Sound measurement percentage in tolerance

[kerfluffel]

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, let's say tolerance is 34.0 to 36.0 dB for each frequency band. let's 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.

 

[jvicens]

Thank you for sharing your interesting question. I am a scientist with expertise in acoustics and I am happy to assist you.

From what you have described, it seems like you are trying to calculate the overall percentage of frequencies that fall within your defined tolerance range. To do this, you will need to consider both the frequencies that are completely within tolerance and those that are close to the tolerance range.

One approach you could take is to define a threshold for what is considered "close" to the tolerance range. For example, you could say that any frequency within 0.5 dB of the tolerance range is considered close. Then, you can include these close frequencies in your overall percentage calculation.

Using your sample numbers, let's say that the threshold for "close" is 0.5 dB. In this case, frequency 3 (36.1 dB) and frequency 4 (33.9 dB) would be considered close to the tolerance range. Therefore, the overall percentage in tolerance would be 75% (3 in tolerance / 4 frequencies * 100 = 75%).

Another approach you could take is to calculate the average distance of each frequency from the tolerance range. This would give you a better representation of how close the out of tolerance frequencies are to the tolerance range. In this case, the overall percentage in tolerance would be 87.5% (average distance from tolerance range = 0.3 dB / 4 frequencies * 100 = 87.5%).

I hope this helps you to better understand how to calculate the overall percentage in tolerance for your 1/3 octave frequencies. If you have any further questions, please don't hesitate to ask.