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Wave sine function

  1. Apr 2, 2016 #1
    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. jcsd
  3. Apr 2, 2016 #2

    PeroK

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    When is the sine function at a maximum? If you have ##y = 3sin(x)## for what value(s) of ##x## is ##y## a maximum?
     
  4. Apr 2, 2016 #3
    3 ???
     
  5. Apr 2, 2016 #4

    PeroK

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    3 is the maximum value of that function, but for which values of ##x## does it have that value?
     
  6. Apr 2, 2016 #5
    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.....
     
  7. Apr 2, 2016 #6
    Thank you .
     
  8. Apr 2, 2016 #7

    PeroK

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    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.
     
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