3 ms·

> the seismic wave pattern is dominated by the signatures of two continent-sized structures near the Earth's core. They are interpreted as regions with unusuall

> the seismic wave pattern is dominated by the signatures of two continent-sized structures near the Earth's core. They are interpreted as regions with unusually high iron content, whose increased density and temperature slow down seismic waves passing through I would have thought that increased density would cause propagation velocity to increase? With heat, density falls so that bit stacks up. What have I got wrong?

whatshisface 3y ago
Increased density slows down propagation. It is easy to come up with false explanations of why, but here is one I think is probably true: If you imagine a bar that has been struck by an xylophone mallet, it makes sense that increasing its inertia would slow down the periods of its alternating motion. You can build traveling waves from sums of its modes of oscillation, and that carries the effect of higher density to wave speed.
Terr_ 3y ago
TLDR: For those waves in solids, propagation speed goes up with stiffness and down with density. The confusion happens because sometimes the thing with a higher speed is little denser... but a lot stiffer. _________ Interesting question. Some searching yields: > The density of a medium is the second factor [after elastic properties] that affects the speed of sound. It takes more energy to make large molecules vibrate than it does to make smaller molecules vibrate. Thus, sound will travel at a slower rate in the more dense object if they have the same elastic properties. > If sound waves were passed through two materials with approximately the same elastic properties such as aluminum (10 psi) and gold (10.8 psi), sound will travel about twice as fast in the aluminum (0.632cm/microsecond) than in the gold (0.324cm/microsecond). This is because the aluminum has a density of 2.7gram per cubic cm which is less than the density of gold, which is about 19 grams per cubic cm. The elastic properties usually have a larger effect that the density so it is important to both material properties. Poking around for an equation, I came across this [1] where the longitudinal/shear waves probably correspond to seismology's P-waves and S-waves. (Edited equations slightly for ASCII readability.) > These elastic waves move through the material with a velocity determined by its elastic modulus and its density, r. > For longitudinal waves this velocity is the sound velocity, C, and C = (E/r)^0.5, where E is Young's modulus. > For shear waves the controlling elastic modulus is the shear modulus, G. For shear waves: C = (G/r)^0.5. [0] https://www.nde-ed.org/Physics/Sound/speedinmaterials.xhtml https://www.nde-ed.org/Physics/Sound/speedinmaterials.xhtml [1] https://www.princeton.edu/~maelabs/mae324/glos324/elasticwaves.htm https://www.princeton.edu/~maelabs/mae324/glos324/elasticwav...

whatshisface 3y ago

Increased density slows down propagation. It is easy to come up with false explanations of why, but here is one I think is probably true: If you imagine a bar that has been struck by an xylophone mallet, it makes sense that increasing its inertia would slow down the periods of its alternating motion. You can build traveling waves from sums of its modes of oscillation, and that carries the effect of higher density to wave speed.

Terr_ 3y ago

TLDR: For those waves in solids, propagation speed goes up with stiffness and down with density. The confusion happens because sometimes the thing with a higher speed is little denser... but a lot stiffer. _________ Interesting question. Some searching yields: > The density of a medium is the second factor [after elastic properties] that affects the speed of sound. It takes more energy to make large molecules vibrate than it does to make smaller molecules vibrate. Thus, sound will travel at a slower rate in the more dense object if they have the same elastic properties. > If sound waves were passed through two materials with approximately the same elastic properties such as aluminum (10 psi) and gold (10.8 psi), sound will travel about twice as fast in the aluminum (0.632cm/microsecond) than in the gold (0.324cm/microsecond). This is because the aluminum has a density of 2.7gram per cubic cm which is less than the density of gold, which is about 19 grams per cubic cm. The elastic properties usually have a larger effect that the density so it is important to both material properties. Poking around for an equation, I came across this [1] where the longitudinal/shear waves probably correspond to seismology's P-waves and S-waves. (Edited equations slightly for ASCII readability.) > These elastic waves move through the material with a velocity determined by its elastic modulus and its density, r. > For longitudinal waves this velocity is the sound velocity, C, and C = (E/r)^0.5, where E is Young's modulus. > For shear waves the controlling elastic modulus is the shear modulus, G. For shear waves: C = (G/r)^0.5. [0] https://www.nde-ed.org/Physics/Sound/speedinmaterials.xhtml https://www.nde-ed.org/Physics/Sound/speedinmaterials.xhtml [1] https://www.princeton.edu/~maelabs/mae324/glos324/elasticwaves.htm https://www.princeton.edu/~maelabs/mae324/glos324/elasticwav...