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 $4km{s}^{-1},$ and that of $P$ wave is $8km{s}^{-1}$ A seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives 4 mins before the first $S$ wave. Assuming the waves travel in straight line, the distance at which the earthquake occurs is

• A. 1880 km
• B. 1920 km
• C. 1960 km
• D. 2020 km

Answer 1

Answer: (B)

$\Delta \left(\frac{\text{ distance }}{\text{ speed }}\right)=\Delta ($ time $)$
$\left(\frac{d}{4000}\right)-\left(\frac{d}{8000}\right)=(4\times 60)s$
$\Rightarrow \frac{d}{4}-\frac{d}{8}=2.4\times 10^5$
$d=8\times 2.4\times 10^{5}m=1920km$