## Activity: Earthquake waves

Contemporary Challenges 2022 (4 years)
In this activity students use the known speed of earthquake waves to estimate the Young's modulus of the Earth's crust.
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This activity follows Solutions to the wave equation

Let's talk about another contemporary challenge (which also is an old one): earthquakes.

In Oregon, earthquakes are quite relevant. The Cascadia subduction zone has had massive earthquakes about every 600 years for the last few millenia. The most recent was in 1700, and had a magnitude of 8.7-9.2, Geologists predict a 37% chance of a magnitude 8.2+ earthquake on the Cascadia subduction zone within the next 50 years. This will probably topple Weniger Hall, so students are advised to graduate promptly.

For $P$-waves in the ground, the shaking motion is in the direction in which the wave propagates. In this case the differential equation is \begin{align} \frac{\partial^2 u}{\partial x^2} &= \frac{\rho}{E} \frac{\partial^2 u}{\partial t^2} \end{align} where $u$ is the displacement from equilibrium of the ground, $\rho$ is the density of the earth's crust, and $E$ is its Young's modulus, which quantifies how hard it is to compress the crust.

The speed of a $P$-wave is about 5 km/s. Estimate the Young's modulus of the crust. Give your answer in units of N/m2.

Learning Outcomes