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