Results 1 to 2 of 2

Math Help - wave beats

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    57

    wave beats

    Wave beats occur when two waves have frequencies that are close but not identical. Start with the expressionsin(w1t)+sin(w2t),where w1~ w2 and w1-w2 is not equal to 0. From this expression, it probably is not obvious why wave beats occur. Can you derive an expression that is equal to the one given but much more useful in accounting for the
    presence of wave beats? (Hints: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), cos("A) = cos(A), and sin("A) = "sin(A).)

    Thanks for the help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by amma0913 View Post
    Wave beats occur when two waves have frequencies that are close but not identical. Start with the expressionsin(w1t)+sin(w2t),where w1~ w2 and w1-w2 is not equal to 0. From this expression, it probably is not obvious why wave beats occur. Can you derive an expression that is equal to the one given but much more useful in accounting for the
    presence of wave beats? (Hints: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), cos("A) = cos(A), and sin("A) = "sin(A).)

    Thanks for the help!
    More hints:

    sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

    sin(A - B) = sin(A)cos(B) - cos(A)sin(B)


    Therefore sin(A + B) + sin(A - B) = 2 sin(A) cos(B) .... (1)

    Let A + B = w1t .... (2)

    Let A - B = w2t .... (3)

    Solve (2) and (3) for A and B in terms of w1t and w2t and substitute into the rigt hand side of (1):

    sin(w1t) + sin(w2t) = ....
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Damped Forced Oscillations and Beats
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: December 8th 2010, 12:15 PM
  2. Mass-Spring System Beats and Resonance
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 21st 2009, 05:27 AM
  3. Replies: 0
    Last Post: September 1st 2009, 07:10 AM
  4. Replies: 0
    Last Post: September 1st 2009, 07:05 AM
  5. Replies: 2
    Last Post: November 6th 2007, 12:05 PM

Search Tags


/mathhelpforum @mathhelpforum