# An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and...

## Question:

An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest, shear (S) waves, which are transverse waves and carry most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. People do not generally feel the P waves, but animals seem to be sensitive to them. Take the density of the material through which these waves travel to be {eq}2.0 \times 10^3 \, \mathrm{kg}/\mathrm{m}^3 {/eq}, the Young's modulus to be {eq}9.8 \times 10^{10} \, \mathrm{N}/\mathrm{m}^2 {/eq}. and the shear modulus to be {eq}3.2 \times 10^{10} \, \mathrm{N}/\mathrm{m}^2 {/eq}. A person reports that her dog started barking 30 seconds "before the earthquake." Approximately how far away was the origin of the earthquake?

## Distance to the Origin of Earth Quake from The Difference in Arrival Time of S Wave and P Wave

Earth quake produces different types of waves of which S wave and P waves are two different body waves. S wave is a transverse wave and travels slower than the P wave which is a pressure wave. So from the difference in arrival time the distance to the location of earth can be calculated by the equation {eq}\Delta t = d * ( \frac { 1 } { v_s } - \frac { 1 } { v_p } ) {/eq}

• {eq}\Delta t {/eq} - difference in arrival time of the S and P waves
• d - distance to the origin of the earth quake from the measuring location
• {eq}v_s {/eq} - speed of S wave
• {eq}v_p {/eq} - speed of P wave

Speed of wave through a medium is given by the equation {eq}v = \sqrt { \frac { Elastic \ \ modulus } { \rho } } {/eq}. Here {eq}\rho {/eq} is the density of the medium