Physics - Sound Wave Question with Solution | TestHub

Velocity of the $S$ waves is $v_1=4.5\mathrm{km}/\mathrm{s}$. The velocity of the $P$ waves is $v_2=8.0\mathrm{km}/\mathrm{s}$. Let the time taken by the $S$ and $P$ waves to reach the seismograph be $t_1$ and $t_2$. It is given that $t_1-t_2=4\min =4\times 60=240\sec$... (i) Let the distance of the epicentre $(\mathrm{km})$ be $S$. Then $$\begin{array}{rl}& S=v_1{t}_1=v_2{t}_2\\ \Rightarrow & 4.5\times t_1-8t_2=0\Rightarrow t_2=\frac{4.5}{8}{t}_1\end{array}$$ Using (i) and (ii) $$\begin{array}{rl}& t_1-t_2=240\Rightarrow t_1\left(1-\frac{4.5}{8}\right)=240\\ \Rightarrow & t_1=\frac{240\times 8}{3.5}=548.5\mathrm{s}\\ \therefore & S=v_1{t}_1=4.5\times 548.5=2468.6\approx 2500\mathrm{km}\end{array}$$