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

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Let vSand vP be the velocities of S and P waves respectively. Let L be the distance between the epicentre and the seismograph. We have: L = vStS (i) L = vPtP (ii) Where, tS and tP are the respective times taken by the S and P waves to reach the seismograph from the epicentre It is given that: vP = 8...
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LetvSandvPbe the velocities ofSandPwaves respectively. LetLbe the distance between the epicentre and the seismograph. We have: L=vStS(i) L=vPtP(ii) Where, tSandtPare the respective times taken by theSandPwaves to reach the seismograph from the epicentre It is given that: vP= 8 km/s vS= 4 km/s From equations (i) and (ii), we have: vStS=vPtP 4tS= 8tP tS= 2tP(iii) It is also given that: tS–tP= 4 min = 240 s 2tP–tP= 240 tP= 240 AndtS= 2 × 240 = 480 s From equation (ii), we get: L= 8 × 240 = 1920 km Hence, the earthquake occurs at a distance of 1920 km from the seismograph. read less
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