Earthquakes are essentially sound waves—called seismic waves—traveling through the earth. Because the earth is solid, it can support both longitudinal and transverse seismic waves. The speed of longitudinal waves, called P waves, is 8000 m/s. Transverse waves, called S waves, travel at a slower 4500 m/s. A seismograph records the two waves from a distant earthquake. If the S wave arrives 2.0 min after the P wave, how far away was the earthquake? You can assume that the waves travel in straight lines, although actual seismic waves follow more complex routes.

Video transcript

Welcome back, everyone. We are making observations about sound waves and we are told that solids can transmit both longitudinal longitudinal and transverse waves. Let's say that the speed at which longitudinal waves travel is denoted by V L and the speed at which transverse waves travel is denoted by V T. Now we're gonna say that V L is greater than V T and that two waves, one of each kind arrive at a recorder located at some point P. And we are told that the time interval between arrival of the two is notated by delta T. And since V L is faster, delta T will be equal to the time of the transverse wave arriving minus the time of the longitudinal wave arriving. And the distance that is covered is L and we need to derive an expression for that. Well, we know that time is just given as velocity over distance. So let's apply that for each of our times here, we have that the time for the transverse wave is equal to the velocity of T divided by L. And we have the time of the longitudinal wave is the velocity of L divided by L now plugging in our terms for T back into our time difference, we get that delta T is equal to once again, TT minus T L which is equal to V T over L minus V L over L. And what we can do is we can flip both fractions and take the L out. And what we get is L is one over V T minus one over V L solving for L here, then we get that L is equal to the time of the transverse wave minus the time of the longitudinal wave all divided by one over the velocity of the transverse wave, the transverse wave minus one over the velocity of the longitudinal wave which corresponds to our final answer. Choice of a. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.