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In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second2. In acoustics or
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
, acceleration (symbol: ''a'') is defined as the rate of change (or time
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
) of
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
. It is thus a vector quantity with dimension
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...
/
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, t ...
2. In
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
, this is m/s2. To accelerate an object (air particle) is to change its velocity over a period. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation \mathbf = \frac where *''a'' is the acceleration vector *''v'' is the velocity vector expressed in m/s *''t'' is time expressed in seconds. This equation gives ''a'' the units of m/(s·s), or m/s2 (read as "metres per second per second", or "metres per second squared"). An alternative equation is: \mathbf = \frac where *\mathbf is the average acceleration (m/s2) *\mathbf is the initial velocity (m/s) *\mathbf is the final velocity (m/s) *\Delta t is the time interval (s) Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we have \mathbf = - \frac \frac = - \omega^2 \mathbf One common unit of acceleration is ''
g-force The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measur ...
'', one ''g'' being the acceleration caused by the gravity of Earth. In
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
, acceleration a is related to
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
F and
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different element ...
m (assumed to be constant) by way of
Newton's second law Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
: F = m a


Equations in terms of other measurements

The Particle acceleration of the air particles ''a'' in m/s2 of a plain sound wave is: a = \delta \cdot \omega^2 = v \cdot \omega = \frac = \omega \sqrt \frac = \omega \sqrt \frac = \omega \sqrt \frac {, class="wikitable" ! Symbol !! Units !! Meaning , - ! ''a'' , m/ s2 , , particle acceleration , - ! ''v'' , m/s , , particle velocity , - ! ''δ'' , m, meters , , particle displacement , - ! ''ω'' = 2''πf'' ,
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before tha ...
s/ s , , angular frequency , - ! ''f'' , Hz,
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that one her ...
, ,
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...
, - ! ''p'' , Pa, pascals , ,
sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by a sound wave. In air, sound pressure can be measured using a microphone, and in water with a hydrophon ...
, - ! ''Z'' , N· s/m3 , , acoustic impedance , - ! ''J'' , W/m2 , , sound intensity , - ! ''E'' , W· s/m3 , , sound energy density , - ! ''P''ac , W,
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wa ...
s , , sound power or acoustic power , - ! ''A'' , m2 , ,
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while ''surface area'' refers to the area of an open su ...


See also

*
Sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...
* Sound particle * Particle displacement * Particle velocity


External links


Relationships of acoustic quantities associated with a plane progressive acoustic sound wave - pdf
Acoustics