Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 weeks ago

Can someone help me linearise this equation?

 I need to linearise this equation in physics. I have the data points for f and for h. I know what f0 is too. I don't know what a and n are though. Someone pls help! Ps. f is there frequency of a resonance and h is the height of the water in the glass.

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  • JOHN
    Lv 7
    4 weeks ago

    f = √[f₀²/(1 + αhⁿ)]

    f² = f₀²/(1 + αhⁿ)

    f₀²/f² = 1 + αhⁿ

    f₀²/f² - 1 = αhⁿ

    log(f₀²/f² - 1) = logα + log(hⁿ)

    log(f₀²/f² - 1) = logα + nlogh

    Plot log(f₀²/f² - 1) against logh

    You should get a straight line,

    lope n and y-intercept logα,

    from which you can read off

    n and logα.

     

  • 4 weeks ago

    You can linearize it as f = linear function of (f0), or

    f = linear function of (alpha), or (h), or (n). You didn't say which one of these is your goal. I will assume that it is "h".

    One of the first steps is to decide what value of (h) you want to center your function around. Then the linear form is f = A + B*( h - center), with A = value of f when h = center.

    The next step is to figure out how much f changes, for a small change in "h". That will give you the value of "B".

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