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