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Physics sound measurement percentage in tolerance


New member
Dec 4, 2018
I have a graph measuring 1/3 octave sounds checking if they fall into a range so they are within a defined tolerance.

If for example, I have 20 specific 1/3 octave frequencies I am looking at, I can figure out a percentage of which of the 20 frequencies fall in tolerance fairly easily.

However, for the frequencies not in tolerance, I want to calculate how much they are in tolerance (how close was it to tolerance). Also, even if some frequencies are in and out of tolerance, what is the overall percentage in tolerance.

Each frequency is measured in dB, so I believe these are logarithmic...I am having difficulty wrapping my head around this so any help would be appreciated.

To have some sample numbers, lets say tolerance is 34.0 to 36.0 dB for each frequency band. lets look at four frequency values:
1. 35.0 - 100% in tolerance
2. 35.9 - 100% in tolerance
3. 36.1 - is out of tolerance, but actually very close to being in tolerance
4. 33.9 - is out of tolerance, but actually very close to being in tolerance

Two of the frequencies above (1&2) are 100% within tolerance, the other two are not. However, the two out of tolerance (3&4) are very close. Overall, the frequencies together are 50% in tolerance (2 in tolerance / 4 frequencies * 100 = 50%). However, in reality the last two frequencies are so close to being in tolerance that 50% would be misleading. How could I get an overall % to better represent the reality? I apologize, I don't know the math terminology for any of this.