# Changing RMS of an audio file?

Hi, I’m new in this site. I searched a lot to solve my issue, but I found nothing.

For a psychology experiment, I need to have different versions of an audio file that have different RMS values. for example let assume RMS of xyz.wav is NNN, and I want to have another version of this audio file with RMS value equal to 1/2 * NNN. Is there any tool, software or plugin to aim this goal? If so, please let me know. It’s urgent.

Note that the level in dB is a ratio relative to “full scale” (0 dB), so valid signal levels are negative numbers. -6 dB is half the amplitude of 0 dB, -12 dB half the amplitude of -6 dB, -18 dB is half the amplitude of -12 dB (an increase of +6 dB doubles the linear amplitude).

You can measure the RMS level of a selection using the “Contrast” too: http://manual.audacityteam.org/o/man/contrast.html

Effect → Amplify can either amplify (by entering a +dB change) or attenuate (by entering a -dB change).

You calculate dB as 20 x Log(X/Xref)
. With digital audio the reference of 0dBFS (zero decibels full scale) is the “digital maximum” of 100%.*

If you just want a change from the current level, you can use the current level as your reference (without knowing it’s actual RMS value). So for example if you want to calculate a 50% reduction in level, you can use 100% as your current reference or 20Log(50/100) or 20Log(0.5). That way you don’t need to know the absolute dB levels (relative to 0dBFS).

Or, to convert dB to a gain or attenuation factor: 10^(dB/20). That is, 10 to the power of (dB/20).

Those formulas apply to digital amplitudes or voltages. If you are working with power, use a factor or 10 instead of 20. i.e., +6dB is a doubling of the signal level but it’s 4 times the power (Watts). That’s simply because when you increase voltage, the current also increases proportionately.

Note that as long as amplification or attenuation is linear**, the peak and average change by the same number of decibels… If you reduce the peaks by 6dB, the RMS is also reduced by 6dB. The ratio remains constant… If your peaks are 10dB greater than the RMS and you change the volume, the peaks will remain 10dB above the RMS. (Since dB are logarithmic, subtraction, the difference, is a ratio.)

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• 0dBFS is the referenced to the maximum value that a “regular” integer WAV file can hold, and it’s the maximum for digital-to-analog and analog-to-digital converters. Floating-point files and Audaciy (which uses floating point internally) use a different numerical reference and they can go over 0dBFS.

With acoustic dBSPL levels, the reference is the quietest sound humans can hear, so those dB numbers are positive. Since we are usually listening with uncalibrated playback systems, the relationship between the digital dBFS level and the dBSPL loudness is usually unknown. But again, the ratio is constant so if you increase the digital level by +6dB, the acoustic loudness also goes up by +6dB (assuming the amplifier doesn’t distort and go non-linear).

** Things get non-linear if you try to push the peaks above 0dB. (When you hit the upper limit and go into distortion, you can boost the RMS level without boosting the peaks.)

Someone may have done this previously … https://en.wikipedia.org/wiki/Equal-loudness_contour