How to have exactly same RMS for two mono sine tracks of different RMS?

Dear senior members and moderators of the Audacity Forums,
I remember an earlier lesson of using the Amplify… tool to have the peak permissible amplitude level for a mono sine track.
I have implemented it for two mono sine tracks to make the two tracks of identical RMS.
However, when I use the Analyze/Measure RMS tool, I find one track at an RMS at -4.01091 dB while the other at -4.01996 dB.
I need to make them exactly equal.
How to?

You can try Loudness Normalization. (Select RMS, not Perceived Loudness.)

Mathematically, the RMS of a pure sine wave is 1/(the square root of 2) times the peak. That’s about 0.707 x peak, or -3dB, and that’s about what I get.

That’s VERY CLOSE! Nothing is perfect in the real (analog) world.

And digital audio is quantized in amplitude and time… That makes it “imperfect”. There are limits to the resolution in both dimensions, and there is no information between the samples.

But, if you amplifying for 0dB peaks, I don’t know why your not getting closer to -3dB.

Negative numbers, so the lower one is -4.01996 dB.
The difference between the two is 4.01996 - 4.01091 = 0.00905 dB

Audacity’s Amplify effect “only” has 3 decimal places, but we can use the Nyquist Prompt for greater precision.

Apply this code using the Nyquist Prompt to the lower level track:

(mult (db-to-linear 0.00905) *track*)

and the track’s RMS level will be increased by 0.00905 dB.

If they are of different frequencies its unlikely you will perceive them as equally loud …

It is because I don’t wish to reach saturation. I used -1 dB peaks.
Thank you, Mr. DVDdoug, Mr. Trebor and Mr. Steve, for your kind inputs.
Mr. Steve, thank you for the Nyquist Prompt Code. I am sure it will work exactly the way you’ve said. If it doesn’t I will get back to you.
Mr. Trebor, yes that could be the reason. I know that our auditory system isn’t exactly linear. In optics too, energy of a photon is dependent on the wave packet’s central frequency. However, 5Hz shouldn’t cause a significant difference. Yes, it doesn’t. But the minute difference bothers me.
Anyway, I now have a hang of your points. So thank you indeed.
Please also be kind to peruse my pending questions or bring a closure to them, informing me that you are working on them. Otherwise, I keep on returning to them to check if I have received a reply.
I am interested particularly on downloading the RAM data of the Noise Profile as a separate file. I have posted two questions with probable codes to Audacity’s GitHub page to meet my objective but haven’t heard from them still. I am not a very competent programmer and don’t have professional experience. So I find myself lacking in these areas.
Best wishes.

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