alt Hacker NewsI don't understand why they believed in such high attenuation numbers.
They quote a book that the public at large (including me) can not check for the 22dB/cm/Mhz number.
The next best quote is the 8.3 dB/cm/Mhz quote. That article is available to the public:
https://pmc.ncbi.nlm.nih.gov/articles/PMC1560344/pdf/nihms94...
However I don't see any expression claiming a linear frequency dependence of attenuation up to 10 MHz.
> the number people will tell you in conversation.
Is very vague. Do your own research, find actual measurement data, don't extrapolate a few sub MHz measurements out to 10 Mhz, especially not if the error bars become ludicrously big.
Since I can't find the quoted frequency coefficient for attenuation I look at the possible candidates in that article: there's Figure 11, Table 1 and Table 3.
My gut feeling tells me they used table 3:
frequency in MHz | Longitudinal attenuation in Nepers per meter
0.272 | 14 +/- 17
0.548 | 53 +/- 43
0.840 | 70 +/- 28
I suspect they discarded the middle frequency because of the large error bar, so they are left with
Mhz | Np per m
0.272 | 14 +/- 17
0.840 | 70 +/- 28
the difference in frequency is 0.568 Mhz
so the difference in attenuation is then 56 +/- 45 Np per m. Yes the standard deviation is almost as large as the value. Let's see if we arrive close to their supposedly "quoted assumed linear frequency dependence of 8.3 dB / cm / Mhz "
2 x (56 Np per m) / ( 0.568 MHz x 100 cm per m x log(10) Np per 10 dB)
= 8.56 dB / cm / Mhz
close to their 8.3 "quote" which is really their own deduction, or whomever "derived" it in "conversation".
If you calculate the error bar: 8.56 +/- 6.88 dB / cm / MHz.
What they independently measured (props! actually good science):
11.18 dB / cm / MHz
Thats 2.62 / 6.88 = 0.38 standard deviations away. Thats not new science in the sense of hypothesis rejection, but a valuable extra datapoint refining the literature of values.
The likelihood of measuring a value 0.38 or more standard deviations away from the expected value would be: 70.4 % so not very surprising at all. Basically in conformance with the 8.56 +/- 6.88 dB / cm / MHz value.
https://www.mathportal.org/calculators/statistics-calculator...
Totally agree regarding not extrapolating to 10 MHz.
I had went down a huge rabbit hole to find the source for the 22 dB/cm/MHz paper that everyone quoted. People reference the Diagnostic Ultrasound textbook; that textbook references an old nondigital ultrasound reference book, which finally references a Fry paper from 1977 [1].
It's funny because the Fry paper never explicitly mentions the number 22 dB/cm/MHz. But there was one figure (Figure 12), where if you fit a line through the data in that figure, you get a slope of 23.5 dB/cm/MHz.
Here's a spreadsheet of me fitting the data: https://docs.google.com/spreadsheets/d/1a70svm-zrzp1SQT5v2m_...
But yes, you're totally right that even the Fry paper Figure 12 was only up to 2 MHz, so it's totally not fair to extrapolate to 10 MHz.
[1] https://pubmed.ncbi.nlm.nih.gov/690336/