions
Standing wave. The red dots represent the wave nodes
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction (refraction) that results.
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
Schematic of light being dispersed by a prism. Click to see animation.
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Formation of a shock wave by a plane.
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A propagating wave packet; in general, the envelope of the wave packet moves at a different speed than the constituent waves.
Animation showing the effect of a cross-polarized gravitational wave on a ring of test particles
One-dimensional standing waves; the fundamental mode and the first 5 overtones.
A two-dimensional standing wave on a disk; this is the fundamental mode.
A standing wave on a disk with two nodal lines crossing at the center; this is an overtone.

Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency.

Revolutions per minute

Number of turns in one minute.

Counterclockwise rotations about the center point where a complete rotation is equal to 1 turn.

It is a unit of rotational speed or the frequency of rotation around a fixed axis.

Cycle per second

A 1000 kilocycle military grade crystal resonator with an octal base
Crystal resonators, the 1940s-era center unit is marked in kc.

The cycle per second was a once-common English name for the unit of frequency now known as the hertz (Hz).

Second

Base unit of time in the International System of Units (SI) (Système International d’unités), commonly understood and historically defined as 1⁄86400 of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each (24 × 60 × 60 = 86400).

A pendulum-governed escapement of a clock, ticking every second

The second is also part of several other units of measurement like meters per second for speed, meters per second per second for acceleration, and cycles per second for frequency.

Oscillation

Repetitive or periodic variation, typically in time, of some measure about a central value or between two or more different states.

An undamped spring–mass system is an oscillatory system
Two pendulums with the same period fixed on a string act as pair of coupled oscillators. The oscillation alternates between the two.
Experimental Setup of Huygens synchronization of two clocks
Oscillation of a sequence (shown in blue) is the difference between the limit superior and limit inferior of the sequence.

The systems where the restoring force on a body is directly proportional to its displacement, such as the dynamics of the spring-mass system, are described mathematically by the simple harmonic oscillator and the regular periodic motion is known as simple harmonic motion.

Phase (waves)

In physics and mathematics, the phase of a periodic function.

Plot of one cycle of a sinusoidal function. The phase for each argument value, relative to the start of the cycle, is shown at the bottom, in degrees from 0° to 360° and in radians from 0 to 2π.
Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.
Phase shifter using IQ modulator
In-phase signals
Out-of-phase signals
Representation of phase comparison.
Left: the real part of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts.
Out of phase AE

In the adjacent image, the top sine signal is the test frequency, and the bottom sine signal represents a signal from the reference.

Vibration

Mechanical phenomenon whereby oscillations occur about an equilibrium point.

One of the possible modes of vibration of a circular drum (see other modes).
Car suspension: Designing vibration control is undertaken as part of acoustic, automotive or mechanical engineering.
Simple mass spring model
Mass–spring–damper model
How a 1 Hz square wave can be represented as a summation of sine waves (harmonics) and the corresponding frequency spectrum. Click and go to full resolution for an animation
Frequency response model
Two degrees of freedom model

Note: angular frequency ω (ω=2 π f) with the units of radians per second is often used in equations because it simplifies the equations, but is normally converted to ordinary frequency (units of Hz or equivalently cycles per second) when stating the frequency of a system.

Sine wave

Mathematical curve defined in terms of the sine trigonometric function, of which it is the graph.

The graphs of the sine (solid red) and cosine (dotted blue) functions are sinusoids of different phases
The oscillation of an undamped spring-mass system around the equilibrium is a sine wave.
Illustrating the cosine wave's fundamental relationship to the circle.
Sine, square, triangle, and sawtooth waveforms

where λ (lambda) is the wavelength, f is the frequency, and v is the linear speed.