2 questions one wave one delta function

[Phymath]

1st question

what the heck does a "minimum" mean when talking about interference in waves, i got a question of the like y = 1.19(1 + 2 cos p)sin(kx - wt + p) is the superpostion function of three waves one which is p out of phase of the first and another which is p out of phase of the second wave. What value of p gives the minimum, i have no idea what that means I'm guessin when the amplitude is 0 or when pi/2 - kx + wt = p but how do i find that?

2nd question

i have the function

$$\int^{\infty}_{-\infty} (6-5x^5)\delta(x) dx$$

now by defintion of the delta function because 0 is contained with-in (as is all numbers) between the limits should it not = 0? thanks anyone

 

[StNowhere]

1st question

what the heck does a "minimum" mean when talking about interference in waves, i got a question of the like y = 1.19(1 + 2 cos p)sin(kx - wt + p) is the superpostion function of three waves one which is p out of phase of the first and another which is p out of phase of the second wave. What value of p gives the minimum, i have no idea what that means I'm guessin when the amplitude is 0 or when pi/2 - kx + wt = p but how do i find that?

2nd question

i have the function

$$\int^{\infty}_{-\infty} (6-5x^5)\delta(x) dx$$

now by defintion of the delta function because 0 is contained with-in (as is all numbers) between the limits should it not = 0? thanks anyone

2nd question:

Delta function:
$$\int^{\infty}_{-\infty} f(x)\delta(x-a) dx = f(a)$$
Using that, it looks to me like your value is 6
I'll look at the first question a little more before I hazard a guess on it.

 

[Phymath]

how is it 6 when $$f(x) = 6-5x^4$$, and $$\delta(x) = \delta(x-0)$$?

 

[HallsofIvy]

Because the "definition" of the delta function that you refer to requires that
$$\int_{-\infty}^{\infty}f(x)\delta(x)dx= f(0)$$!