Earthquakes generate sound waves inside the Earth. Unlike gases, the Earth can experience both transverse and longitudinal sound waves. Typically the speed of S wave is about `4.0 kms^(-1)` and that of P wave is `8.0 kms^(-1)`. A seismograph records P and S waves from an earthquake . The first P waves arrives 4 min before the first S wave. Assuming the waves traveling straight line, at what distanc does the earthquake occur ?

Explanation

`v_(s) = 4 xx 10^(3)ms^(-1) , v_(P) =8 xx 1^(3) ms^(-1)` ` t_(s) =( t_(p)+ 240 ) s`
i.e., `(x) /(4 xx 10^(3)) - (x )/(8 xx10^(3)) = 240`
i.e. `( x )/( 10^(3)) [(1)/(4)- ( 1)/(8)]= 240 ` `x [( 2-1)/( 8)] =240 xx 10^(3)`
or ` x =240 xx8 xx10^(3) ` ` x =1920 xx 10^(3) m`
or `x =1920 km`