waveform – Is the amplitude -1 as loud as amplitude 1?

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 value -1 (underpressure for your eardrum).

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.)