# Wave sine function

1. Apr 2, 2016

### Nanu Nana

1. The problem statement, all variables and given/known data
A sine function is given.And the question is At which time does the deflection (y) reaches a maximum?
y= 3sin (800πxt+π/3)

2. Relevant equations
y= A sin (wt+Φ)
A=amplitude
w= angular frequency
Φ= initial phase

3. The attempt at a solution

I already have solution. But I don't understand it .
800πt+π/3 =π/2 +kx2xπ
800πt=π/6 + k x2xπ
t=1/4800 + k x 1/400
What does that k stands for ? and why is it kx2xπ and π/2 why not π/6

2. Apr 2, 2016

### PeroK

When is the sine function at a maximum? If you have $y = 3sin(x)$ for what value(s) of $x$ is $y$ a maximum?

3. Apr 2, 2016

3 ???

4. Apr 2, 2016

### PeroK

3 is the maximum value of that function, but for which values of $x$ does it have that value?

5. Apr 2, 2016

### drvrm

your y is function of t and you are writing condition for it -
you know that a sine function oscillates between zero and 1 - so you are putting the condition as first maxima will be at pi/2, but for a wave there will be second, third maxima of y....and so on ,that is written as additional term where k=0,1,2,..... can be substituted and again one can get maxima- as after 2.pi addition one again reaches the max. y value... one can draw a diagram of y- phase curve and see how it repeats

so you get first maxima at t=1/4800 and second at t=1/4800 +1/400 (k=1) , and so on.....

6. Apr 2, 2016

Thank you .

7. Apr 2, 2016

### PeroK

That's the answer given on plate. However, you should note that:

1) Sine oscillates between -1 and 1 (not 0 and 1).

2) Sine has maxima for negative integer $k$ in addition to posiive integers.