1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Harmonic wave / wave problem

  1. Jul 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Please kindly help me.
    Actually I dont quite understand what the meaning of harmonic wave is and the mathematics that expresses it.
    h(x,y;t) = h sin(wt-kx+δ)
    h represents the position of the particle in a particular time? Or the wave motion?
    What is the physical meaning of w, k? What are they describing? Why the function is written as h sin(wt-kx+d)?
    Can you explain that? My mathematic is not very good, to be honest.

    1) What is the distance between two maxima/minima in an interference pattern of two waves u1 and u2 described by
    u1(x) = cos(k1 x); u2(x) = cos(k2 x)
    What happens when k1=k2?

    2) "The so-called nami-water is good to our body!" Is the statement scientific (falsifiable), and why?

    2. Relevant equations



    3. The attempt at a solution
    The distance between two maxima/minima in an interference pattern = the interfered wave's wavelength?
     
  2. jcsd
  3. Jul 8, 2013 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    That equation doesn't make much sense. You have h both sides (do you mean h(x,y;t) = A sin(wt-kx+δ), or maybe h(x,y;t) = hmax sin(wt-kx+δ)?), and y does not appear on the right.
    If you mean h(x, t) = A sin(wt-kx+δ), that is defining a function.
    It helps to understand that when we write y=y(x) we make a 'pun'. The y on the left is a variable; the y on the right is a function. They are not really the same thing. But the practice is so standard that e.g. y(x) = 2x is commonly used as a shorthand for y = y(x) = 2x. I.e. defining the function y(x) is taken as an implicit definition of a variable of the same name.
    In the present case, the equation h(x, t) = A sin(wt-kx+δ) defines a function h(x, t) and a variable h. The variable h represents a displacement from an average state (position, usually). So the answer to your question is 'both'.
    If we fix some point along the line x, we get h = A sin(wt+c). This shows that h varies over time, repeating every interval 2π/w: sin(w(t+2π/w)+c) = sin(wt+2π+c) = sin(wt+c). So the frequency is w.
    If we fix on a point in time and look along the line, we see a shape that repeats every 2π/k. So we say the wavelength is 2π/k.
    If we fix on some peak in the curve and ask how that moves over time, we want wt-kx = constant. I.e. x = (w/k)t + constant. This means that the wave pattern moves at speed w/k.
    So what is the equation for the combined wave?
    Do you know any trig formula that allows you to write that differently?
     
  4. Jul 12, 2013 #3
    Yes, I mean h(x, t) = A sin(wt-kx+δ).

    1) What is the distance between two maxima/minima in an interference pattern of two waves u1 and u2 described by
    u1(x) = cos(k1 x); u2(x) = cos(k2 x)
    So what is the equation for the combined wave?
    I dont know. It is just shown for me this question. So I ask it here. Do you have any idea?
     
  5. Jul 12, 2013 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Most obviously, it's u(x) = u1(x)+u2(x) = cos(k1 x)+ cos(k2 x). But to answer the question it will help to write this differently. Do you know a trig formula involving cos(A)+cos(B)?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Harmonic wave / wave problem
  1. Harmonic Waves (Replies: 3)

  2. Harmonic wave (Replies: 4)

  3. Harmonic wave (Replies: 1)

Loading...