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What function or operation am I looking for?

  1. Mar 10, 2012 #1
    First, I am sorry for very unspecific topic, but I really have no clue what I am looking for. I need some way how in mathematical terms describe things like following:
    I have line segment of length [itex]l[/itex] and I have sine function with period length [itex]\lambda[/itex] originating at one end of line segment. If [itex]l[/itex]=[itex]\lambda[/itex] I can easily count that there will be three points on the segment where sine value will be 0. But If [itex]\lambda[/itex] is slightly shorter there still will be three such points until [itex]l=\frac{3}{2}\lambda[/itex]. Then there will be four of them. How can I describe number of such points as [itex]f(l,\lambda)[/itex]?
    What should I look for/study? Frankly I wouldn't be surprised if it is something really basic, because I tend to miss basic things :/ Thank you in advance
     
  2. jcsd
  3. Mar 11, 2012 #2
    So, you want to know how many zeroes are in a sine wave [itex]l/\lambda[/itex] periods long. Which should be [itex]\lfloor 2l/\lambda \rfloor+1[/itex] zeroes in total, where the brackets represent the floor function.
     
  4. Mar 11, 2012 #3
    Thank you. I never heard of floor function before. Now it is clear, that in general I was looking for floor/ceiling functions.
     
  5. Mar 11, 2012 #4
    You're welcome!

    If the ratio [itex]2l/\lambda[/itex] is positive (as it will presumably be in your case), then [itex]\lfloor 2l/\lambda \rfloor[/itex] is simply the integer part of that ratio. For example, if [itex]2l/\lambda[/itex] was 17.936, then [itex]\lfloor 2l/\lambda \rfloor[/itex] would be just 17.
     
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