Simultaneous waves question 1.24

[can't_think_of_a_name]

Go to the link below and click on page 49 and question 1.24.
https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

So assuming I am understand the question correctly Bob and Alice have the same location in both frames.

Event 0 everything is 0.

event 1
I assume both Alice and Bob are at the same location for every location. So I am just doing the calculations once for
Alice's frame for Alice and Bob's frame for Bob. I am not sure if the question asked it but I also did prime frame for  Alice and Bob.

gamma = 2
v = .866c
t = 1 sec
I go
d = vt = (1 s)(.866c) = .866LS (for lorentz transform)
Then t =  2 I could do the calculation or mulitply everything by 2. For t =  3 multiply by 3 etc
Now to find t' for event 1
t' = gamma (t -xv /c^2)
t' = 2(1 sec - (.866LS)(.866c) )
t' = .5 sec.
Now to get event 2 variables multiply time by 2 to get event 3 multiply 3.
Here is my basic formula

t_event_number = t_1_or_t'_1 (event_number)

t_event_number = t_1
t'_event_number = t_1'

 

Let me show an example
t_1' = .5 and t_1 = 1  
While, event number =  0 - infinity
Is this correct?