A wave is represented by y = A sin (kx + ωt). Draw two cycles of the wave from x = 0 to x = 2λ at a) t = 0; b) t = T/4, where T = 1/f = 2∏/ω
y = A sin (kx+ωt)
k = 2∏/λ (number of wave peaks)
The Attempt at a Solution
I had a really hard time on this problem. From what I could do, for part a, I plugged in t = 0 and from that, I know we would end up with the equation:
y = A sin (kx)
From this, I gathered that the wave would be traveling in a -x direction since the sin function is positive. Outside of that though, I had no idea or understanding how to properly draw it...
Part b, the best I could gather is that in plugging in t = T/4, we'd get an equation of:
y = A sin (kx +ω(T/4)).
In taking T = 2∏/ω
We can find ω and get an equation of:
ω = 2∏/T
So our equation will then look like:
y = A sin (kx + (2∏/T) (T/4))
In simplifying the equation further, we get:
y = A sin (kx +∏/2)
Once again though, I'm lost how to properly draw it. I would really appreciate any guidance on to go about drawing it out. Would this equation also show that the wave is moving in the -x direction?