### 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 *v*_{S}and *v*_{P} be the velocities of *S* and *P* waves respectively.

Let *L *be the distance between the epicentre and the seismograph.

We have:

*L* = *v*_{S}*t*_{S} …**(i)**

*L* = *v*_{P}*t*_{P} …**(ii)**

Where,

*t*_{S} and *t*_{P} are the respective times taken by the *S* and *P* waves to reach the seismograph from the epicentre

It is given that:

*v*_{P} = 8 km/s

*v*_{S} = 4 km/s

From equations **(i)** and **(ii)**, we have:

*v*_{S }*t*_{S} = *v*_{P }*t*_{P}

4*t*_{S} = 8 *t*_{P}

*t*_{S} = 2 *t*_{P} …**(iii)**

It is also given that:

*t*_{S} – *t*_{P} = 4 min = 240 s

2*t*_{P} – *t*_{P} = 240

*t*_{P} = 240

And *t*_{S} = 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.