Question

a seismograph records two types of waves from an earthquake. p-waves arrive first and travel through both solid and liquid materials at 6 km/s. s-waves arrive later and only travel through solid materials at 3.5 km/s. if a seismograph station is 420 km away from an earthquake epicenter, approximately how much time will pass between the arrival of the p-wave and the s-wave?

70 seconds

120 seconds

50 seconds

30 seconds

Explanation:

Step1: Calculate time for P - wave

We know that the formula for time is $t=\frac{d}{v}$, where $d$ is distance and $v$ is velocity. For P - waves, $d = 420\space km$ and $v=6\space km/s$. So, $t_{P}=\frac{420}{6}=70\space s$.

Step2: Calculate time for S - wave

For S - waves, $d = 420\space km$ and $v = 3.5\space km/s$. Using the same formula $t=\frac{d}{v}$, we get $t_{S}=\frac{420}{3.5}=120\space s$.

Step3: Calculate time difference

The time difference $\Delta t=t_{S}-t_{P}$. Substituting the values of $t_{S}$ and $t_{P}$, we have $\Delta t = 120 - 70=50\space s$.

Answer:

50 seconds