Doppler, echo, attenuation

[Function]

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:

 

[math]\alpha = 10\cdot \log{\frac{I_0}{I_x}}[/math]

 

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

 

How is this even legal in physics? He basically states that [math]\text{dB}\cdot\text{cm}^{-1}[/math] 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:

 

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

 

[math]\Leftrightarrow \frac{I_0}{I_x}=100[/math]

 

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 January 26, 2017 by Function

[swansont]

 

How is this even legal in physics? He basically states that [math]\text{dB}\cdot\text{cm}^{-1}[/math] 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

[Function]

 

 

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 ...

[swansont]

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

[Function]

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

 

How did you get that?

Edited January 26, 2017 by Function

[swansont]

How did you get that?

Physics class.