Short answer
The auditory system remains active during sleep.
Background
Filtering of sensory input during sleep is a recognized phenomenon and indeed the senses are typically lulled during sleep. This phenomenon is, at least partly, caused by thalamic gating. Thalamic gating is caused by the thalamus entering a state in which slow-wave activity disrupts or even blocks incoming sensory input (Coulon et al., 2012). However, the auditory system remains active during sleep and during the full sleep/wake cycle auditory stimulation will evoke responses in various parts of the central auditory system beyond the thalamus (Issa & Wang, 2008).
In fact, when supra-threshold stimuli are intense enough, they invariably result in wakefulness. Auditory stimuli result in so-called K-complexes in the cortex, which are believed to be functional and specialized sensory responses during sleep (Velutti, 1997).
Hence, when you ask...
The sound I make is around 150 ms long, so I don't understand how someone who is being awakened and transitioning from sleep into consciousness would have the ability to distinctively recognize it.
...the answer is that the auditory system is active enough to process and recognize the sound. Further, the typical modulation frequency of speech is about 4 Hz (Leong & Goswami, 2014), i.e., the typical syllable length is about 250 ms, meaning that sounds with a duration of 150 ms are long enough to be processed.
References
- Coulon et al., Pflugers Arch (2012); 463(1): 53-71
- Issa 7 Wang, J Neurosci (2008); 28(53): 14467–480
- Leong & Goswami, Front Hum Neurosci (2014)
- Velutti, J Sleep Res (1997); 6: 61–77