# Is the amplitude -1 as loud as amplitude 1?

I am uncertain about the concept of the sine wave's amplitudes: for a say 1 hz sine wave is the oscillation between loud and silent parts to be thought of as oscillation between amplitudes 1 and -1, in other words is an amplitude of -1 as loud as amplitude 1?

• Amplitude must have a unit, such as a decibel (with an explicit or implied reference). In other words, 1 or -1 what? Feb 8, 2023 at 11:55
• @ToddWilcox -1 to +1 is the display values such as Audacity use as "full scale". Feb 8, 2023 at 13:01
• Yep, -1 and +1 have the same amplitude. Feb 8, 2023 at 13:11
• @Tetsujin huh. Huh? Not 0 dBFS? Oh wait maybe it’s the signed int sample value scaled to 1 so you don’t have to keep track of 16, 24, and 32 bit values? Feb 8, 2023 at 18:17

for a say 1 hz sine wave is the oscillation between loud and silent parts

No loud and no silent parts for 1 Hz frequency, sorry. You will hear nothing… ;-)

The perceived sound is an oscillation of air (or water, if you dive into it) – you may imagine air oscillating in the direction to your ear and then from your ear, repeatedly.

It means that the pressure to your eardrum

• progressively increases to reach your +1 maximum value (in some linear units),

• then progressively decreases to 0 (no pressure),

• continuing decreasing to the value -1
(underpressure for your eardrum, with its maximal value at -1).

So +1 and -1 values are both maximum values for the pressure / underpressure to your eardrum, but hardly to say that there are maximum values for the perceived loudness of the sound.

During one oscillation of the sine wave (0 to +1 to 0 to -1) we don't perceive changes in loudness, we perceive something as an average value.

(Similarly, the needle of a voltmeter plugged into the 230 V / 50 Hz electric outlet don't oscillate between -325 V and +325 V – it stays at the 230 V value.)