Answer to Question #118097 in Physics for Fiona

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 the same and is λ = 405 m. While the frequencies of the Event-1 and
Event-2 are 45 and 32 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

(a) Which earthquake event is going to reach to you first? 

To answer this question, we must first calculate the velocity of the waves:

$$v_1=\lambda f_1,\\ v_2=\lambda f_2.$$

We know the velocity, let's calculate time!

$$t_1=\frac{d}{v_1}=\frac{d}{\lambda f_1}=\frac{10^5}{405\cdot 45}=5.49\text{ s},\\ \space\\ t_2=\frac{d}{v_2}=\frac{d}{\lambda f_2}=\frac{10^5}{405\cdot 32}=7.72\text{ s}.$$

The first earthquake event will reach the region first.

(b) What would be the time difference between their arrival?

Just subtract one time from another:

$$\Delta t=t_2-t_1=7.72-5.49=2.23\text{ s}.$$