Answer to Question #118097 in Physics for Fiona

Question #118097
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?
1
Expert's answer
2020-05-25T11:04:47-0400

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


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


v1=λf1,v2=λf2.v_1=\lambda f_1,\\ v_2=\lambda f_2.

We know the velocity, let's calculate time!


t1=dv1=dλf1=10540545=5.49 s, t2=dv2=dλf2=10540532=7.72 s.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:


Δt=t2t1=7.725.49=2.23 s.\Delta t=t_2-t_1=7.72-5.49=2.23\text{ s}.

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