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Doppler, echo, attenuation


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#1 Function

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Posted 26 January 2017 - 06:13 PM

Hello everyone

 

Let me address, after a long time, again the experts in the truly bizarre domain which goes by the name "physics":

 

In my course, my professor says:

 

\alpha = 10\cdot \log{\frac{I_0}{I_x}}

 

With \alpha the attenuation of ultrasonic sound waves in a tissue, expressed in \text{dB}\cdot\text{cm}^{-1}, I_0 the intensity of the ultrasonic sound wave upon entrance of the tissue (or rather, right before it) and I_x the remainder intensity after passage through the tissue of width x.

 

How is this even legal in physics? He basically states that \text{dB}\cdot\text{cm}^{-1} is dimensionless. Which clearly isn't the case.

 

Then, he states that alpha is about 20 dB/cm in bone tissue. I can understand that per cm progression of the sound waves in bone, their volume decrease with 20 dB.

 

But:

 

20 \text{ dB}\cdot\text{cm}^{-1}=10\cdot\log{\frac{I_0}{I_x}}

 

\Leftrightarrow \frac{I_0}{I_x}=100

 

Which insinuates the invariability of the intension as the sound wave penetrates the tissue.

 

Ergo, I don't find it possible for me to solve the question by what factor the original intensity is divided when the sound wave travels 2 cm in bone.

 

Intuition says: 10,000. But if the formula is correct, and the attenuation is indeed completely independent of the depth, it should be, and remain forever, 100. Please don't tell me that's true.

 

Thanks;

 

F


Edited by Function, 26 January 2017 - 06:20 PM.

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So I guess we are who we are for a lot of reasons. And maybe we'll never know most of them.

But even if we don't have the power to choose where we come from, we can still choose where we go from there.

We can still do things. And we can try to feel okay about them.

 

– Steven Chobsky in The Perks of Being a Wallflower


#2 swansont

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Posted 26 January 2017 - 06:30 PM

 

How is this even legal in physics? He basically states that \text{dB}\cdot\text{cm}^{-1} is dimensionless. Which clearly isn't the case.

 

 

 

Nope. The constant out in front has units. It's not just 10, it's 10 dB/cm


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#3 Function

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Posted 26 January 2017 - 06:32 PM

 

 

Nope. The constant out in front has units. It's not just 10, it's 10 dB/cm

 

Explains half of my problem. Thank you very much for that.

 

So what about the apparently indifferent factor of 100 = I0/Ix? Is intensity invariable through a medium? That'd be very counter-intuitive ...


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So I guess we are who we are for a lot of reasons. And maybe we'll never know most of them.

But even if we don't have the power to choose where we come from, we can still choose where we go from there.

We can still do things. And we can try to feel okay about them.

 

– Steven Chobsky in The Perks of Being a Wallflower


#4 swansont

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Posted 26 January 2017 - 06:53 PM

The equation for intensity through the medium is going to look like I = I0 10^-ax


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#5 Function

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Posted 26 January 2017 - 06:57 PM

The equation for intensity through the medium is going to look like I = I0 10^-ax

 

How did you get that?


Edited by Function, 26 January 2017 - 06:57 PM.

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So I guess we are who we are for a lot of reasons. And maybe we'll never know most of them.

But even if we don't have the power to choose where we come from, we can still choose where we go from there.

We can still do things. And we can try to feel okay about them.

 

– Steven Chobsky in The Perks of Being a Wallflower


#6 swansont

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Posted 26 January 2017 - 10:34 PM

How did you get that?


Physics class.
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Minutus cantorum, minutus balorum, minutus carborata descendum pantorum          To go to the fortress of ultimate darkness, click the up arrow ^

I am not a minimum-wage government shill.             Forget it, Jake — it's Crackpottown.

My SFN blog: Swans on Tea                                                           

 

 

                                                                                                                     

 

 





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