# What are S waves and P waves

## Mechanical waves

The adjacent picture shows schematically the propagation of earthquake waves.

Four types of waves can occur in earthquakes:

Sky waves | Longitudinal or P waves | |

Transversal or S waves | ||

Surface waves | Love waves | |

Rayleigh waves |

•The **Sky waves** have their starting point in the center (focus) of the earthquake, which can lie up to a few hundred kilometers below the earth's surface (depth). From there they cross the earth.

• There are those **P waves** (like sound) compression or longitudinal waves that can penetrate solid, liquid and gaseous bodies. P waves have the highest speed of propagation, which can be between 6 km / s and 14 km / s. You will therefore be the first to reach a certain earthquake detector (hence the name primary wave or P wave).

•The **S waves** (Secondary waves) are transverse shear waves that can propagate at speeds of 3.5 km / s to 7.4 km / s and therefore only reach the above earthquake detector after the P waves. They can only penetrate solids (e.g. not the liquid outer core of the earth).

•The **RAYLEIGH****-** and **LOVE****-Waves** (named after their discoverers) are bound to the surface of the earth. The RAYLEIGH waves are characterized by an elliptical particle movement in the vertical plane. With the LOVE waves, there is also a shear movement parallel to the earth's surface.

The frequencies of the earthquake waves are in the range between 0.1 Hz and 30 Hz.

Due to the different propagation speeds of P and S waves, they also arrive at a seismographic station at different times. The distance of the epicenter can be inferred from the difference in transit time. The exact location of the epicenter is usually determined as the intersection of the distances to three or more stations.

The vibrations triggered by the earthquake waves can be identified with the aid of the greatly simplified **Seismograph** to register. The loosely suspended pendulum body remains largely at rest due to its inertia in the event of vibrations. A pen hung on the body records the rashes on a recording paper attached to the floor and creates a picture **Seismogram**.

a) Earthquakes can propagate in the earth's crust both by longitudinal waves and by transverse waves. On the other hand, it can be observed that the propagation deep inside the earth always occurs through longitudinal waves. What can we conclude from this about the state of matter in the earth's interior?

b) A seismograph first registers the P waves and then the S waves. Estimate the distance of the station from the earthquake center if eight minutes elapse between the occurrence of the two faults. Assume a speed of 10 km / s for the P and 5.8 km / s for the S waves.

c) The following seismogram was recorded in Göttingen in 1906. P means the direct P-wave, PP the one reflected once on the earth's surface and PPP the P-wave reflected twice on the earth's surface (analogous designation for S-wave). What earthquake could it have been?

a) Matter cannot be in a solid state, otherwise both types of waves would be possible

b) For the distance \ (x \) from the center of the earthquake \ (x = {c _ {\ rm {P}}} \ cdot t \ quad (1) \) or \ (x = {c _ {\ rm {S}) }} \ cdot \ left ({t + \ Delta t} \ right) \ quad (2) \). Equating \ ((1) \) and \ ((2) \) results in \ [{c _ {\ rm {P}}} \ cdot t = {c _ {\ rm {S}}} \ cdot \ left ({ t + \ Delta t} \ right) \ Leftrightarrow t \ cdot \ left ({{c _ {\ rm {P}}} - {c _ {\ rm {S}}}} \ right) = {c _ {\ rm { S}}} \ cdot \ Delta t \ Leftrightarrow t = \ frac {{{c _ {\ rm {S}}} \ cdot \ Delta t}} {{{c _ {\ rm {P}}} - {c_ { \ rm {S}}}}} (3) \] Inserting \ ((3) \) into \ ((1) \) results in \ [x = {c _ {\ rm {P}}} \ cdot \ frac {{{c _ {\ rm {S}}} \ cdot \ Delta t}} {{{c _ {\ rm {P}}} - {c _ {\ rm {S}}}}} \] Insertion of the given values returns \ [x = 10 \ cdot {10 ^ 3} \ frac {{\ rm {m}}} {{\ rm {s}}} \ cdot \ frac {{5.58 \ cdot {{10} ^ 3 } \ frac {{\ rm {m}}} {{\ rm {s}}} \ cdot 480 {\ rm {s}}}} {{10 \ cdot {{10} ^ 3} \ frac {{\ rm {m}}} {{\ rm {s}}} - 5.58 \ cdot {{10} ^ 3} \ frac {{\ rm {m}}} {{\ rm {s}}}}} = 6.6 \ cdot {10 ^ 6} {\ rm {m}} = 6.6 \ cdot {10 ^ 3} {\ rm {km}} \]

c) The time difference between the P and S waves is approx. \ (600 \ rm {s} \). An invoice like a partial task **b)** supplies

\ [x = 8.3 \ cdot {10 ^ 3} {\ rm {km}} \] This is roughly the distance between Göttingen and San Francisco, where a devastating earthquake took place in 1906 (see picture).

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