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Need help understanding algebra involved with nodal and antinodal lines

  1. Oct 22, 2011 #1
    There is a crucial aspect of this unit that Im not understanding and that is how to find how many nodal or anti nodal lines are in the equation.

    relevant formulas:
    So if im looking for how many anti nodal lines exist I use the formula | dsinθmax = n*λ |

    So lets say I have d and λ
    d = 51cm and λ = 4

    So we need to solve for n

    1. Now on the board, the teacher will write the formula | dsinθmax = n*λ |

    2. from there we get | sinθmax = (n*λ) / d | which cannot be greater than 1.

    3. so | (n*λ) / d ≤ 1 |

    4. then we get | n ≤ (d / λ) |

    5. n = (51 / 4)

    6. n = 12.75

    then you get the answer for n.
    I just dont get at all how you get from 3. to 4. algebraically
    i really need this cleared up. I need to understand how that works. I hope someone can explain it to me
    thanks
     
    Last edited: Oct 22, 2011
  2. jcsd
  3. Oct 22, 2011 #2
    I'm not entirely sure if this is real, but regardless, here you go:

    [tex]\left| \frac{n\lambda}{d}\leq1\right|[/tex]
    [tex]\left| \frac{n\lambda}{d}\frac{d}{\lambda}\leq \frac{d}{\lambda} \right|[/tex]
    [tex]\left| n\leq\frac{d}{\lambda}\right|[/tex]
     
    Last edited: Oct 22, 2011
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