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2 questions one wave one delta function

  • Thread starter Phymath
  • Start date
  • #1
184
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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

[tex]
\int^{\infty}_{-\infty} (6-5x^5)\delta(x) dx[/tex]

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
 

Answers and Replies

  • #2
15
0
Phymath said:
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

[tex]
\int^{\infty}_{-\infty} (6-5x^5)\delta(x) dx[/tex]

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:
[tex]
\int^{\infty}_{-\infty} f(x)\delta(x-a) dx = f(a)[/tex]
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.
 
  • #3
184
0
how is it 6 when [tex]f(x) = 6-5x^4[/tex], and [tex]\delta(x) = \delta(x-0)[/tex]?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,770
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Because the "definition" of the delta function that you refer to requires that
[tex]\int_{-\infty}^{\infty}f(x)\delta(x)dx= f(0)[/tex]!
 

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