Waves

Question : 26

Total: 27

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 4.0‌km‌s–1, and that of P wave is 8.0‌km‌s–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?

Solution:

Let v1,v2 be the velocities of S waves and P waves, and t1,t2 be the time taken by these waves to travel to the position of seismograph. If l is the distance of occurrence of earthquake from the seismograph, then
l=v1t1=v2t2...(i)
Now, v1=4‌km‌s−1 and v2=8‌km‌s−1...(ii)
∴4t1=8t2 or t1=2t2
Also, t1−t2=4‌min=240s
Using (ii), 2t2−t2=240s;t2=240s
t1=2×t2=2×240=480s
Now, from (i) l=v1t1=4×480=1920‌km
Hence earthquake occurs 1920 km away from the seismograph.

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