Answer to Question #118681 in Physics for Akhona Mlotshwa

Question

Two earthquake events happen exactly at the same time. Their locations are 100 km (Event-1) and
200 km (Event-1) away from your city, respectively. The wavelength of the transverse surface waves
generated from both the events is same and is λ = 432 m. While the frequencies of the Event-1 and
Event-2 are 10 and 38 Hz, respectively. (a) Which earthquake event is going to reach to you first?
(b) What would be the time difference between their arrival? [

Answer 1

Find speed of waves:

$v=\lambda f,\\ v_1=432\cdot10=4320\text{ m/s},\\ v_2=432\cdot38=16416\text{ m/s}.$

The time for the wave to reach the points:

$t_1=\frac{d_1}{v_1}=\frac{100000}{4320}=23\text{ s}.\\ \space\\ t_2=\frac{d_2}{v_2}=\frac{200000}{16416}=12\text{ s}.$

The second event will occur first.

The time difference:

$\Delta t=t_1-t_2=23-12=11\text{ s}.$