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Wave Function in specific range

I obtained the following from a book.

Question is:

Periodic Sawtooth described by the following;

f(x) = x/2∏ for 0<x<2∏
f(x+2∏) = f(x) for -∞<x<+∞


The solution is:

If x = 0
y = 0

If x = 2∏
y = 2∏/2∏ = 1

If x = 4∏
y = f(2∏+2∏) = 2∏ = 1

Can anyone explain to me why when x = 4∏ y = 1 ? I'm not clear on that bit.

I would just think if you're putting x = 4∏ into the 2nd equation in the question you would get y = f(4∏+4∏) = f(8∏)

I know a full rotation is 2 ∏, so I can see how 8∏ would be the same as 2∏, but then how did they go from 2∏ to 1 in the part above which I have emboldened?

Thank you
Reply 1
Avatar for ztibor
ztibor
10
Original post by little pixie
I obtained the following from a book.

Question is:

Periodic Sawtooth described by the following;

f(x) = x/2∏ for 0<x<2∏
f(x+2∏) = f(x) for -∞<x<+∞


The solution is:

If x = 0
y = 0

If x = 2∏
y = 2∏/2∏ = 1

this dividing is true for only 0<x<2TT

if A=2TT so x+2TT=2TT ->x=0
f(A)=f(0)

If x = 4∏
y = f(2∏+2∏) = 2∏ = 1

f(4TT) -> x+2TT=4TT -> x=2TT for f(2TT) -> x+2TT=2TT -> x=0 -> f(0)

Generally: for f(x)=f(x+k2TT) where k integer (including 0, +/-1 ....)
(edited 12 years ago)
Reply 2
Avatar for capital S
capital S
can you guys just write "pi" next time, or use latex: π\pi

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