This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This model has been accepted and reinforced by decades of subsequent calculations, including those from nuclear test explosions, which can be measured very precisely.Īs sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. She calculated that the amplitude of the waves must be caused by the existence of a solid inner core within the liquid core. However, Lehmann had installed the European instruments herself, and so trusted their accuracy. Up until that point, seismologists had explained such shadow waves as being caused by some type of diffraction (as Gutenberg himself assumed) or a result of faulty seismometers. In 1936, Inge Lehmann began investigating P-waves from a New Zealand earthquake that had unexpectedly reached Europe, which should have been in the shadow region. In 1914, Beno Gutenberg used differences in wave speeds to determine that there must be a liquid core within the mantle. In fact, the discoveries of the structure of the Earth, illustrated in the figure above, resulted from earthquake observations. Seismologists and geophysicists use properties and velocities of earthquake waves to study the Earth's interior, which due to it's depth and pressure is not observable through many other means. S-waves cannot be supported by the liquid core, producing shadow regions. Both waves travel at different speeds in the different regions of Earth, but in general, P-waves travel faster than S-waves. Because S-waves do not pass through the liquid core, two shadow regions are produced ( Figure 17.11).įigure 17.11 Earthquakes produce both longitudinal waves (P-waves) and transverse waves (S-waves), and these travel at different speeds. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. Both types of earthquake waves travel slower in less rigid material, such as sediments. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). The bulk modulus of granite is greater than its shear modulus. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. Seismic waves, which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. ![]() Explain why this is so.Īlthough sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. However, you see the other shell for several milliseconds before you hear the explosion. ![]() You hear the explosion of one as soon as you see it. Imagine you observe two firework shells explode. Differentiating with respect to the density, the equation becomes ![]() Taking the natural logarithm of both sides yields ln p − γ ln ρ = constant. The number of moles and the molar mass are constant and can be absorbed into the constant p ( 1 ρ ) γ = constant. ![]() The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = n M ρ. Adiabatic processes are covered in detail in The First Law of Thermodynamics, but for now it is sufficient to say that for an adiabatic process, p V γ = constant, p V γ = constant, where p is the pressure, V is the volume, and gamma ( γ ) ( γ ) is a constant that depends on the gas. A process where heat is not added or removed from the system is known as an adiabatic system. During the process of compression and expansion of the gas, no heat is added or removed from the system. Ĭonsider a sound wave moving through air. ρ v d v = − d p ( − v d ρ ) v = − d p v = d p d ρ. Ρ v d v = − d p ( − v d ρ ) v = − d p v = d p d ρ.
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