1. ## earthquake

When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.03 km/s and the secondary, or S, wave has a speed of about 5.63 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 77.9 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far is the seismograph from the earthquake?

2. Originally Posted by lovinhockey26
When an earthquake occurs, two types of sound waves are generated and travel through the earth. The primary, or P, wave has a speed of about 8.03 km/s and the secondary, or S, wave has a speed of about 5.63 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 77.9 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far is the seismograph from the earthquake?
You know that the distance is calculated by:

$\displaystyle d = v \cdot t$

Both waves travel the same distance

$\displaystyle d = v_P \cdot t_P$ and

$\displaystyle d = v_S \cdot t_S$. Use the fact that $\displaystyle t_S - t_p = 77.9\ s$ :

$\displaystyle v_P \cdot t_P = v_S \cdot (t_P + 77.9)$ . After a few steps you'll get:

$\displaystyle t_P=\frac{v_S \cdot 77.9}{v_P - v_S}\approx 182.7\ s$

And now you can calculate the distance to the earthquake.

3. Hello, lovinhockey26!

When an earthquake occurs, two types of sound waves are generated
and travel through the earth.
The primary or $\displaystyle P$ wave has a speed of about 8.03 km/s
and the secondary or $\displaystyle S$ wave has a speed of about 5.63 km/s.

A seismograph, located some distance away, records the arrival of the $\displaystyle P$ wave
and then, 77.9 s later, records the arrival of the $\displaystyle S$ wave.

Assuming that the waves travel in a straight line,
how far is the seismograph from the earthquake?

The $\displaystyle P$ wave travels for t seconds at 8.03 km/sec.
. . Its distance is: .$\displaystyle 8.03t$ feet.

The $\displaystyle S$ wave travels for $\displaystyle (t+77.9)$ seconds at 5.03 km/sec.
. . Its distance is: .$\displaystyle 5.03(t+77.9)$ feet.

These distances are equal: .$\displaystyle 8.03t \;=\;5.63(t + 77.9)$

Go fot it!