Waves

Question : 26 of 27

Marks: +1, -0

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\ \mathrm{km}\,\mathrm{s}^{-1}

, and that of P wave is

8.0\ \mathrm{km}\,\mathrm{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?

Solution:

Let

v_1, v_2

be the velocities of S waves and P waves, and

t_1, t_2

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=v_1 t_1=v_2 t_2

...(i)

Now,

v_1=4\ \mathrm{km}\,\mathrm{s}^{-1}

and

v_2=8\ \mathrm{km}\,\mathrm{s}^{-1}

...(ii)

\therefore 4 t_1=8 t_2

t_1=2 t_2

Also,

t_1-t_2=4\ \mathrm{min}=240\ \mathrm{s}

Using (ii),

2 t_2-t_2=240\ \mathrm{s};\ t_2=240\ \mathrm{s}

t_1=2\times t_2=2\times 240=480\ \mathrm{s}

Now, from (i)

l=v_1 t_1=4\times 480=1920\ \mathrm{km}

Hence earthquake occurs 1920 km away from the seismograph.

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