P-waves are type of elastic wave, also called seismic waves, that can travel through
gasThis page is about the physical properties of gas as a state of matter. For the uses of gases, and other meanings, see Gas .A gas is one of four states of matter. Near absolute zero, a substance exists as a solid...
es (such as
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
s), elastic solids and liquids, including the
EarthEarth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density...
. P-waves can be produced by earthquakes and recorded by
seismometerSeismometers are instruments that measure and record motions of the ground, including those of seismic waves generated by earthquakes, nuclear explosions, and other seismic sources...
s. The name P-wave stands for
primary wave, as the P-wave is the fastest among the elastic waves, compared to the
S-waveA type of seismic wave, the S-wave, secondary wave, or shear wave is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves....
s and surface waves.
In isotropic and homogeneous solids, the
polarizationPolarization is a property of waves that describes the orientation of their oscillations. This article primarily covers the polarization of electromagnetic waves such as light, although other types of wave also exhibit polarization....
of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy.
where
K is the
modulus of incompressibilityThe bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to cause a given relative decrease in volume. Its base unit is Pascal....
,
' is the modulus of rigidity and ' the
densityThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
of the material through which the wave is propagating.
Of these, density shows the least variation so the velocity is mostly controlled by
K and
μ.
The elastic moduli
P-wave modulusIn linear elasticity, the P-wave modulus , also known as the longitudinal modulus, is one of the elastic moduli available to describe isotropic homogeneous materials.It is defined as the ratio of axial stress to axial strain in a uniaxial strain state...
, , is defined so that and thereby .
Typical values for P-wave velocity in earthquakes are in the range 5 to 8 km/s
In isotropic and
homogeneousIn mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group,...
solids, the
polarizationPolarization is a property of waves that describes the orientation of their oscillations. This article primarily covers the polarization of electromagnetic waves such as light, although other types of wave also exhibit polarization....
of P-waves is always
longitudinalLongitudinal waves are waves that have the same direction of oscillations or vibrations along or parallel to their direction of travel, which means that the oscillations of the medium is in the same direction or opposite direction as the motion of the wave. Mechanical longitudinal waves have been...
.
P-waves are type of elastic wave, also called seismic waves, that can travel through
gasThis page is about the physical properties of gas as a state of matter. For the uses of gases, and other meanings, see Gas .A gas is one of four states of matter. Near absolute zero, a substance exists as a solid...
es (such as
soundSound is a travelling wave which is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing and of a level sufficiently strong to be heard, or the sensation stimulated in organs of hearing by such vibrations.- Perception of sound...
s), elastic solids and liquids, including the
EarthEarth is the third planet from the Sun. It is the fifth largest of the eight planets in the solar system, and the largest of the terrestrial planets in the Solar System in terms of diameter, mass and density...
. P-waves can be produced by earthquakes and recorded by
seismometerSeismometers are instruments that measure and record motions of the ground, including those of seismic waves generated by earthquakes, nuclear explosions, and other seismic sources...
s. The name P-wave stands for
primary wave, as the P-wave is the fastest among the elastic waves, compared to the
S-waveA type of seismic wave, the S-wave, secondary wave, or shear wave is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves....
s and surface waves.
In isotropic and homogeneous solids, the
polarizationPolarization is a property of waves that describes the orientation of their oscillations. This article primarily covers the polarization of electromagnetic waves such as light, although other types of wave also exhibit polarization....
of a P-wave is always longitudinal; thus, the particles in the solid have vibrations along or parallel to the travel direction of the wave energy.
Speed of P-waves
where
K is the
modulus of incompressibilityThe bulk modulus of a substance measures the substance's resistance to uniform compression. It is defined as the pressure increase needed to cause a given relative decrease in volume. Its base unit is Pascal....
,
' is the modulus of rigidity and ' the
densityThe density of a material is defined as its mass per unit volume. The symbol of density is ρ .- Formula :Mathematically:where: is the density, is the mass, is the volume....
of the material through which the wave is propagating.
Of these, density shows the least variation so the velocity is mostly controlled by
K and
μ.
The elastic moduli
P-wave modulusIn linear elasticity, the P-wave modulus , also known as the longitudinal modulus, is one of the elastic moduli available to describe isotropic homogeneous materials.It is defined as the ratio of axial stress to axial strain in a uniaxial strain state...
, , is defined so that and thereby .
Typical values for P-wave velocity in earthquakes are in the range 5 to 8 km/s
Polarization
In isotropic and
homogeneousIn mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group,...
solids, the
polarizationPolarization is a property of waves that describes the orientation of their oscillations. This article primarily covers the polarization of electromagnetic waves such as light, although other types of wave also exhibit polarization....
of P-waves is always
longitudinalLongitudinal waves are waves that have the same direction of oscillations or vibrations along or parallel to their direction of travel, which means that the oscillations of the medium is in the same direction or opposite direction as the motion of the wave. Mechanical longitudinal waves have been...
. This means that the particles in the body have vibrations along or parallel to the direction of travel of the wave energy.
As an earthquake warning
Earthquake advance warning is possible by detecting the non-destructive primary waves that travel more quickly through the earth's crust than do the destructive secondary and
Rayleigh waveRayleigh waves are a type of surface acoustic wave that travels on solids. They are produced on the Earth by earthquakes, in which case they are also known as "ground roll", or by other sources of seismic energy such as an explosion or even a sledgehammer impact...
s. The amount of advance warning depends on the delay between the arrival of the P-wave and other destructive waves, generally on the order of seconds up to about a minute maximum for deep, distant, large quakes. The effectiveness of advance warning depends on accurate detection of the P-waves and compensation for ground vibrations caused by local activity (such as trucks or construction work).
P-wave shadow zone
Almost all the information available on the structure of the Earth's deep interior is derived from observations of the travel times,
reflectionReflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
s,
refractionRefraction is the change in direction of a wave due to a change in its velocity. This is most commonly observed when a wave passes from one medium to another...
s and phase transitions of seismic body waves, or normal modes. Body waves travel through the fluid layers of the Earth's interior, but P-waves are refracted slightly when they pass through the transition between the semisolid
mantleThe mantle is a part of an astronomical object. The interior of the Earth, similar to the other terrestrial planets, is chemically divided into layers. The mantle is a highly viscous layer between the crust and the outer core. Earth's mantle is about 2,970 km thick rocky shell that...
and the liquid outer core. As a result, there is a P-wave "shadow zone" between 104° and 140°, where the initial P-waves are not registered on
seismometerSeismometers are instruments that measure and record motions of the ground, including those of seismic waves generated by earthquakes, nuclear explosions, and other seismic sources...
s. In contrast,
S-waveA type of seismic wave, the S-wave, secondary wave, or shear wave is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves....
s do not travel through liquids, rather, they are
attenuatedIn physics, attenuation is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead....
.
See also
- S-Wave
A type of seismic wave, the S-wave, secondary wave, or shear wave is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves....
- Elastic wave
- Lamb waves
Lamb waves propagate in solid media. They are elastic waves whose particle motion lies in the plane defined by the plate normal and the direction of wave propagation. In 1917, the English mathematician Horace Lamb published his classic analysis and description of acoustic waves of this type. Their...
- Longitudinal wave
Longitudinal waves are waves that have the same direction of oscillations or vibrations along or parallel to their direction of travel, which means that the oscillations of the medium is in the same direction or opposite direction as the motion of the wave. Mechanical longitudinal waves have been...
- Love wave
In elastodynamics, Love waves are essentially horizontally polarized shear waves guided by an elastic layer, which is "welded" to an elastic half space on one side while bordering a vacuum on the other side...
- Surface wave
In physics, a surface wave is a mechanical wave that propagates along the interface between differing media, usually two fluids with different densities. A surface wave can also be an electromagnetic wave guided by a refractive index gradient...
External links