Question

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 8.0 km/s and the secondary, or S, wave has a speed of about 4.5 km/s. A seismograph, located some distance away, records the arrival of the P wave and then, 77.2 s later, records the arrival of the S wave. Assuming that the waves travel in a straight line, how far (in terms of m) is the seismograph from the earthquake?

Answer 1

Answer:$d=7.94\times 10^5\ m$

Explanation:

Given

Speed of Primary wave $v_1=8\ km/s$

Speed of secondary wave $v_2=4.5\ km/s$

difference in timing of two waves are $77.2\ s$

Suppose both travel a distance of d km then

$t_1=\frac{d}{8}\quad \ldots (i)$

$t_2=\frac{d}{4.5}\quad \ldots (ii)$

Subtract (ii) from (i)

$\frac{d}{4.5}-\frac{d}{8}=77.2$

$d[\frac{1}{4.5}-\frac{1}{8}]=77.2$

$d[0.0972]=77.2$

$d=794.23\ km$

$d=7.94\times 10^5\ m$