Calculating Time Difference for P & Rayleigh Waves at Point B

[vipertongn]

Homework Statement

Two points A and B on the surface of the Earth are at the
same longitude and 60.0° apart in latitude. Suppose that an
earthquake at point A creates a P wave that reaches point B
by traveling straight through the body of the Earth at a constant
speed of 7.80 km/s. The earthquake also radiates a
Rayleigh wave, which travels across the surface of the Earth in
an analogous way to a surface wave on water, at 4.50 km/s.
What is the time difference between the arrivals of the
two waves at B? Take the radius of the Earth to be 6370 km.

I have the solution for this but I'm confused as to how to find the distance and the speed in this case. Can someone explain to me step by step as to why he distance is said to be like 2Rsin(30)?

 

[Delphi51]

 

[vipertongn]

what if they were 25 degrees apart woud i then use 25/2?

 

[Delphi51]

You should draw the diagram and see for yourself! If you have any difficulty with a problem, draw a diagram - it will help you organize the problem, your thoughts, and help you deduce a solution. Yes, when you split any angle in half like that you create a pair of right triangles so you can use the 2*sin(A/2) trick.

 

[vipertongn]

ok so i tried 2(6.37e6)sin(25/2) which gets 2.76e6

I know from that you want to obtain the the time with given velocities. so for my values i have v1=6000m/s and v2-4400m/s

i divide 2.76e6 m/ 6000m/s to get 459.6s and with the other one 626.69s

i subtract the values and i end up with 167.09, however that's incorrect. can you check my work?

its hard for me to visualize it since its using terms like latitude and longitude so i can't really draw where what is.

 

[Delphi51]

A bit confusing since you haven't stated the actual question with the 25 degrees. For the surface wave I get
distance = 25/360*2*pi*r = 2779 km
time = 2779/4.400 = 632 seconds.

 

[vipertongn]

Two points A and B on the surface of the Earth are at the
same longitude and 25.0° apart in latitude. Suppose that an
earthquake at point A creates a P wave that reaches point B
by traveling straight through the body of the Earth at a constant
speed of 6 km/s. The earthquake also radiates a
Rayleigh wave, which travels across the surface of the Earth in
an analogous way to a surface wave on water, at 4.40 km/s.
What is the time difference between the arrivals of the
two waves at B? Take the radius of the Earth to be 6370 km.