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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-15 Waves



Q.26:- 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?

 

 

Answer:-



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:
tStP = 4 min = 240 s
2tPtP = 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.