Relating to period of a function.

[M. next]

If we have f(k)=Asin($\frac{xa}{2}$). Then it was mentioned that f(x) is a periodic function with period $\frac{Δx.a}{2}$=π. How come?

Thanks!

Please note, A and a are constants.

 

[Mark44]

If we have f(k)=Asin($\frac{xa}{2}$).

This should be f(x) = A sin($\frac{xa}{2}$). The only variable here is x. k doesn't appear at all in the formula for this function.

Then it was mentioned that f(x) is a periodic function with period $\frac{Δx.a}{2}$=π. How come?

This is wrong, and I have no idea where you got this.

The sine and cosine functions are periodic. The period of both sin(x) and cos(x) is 2$\pi$. The period of sin(Kx) and cos(Kx) is $\frac{2 \pi}{K}$.

What then would be the period of sin((a/2)x)?

Thanks!

Please note, A and a are constants.

 

[M. next]

Sorry it is x, I typed it by mistake. It should be 4π/a. But here they related the variable of the sin function "x" to the period in some way I didn't understand.. (i.e, the formula that I wrote in my first post and that you quoted second).
Thanks

 

[Mark44]

Sorry it is x, I typed it by mistake. It should be 4π/a. But here they related the variable of the sin function "x" to the period in some way I didn't understand.. (i.e, the formula that I wrote in my first post and that you quoted second).
Thanks

If the period of sin(Kx) is $2\pi/K$, what is the period of sin((a/2)x)?

 

[M. next]

I answered you previously, it would be 4π/a

 

[Mark44]

You said it "should be 4π/a", which I interpreted to mean that you knew that was the answer, but didn't know how it was obtained.

You asked about the formula in your first post (and that I quoted). I have no idea what they mean by that formula, especially the part with Δx.

 

[M. next]

Yes. Neither do I. Thank you anyway!