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Problem Involving Exponentials (Sound)

  1. Mar 27, 2006 #1
    I'm doing a piece of A-level physics coursework at school at the moment and seens I do Maths as well this shouldn't be hard for me, but I just can't get my head around it. So, any help would be really apprieciated!

    For my coursework, I'm testing different materials for sound-proofing and then looking at the structure of the material - seeing which works best and why.

    One side I have a signal generator with a speaker set a set distance away from a microphone and an oscilloscope (that measures the potential difference, or the voltage). In between the gap I insert materials and measure the change in the voltage (for example, with just air in the gap I recieved a reading of 20mv, when cardboard was inserted it dropped to 10mv).

    After my first practical I realised a problem...I didn't even think to take into account the thickness of the material, and they were all of different thicknesses! I spoke to my Teacher about this and he came up with the idea of using an equation using logs to find a constant that would over come this problem.

    He said:

    He said that plotting the Voltage (from the material) against thickness would result in an exponential curve and hence you could state:

    Vm = Vo x e^(-ct)

    Where Vm is the voltage from a material (the reading), Vo is in air, c is some unknown constant and t is the thickness.

    He then took logs (simple enough):

    lnVm = lnVo - ct
    lnVo = lnVm + ct

    Then apparently you can plot lnV against t to get a gradient, which is C.

    Could someone please explain how you get from that final equation to plotting that graph? And also how I would reapply the answer with the constant to my old data to form the new more exact data.

    Thanks, Rich.

    Sorry about the long read!
     
  2. jcsd
  3. Mar 27, 2006 #2

    Kurdt

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    The reason logs are used is to produce a straight line graph in which the radient is constant. This is done to make it easier to find c. So you'd plot the natural log of frequency against t and work out the gradient to find c and you can stick it back in the original equation.
     
  4. Mar 27, 2006 #3

    HallsofIvy

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    First, you don't go from "that final equation to plotting that graph"! You go the other way. Do exactly what your teacher suggested: plot log of voltage against time. Assuming your basic idea is correct, that the function really is exponential, you should get approximately a straight line. You can calculate the slope of the line and get its equation, then work back to the exponential.
     
  5. Mar 27, 2006 #4
    Yeah, I understand and get all that.

    Just need to know how I would then apply this back to get my new set of results were every material has the same thickness.
     
  6. Mar 28, 2006 #5
    bump please
     
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