The Difference Between P waves and S waves

Types of Waves: Mechanical Body Waves:

P and S waves are mechanical body waves.

A mechanical wave is a wave that must travel through a medium, such as the ground or air. The energy of a mechanical wave is transferred from one molecule to another as it propagates (or travels) through its medium. They differ from electromagnetic waves, which can travel through a vacuum.

Types of mechanical Waves

• Sound Waves
• Water Waves
• Waves on a Spring
• Seismic (Earthquake Waves)

A body wave is a type of seismic wave that moves through the Earth's interior. They differ from surface waves, which travel along the Earth's surface.

Characteristics of Body Waves

• Move through deep layers of rock
• Have more energy than surface waves
• Arrive at seismometer location first

Body waves are the first waves to be felt on the surface after an earthquake. Since they can move through deep layers of rock, they follow a shorter ray path than a surface wave. A ray path is the direction the wave follows as it propagates away from the locus (or origin) through the Earth.

Cause and Origin of P and S Waves:

P and S waves are caused by the initial rupture of an earthquake. The rupture occurs when two sides of a fault slip past one another and energy is released. The stored pressure then travels away from the hypocenter radially in the form of P and S waves. Thus, P and S waves both originate or begin at the earthquake loci , where ruptures first occurs at depth. The locus is different than the epicenter, which is the surface location of the earthquake.

Primary Waves: What are P Waves?

P waves are called primary waves because they are the first waves to arrive at any location after an earthquake.

Characteristics of P waves (also known as Primary Waves)

• Compressional or lateral waves
• Arrive at seismometer first
• Cause upward or downward motion when they reach the surface
• Least destructive of all seismic waves

P Wave Motion

P waves are compressional. They vibrate parallel to the direction the wave is moving. The first upward or downward jolt felt is the P wave arrival.

These can be created at home by using a spring or slinky with fixed ends. If one person gathers a few coils and compresses them at one end before releasing them, then a compressional wave will travel from one end of the spring to the other.

P waves are compressional and vibrate parallel to the direction of propagation

P Wave Speed

P waves are the fastest moving waves. Their velocity is generally given by:

{eq}V_P=\sqrt{\frac{k+4/3μ}{ρ}} {/eq}

Where k is the bulk modulus (compressibility), μ is the shear modulus (rigidity), and ρ is the density of the rock or medium the wave is being transmitted through. Compressibility is the ability of a medium to reduce in volume under pressure, and rigidity is the ability of a medium to be bent or shaped.

P waves travel at approximately 7 km/s at the surface of the Earth.

Where do P waves move? Medium and Depth:

P waves move faster in less dense rocks and slower in denser ones.

Which Media can P-waves propagate through? How fast do they move?

P waves also increase velocity with depth until they reach the core-mantle boundary, where the wave slows down to about 7 km/s before increasing again. This is due to the fact that the outer core is a liquid and the shear modulus (or rigidity) is zero. The P- wave increases in speed to about 11 km/s when it passes into the solid inner core.

Due to the difference in speed through a liquid, P waves are refracted within the outer core and leave something known as a Shadow Zone on the Earth's surface. The P wave shadow zone is the area on the surface where no P waves are felt or measured after the occurrence of an earthquake. This zone is located at angular distances of 104 to 140 degrees from the earthquake location.

P waves leave a shadow zone on the Earth located 104 to 140 degrees away from the epicenter. The existence of the shadow zone helped scientists discover that the outer core was liquid.

Secondary Waves: What are S waves?

S Waves are called Secondary waves because they arrive second after the P wave.

Characteristics of S Waves (also known as Secondary Waves)

• Shear or waves
• Sine-shaped
• Arrive at seismometer second to the primary P wave
• The most destructive of all seismic waves.

S waves can also sometimes cause liquefaction to occur. Liquefaction is a phenomenon that happens when loosely packed sediment loses its strength due to strong ground shaking at or near the surface.

Earthquakes with Liquefaction include:

• 1964 Niigata Earthquake in Japan
• 1989 Loma Prieta Earthquake in California

S Wave Movement

S waves are called transverse waves because they vibrate perpendicular to the direction the wave travels.

S wave motion can also be created at home. Taking a string or slinky with one or both ends fixed, a person moving one side of the string side-to-side can see how the wave travels down the string.

The side-to-side motion creates a rolling effect on the surface that can cause major damage. Most of the shaking you feel after an earthquake comes from S waves.

S waves cause particles to vibrate perpendicular to the direction the wave travels.

S Wave Speed:

S waves travel slower than P waves. Their velocity relies only on the shear modulus (rigidity) and density:

{eq}V_S=\sqrt{\frac{μ}{ρ}} {/eq}

Consequently, S waves are approximately 1.7 times slower than P waves when moving through a solid medium. Thus, near the surface of the Earth, they have an average velocity of approximately 4 km/s.

Where Do S Waves Move? Medium and Depth:

S waves also move faster in less dense rock. However, the rigidity of the material also plays a large role. If the material is not rigid, S-waves will propagate more slowly.

Which Media do S Waves propagate through? How fast do they move?

	Ability to propagate	Velocity Range (km/s)
Rock	yes	0.6 (unconsolidated sediment) to 8 (deep in the mantle)
Gas	no	0
Liquid	no	0

S waves also increase in velocity with depth. Like P waves, they increase in speed with depth until they reach the outer core. At the core mantle boundary, S waves have an average velocity of approximately 8 km/s. Within the inner core, S-waves reach a velocity of 4 km/s.

Because of the inability of S waves to move through the liquid core, they also leave a shadow zone on the Earth's surface. The S wave shadow zone is larger than the P wave shadow zone, and no S waves are measured after an angular distance 103 degrees away from the earthquake's source.

Using P and S waves to find Epicenters:

P and S waves can be used to locate the epicenter of an earthquake. Since P waves are faster than S waves, the larger the arrival time difference between the two waves is, the farther that location is from the epicenter.

Locating the epicenter

The epicenter location can be determined using the following equation

{eq}t_S-t_P=\frac{x}{V_S}-\frac{x}{V_P}=x(\frac{1}{V_S}-\frac{1}{V_P}) {/eq}

where {eq}t_S {/eq} and {eq}t_P{/eq} are the arrival times of S and P waves at the seismometer, respectively, and x is the distance traveled.

• One location can be used to find the distance to the epicenter
• Two locations pinpoint two potential locations for the epicenter.
• Three locations allow you to determine the actual location of the epicenter.

An example of using P and S waves to find the epicenter of an earthquake in California

Lesson Summary:

Primary (P) and secondary (S) waves are the two types of seismic body waves. Their names come from when they first arrive and are felt at a location on the earth after an earthquake. They are mechanical waves (not electromagnetic) and need a medium, such as rock, to propagate through.

P waves and S waves differ in several ways. P waves can travel through any media (including liquid and gas), but S waves can only travel through solid media like rock. P waves travel faster than S waves. The difference in travel times can be used to determine the epicenter of the earthquake. Three locations are needed to pinpoint the exact epicenter.

Facts to remember

• P and S Waves originate at earthquake loci
• P waves are compressional and S waves are transverse
• P waves arrive at seismometer first.
• S Waves are more destructive and can cause liquefaction
• Difference in P and S Wave travel times can be used to find the epicenter