Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
is the number of occurrences of a repeating event per unit
time. It is also referred to as
temporal frequency.
The
period is the duration of one
cycle in a repeating event, so the period is the
reciprocal of the frequency.
Definitions and units
For
cyclical processes, such as
rotation,
oscillations, or
waves, frequency is defined as a number of
cycles, or periods, per unit time. In
physics and
engineering disciplines, such as
optics,
acoustics, and
radio, frequency is usually denoted by a Latin letter
f or by a Greek letter
ν (nu).
In
SI units, the unit of frequency is
hertz (Hz), named after the German physicist
Heinrich Hertz. For example, 1 Hz means that an event repeats once per
second.
The period is usually denoted as
T, and is the
reciprocal of the frequency
f:
T = \frac{1}{f}.
The
SI unit for period is the second.
Measurement
By timing
To calculate the frequency of an event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.
Frequency of waves
Frequency has an inverse relationship to the concept of
wavelength, simply, frequency is inversely proportional to wavelength
λ (lambda). The frequency
f is equal to the
phase speed v of the
wave divided by the wavelength
λ of the wave:
f = \frac{v}{\lambda}.
In the
special case of electromagnetic waves moving through a
vacuum, then
v = c , where
c is the
speed of light in a vacuum, and this expression becomes:
f = \frac{c}{\lambda}.
When
waves from a
monochromatic source travel from one
medium to another, their frequency remains exactly the same — only their
wavelength and
speed change.
Examples
Physics of light
Radiant energy is energy which is propagated in the form of electromagnetic waves. Most people think of natural sunlight or
electrical light, when considering this form of
energy. The type of light which we perceive through our optical
sensors (eyes) is classified as white light, and is composed of a range of colors (red, orange, yellow, green, blue, indigo, violet) over a range of
wavelengths, or frequencies.
Visible (white) light is only a small fraction of the entire spectrum of
electromagnetic radiation. At the short end of that wavelength scale is
ultraviolet (UV) light from the sun, which cannot be seen. At the longer end of that spectrum is
infrared (IR) light, which is used for
night vision and other
heat-seeking devices. At even shorter wavelengths than UV are
X-rays and
Gamma-rays. At longer wavelengths than IR are
microwaves,
radio waves, electromagnetic waves in
megahertz and
kHz range, as well as natural waves with frequencies in the
millihertz and
microhertz range. A 2
millihertz wave has a wavelength approximately equal to the distance from the earth to the sun. A
microhertz wave would extend 0.0317
light years. A
nanohertz wave would extend 31.6881
light years.
Electromagnetic radiation is classified according to the frequency (or wavelength) of the light wave. This includes (in order of increasing frequency):
natural electromagnetic waves,
radio waves,
microwaves,
terahertz radiation,
infrared (IR) radiation,
visible light,
ultraviolet (UV) radiation,
X-rays and gamma rays. Of these, natural electromagnetic waves have the longest wavelengths and gamma rays have the shortest. A small window of frequencies, called the visible spectrum or light, is sensed by the eye of various organisms, with variations of the limits of this narrow spectrum.
Physics of sound
Sound is
vibration transmitted through a
solid,
liquid, or
gas; particularly, sound means those vibrations composed of
frequencies capable of being detected by ears. For humans, hearing is limited to frequencies between about 20
Hz and 20,000 Hz (20
kHz), with the upper limit generally decreasing with age. Other
species have a different range of hearing. For example, some dog breeds can perceive vibrations up to 60,000 Hz.
As a signal perceived by one of the major
senses, sound is used by many species for
detecting danger,
navigation,
predation, and
communication.
The mechanical vibrations that can be interpreted as sound are able to travel through all
forms of matter:
gases,
liquids,
solids, and
plasmas. The matter that supports the sound is called the
medium. Sound cannot travel through
vacuum.
Longitudinal and transverse waves
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
Sound is transmitted through gases, plasma, and liquids as
longitudinal waves, also called
compression waves. Through solids, however, it can be transmitted as both
longitudinal and
transverse waves. Longitudinal sound waves are waves of alternating
pressure deviations from the
equilibrium pressure, causing local regions of
compression and
rarefaction, while
transverse waves in solids, are waves of alternating
shear stress.
Matter in the medium is periodically displaced by a sound wave, and thus oscillates. The energy carried by the sound wave converts back and forth between the potential energy of the extra
compression (in case of longitudinal waves) or lateral displacement
strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium.
Sound wave properties
Sound waves are characterized by the generic
properties of waves, which are
frequency,
wavelength,
period,
amplitude,
intensity,
speed, and
direction (sometimes speed and direction are combined as a
velocity vector, or wavelength and direction are combined as a
wave vector).
Transverse waves, also known as
shear waves, have an additional property of
polarization.
Sound characteristics can depend on the type of sound waves (longitudinal versus transverse) as well as on the
physical properties of the transmission medium.
Whenever the
pitch of the soundwave is affected by some kind of change, the distance between the sound wave maxima also changes, resulting in a change of
frequency. When the loudness of a soundwave changes, so does the amount of compression in airwave that is travelling through it, which in turn can be defined as
amplitude.
In
music and
acoustics, the frequency of the
standard pitch A above
middle C on a
piano is usually defined as
440 Hz, that is, 440 cycles per second () and known as concert
pitch, to which an
orchestra tunes.
Other examples
In
Europe,
Africa,
Australia, Southern
South America, most of
Asia, and
Russia, the frequency of the
alternating current in
household electrical outlets is 50 Hz (close to the
tone G), whereas in
North America and Northern
South America, the frequency of the
alternating current is 60 Hz (between the
tones B♭ and B — that is, a
minor third above the European frequency). The frequency of the '
hum' in an
audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.
Period versus frequency
As a matter of convenience, longer and slower waves, such as
ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like
audio and
radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:
Other types of frequency
- Angular frequency ω is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves):
\omega=2\pi f\,.
Angular frequency is measured in
radians per second (rad/s).
- Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
- Wavenumber is the spatial analogue of angular frequency. In case of more than one spacial dimension, wavenumber is a vector quantity.
See also
