I'm about to start my next semester at university, I've brought the books and thought I'll make a head start on going through them.

I'm currently working through chapter 1 of The Physics and Technology of Diagnostic Ultrasound at the end of the chapter there are a set of question, I've worked through all and managed to work out the formulas for the answers.

1 question in particular which reads:

An Ultrasound machine has a dynamic range (defined as ratio of the largest echo to the smallest echo) of 1,380,000. What is the dynamic range expressed in dB?

now the answer they have written is 61.4 dB - I'm trying to find / workout the formula which is used to determine this, now after googling this question I stumbled upon what is db noise floor dynamic range

Which gave me some idea, but even confused me a little, so I'm here today to see if someone could help me understand the answer / what formula was used to get to the given answer in better context.

  • $\begingroup$ A decibel is a ratio to a reference value. This link may help: arrl.org/files/file/Instructor%20resources/… $\endgroup$ – Ernie Feb 20 '17 at 2:52
  • $\begingroup$ Thanks for the reference, I'm still slightly confused on working out the formula for it. Could you perhaps be able to show me an example? $\endgroup$ – Code Ratchet Feb 20 '17 at 7:53
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    $\begingroup$ @Code_Ratchet : Decibels use logarithms in order to make the numbers easier to work with. I added an answer that may help you. Remember that the greatest intensity is expressed as a ratio to the lowest (1,380,000/1) when calculating decibels. $\endgroup$ – Ernie Feb 20 '17 at 21:59

Decibels measure relative intensity at a point of interest compared to some reference point. If you want to measure the relative intensity of ultrasound (scroll down to section 4.2 of the link), you could use the lowest intensity as the reference point in order to get a positive decibel reading.

In your question, the highest intensity is 1,380,000 times greater than the lowest. The dynamic range expressed in decibels uses logarithms to measure the ratio of highest to lowest (1,380,000 / 1). If you use the lowest point of the range as your defined reference point, the intensity of the largest relative to the smallest, expressed in decibels, is 10 * Log(to the base 10) of (1,380,000/1) = 61.4 dB.

If you use the highest intensity as your reference point, you would get a negative value (-61.4). You can work this out using the Log key on your calculator.

  • $\begingroup$ Thank you for the explanation and the formula, helped me greatly. $\endgroup$ – Code Ratchet Feb 21 '17 at 0:16

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