 # Earthquakes generate sound waves inside the earth

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal § sound waves. Typically the speed of S wave is about 4.0kms’1 and that ofP wave is 8.0 km. A seismograph records P and S waves from an earthquake. The first-P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?

Let \$v_{ 1 }\$, \$v_{ 2 }\$ be the velocities of 5 wave and P wave and \$t_{ 1 }\$,\$t_{ 2 }\$ be the time taken by these waves to reach the seismograph.
l = distance of occurrence of earthquake from the seismograph.

\$v_{ 1 }\$\$t_{ 1 }\$ = \$v_{ 2 }\$\$t_{ 2 }\$

\$v_{ 1 }\$ = 4 km \${{s}^{-1}}\$
\$v_{ 2 }\$ = 8 km\${{s}^{-1}}\$

4\$t_{ 1 }\$=8\$t_{ 2 }\$ ===> \$t_{ 1 }\$ = 2 \$t_{ 2 }\$
\$t_{ 1 }\$ - \$t_{ 2 }\$ = 4 min = 240s

On solving, \$t_{ 2 }\$ = 240 s
===> \$t_{ 1 }\$ = 2\$t_{ 2 }\$ = 2 x 240 = 480 s
====> l = \$v_{ 1 }\$\$t_{ 1 }\$ = 4 x 480 = 1920 km