Amplitude, Period and Frequency

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Key Questions

  • If #f(x)=asin(bx)# or #g(x)=acos(bx)#, then their amplitudes are #|a|#, and the periods are #{2pi}/|b|#.


    I hope that this was helpful.

  • Frequency and period are related inversely. A period #P# is related to the frequency #f#
    # P = 1/f#

    Something that repeats once per second has a period of 1 s. It also have a frequency of # 1/s#. One cycle per second is given a special name Hertz (Hz). You may also say that it has a frequency of 1 Hz.

    A sin function repeats regularly. Its frequency (and period) can be determined when written in this form:

    #y(t) = sin(2pi f t)#

  • #"(Amplitude)"=1/2["(Highest Value)"-"(Lowest Value)"]#


    graph{4sinx [-11.25, 11.25, -5.62, 5.625]}

    In this sine wave the highest value is #4# and the lowest is #-4#

    So the maximum deflection from the middle is #4#k.

    This is called the amplitude

    If the middle value is different from #0# then the story still holds
    graph{2+4sinx [-16.02, 16.01, -8, 8.01]}

    You see the highest value is 6 and the lowest is -2,
    The amplitude is still #1/2 (6- -2)=1/2 *8=4#

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