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Question
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 of S 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 S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?
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Solution 1
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 km/s
vS = 4 km/s
From equations (i) and (ii), we have:
vS tS = vP tP
4tS = 8 tP
tS = 2 tP (iii)
It is also given that:
tS – tP = 4 min = 240 s
2tP – tP = 240
tP = 240
And tS = 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
Solution 2
Here speed of S wave, υs = 4.0 km s-1 and speed of P wave, υp = 8.0 km s-1. Time gap between P and S waves reaching the resimograph, t = 40 min = 240 s.
Let distance of earthquake centre = sKm
`:. t = t_s - t_p = S/v_s - S/v_p = S/4.0 - S/8.0 = S/8.0 = 240 s`
or `s = 240 xx 8.0 = 1920 km`
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