# Amplitude Manipulation as it Relates to Volume

Hey,

So I am kind of new to audio programming and I have been fiddling with the amplitude of PCM waves in order to change volume (I feel like this may be frowned upon), and I was wondering if someone could correct me if I am incorrect.

(The following is made under the assumption that there is no loss of accuracy while converting from higher amplitude to lower amplitude)

1)So my understanding is that if I have an unmodified audio file ‘A’ and I create audio file ‘B’ with the amplitude of each wave being 10% of the original, then the result should be that ‘B’ should be 10% as loud as ‘A’.

2)Now if I play file ‘A’ at volume ‘x’ and I play ‘B’ at volume ‘10x’, they should sound the same.

The reason I ask is that I have been trying to code this (too much code to put in) and I have am skeptical of the quality of the audio in my results. It sounds as if ‘A’ sounds better than ‘B’ and I am almost completely certain there is no loss in accuracy from converting ‘A’ to ‘B’.

I would really appreciate any help with this and thank you for your time.

“Loudness” is not the same as “Amplitude”. See here: http://en.wikipedia.org/wiki/Loudness

If your tracks are 32-bit float format, amplifying is extremely accurate.
For example, if you apply the Amplify effect with a setting of -10 dB, and then apply the Amplify effect with a setting of +10 dB the result should sound identical to the original.

Thank you Steve.

If I understand this correctly, by increasing the Amplitude uniformly across all frequencies, the sound will not sound the same as increasing its Loudness (which will increase the amplitude of certain amplitudes more than others to fit subjective measures).

There are several problems at once:

1. The loudness generally computes logarithmically, not linear, so 10% amplitude are only 1% power, what equals approx. 1% loudness. There is an overview chart in the Wikipedia under Decibel, where this can be better seen than in a math formula.

2. The human hearing and the audio processing inside the brain also do not work linear, what has to the constequence that even if you change the volume level of all frequencies equally, the frequency perception inside the brain will not be the same at low volume levels and high volume levels. This is what the non-linear curves under Loudness express.

The practical problem is that the frequency perception inside the end-users (listeners) brain depends on the volume level of his/hers hifi equipment at home, what nobody can exactly predict. That’s the reason why audio engineering is only 10% math knowledge and 90% experience.

The important point with mathematical loudness is to understand logarithmic Decibel math. But because math is very precise, while the human brain is not, high-precision math will help not really much with acoustical volume levels. Here the ears are more important than the computer.

• edgar

Thank you for the further clarification. I understand it now. Thanks a lot.

Also reference Chris’s Compressor…

– Chris’s Compressor
http://theaudacitytopodcast.com/chriss-dynamic-compressor-plugin-for-audacity/

He created a show sound compressor (and plugin) that mimics in an amazing way the process that radio stations use so you don’t have to constantly run the car volume control up and down during a show. Changing the Compression number from 0.5 to 0.77 and it comes startlingly close to the local KPCC radio station.

So if you’re designing a compressor, that’s your competition. It doesn’t seem to be doing anything, but for some reason, the loudness variations are gone.

Koz