=design =audio
Emergency vehicle sirens
typically use a narrow tone with frequency swept up and down. That was
chosen because it's very noticeable relative to the amount of power used,
but minimizing power needed for noticeable sirens isn't very important.
What's much more important is making it easy for humans to tell where the
sound is coming from. For the same reason, the beeping typically used by
heavy vehicles going backwards is a poor choice.
Audio localization
by humans uses phase correlation, where the waveform each ear receives is
compared, and the relative delay is determined. (Probably using a Fourier
transform.) So, if you want to design a sound so that people can tell where
it's coming from, it should have minimal repetitiveness. Noise is good
for that, so let's start there. White noise has been
proposed for sirens for this reason, but I prefer pink noise. Humans are also good at localizing crackling
noises, but those have a greater tendency to scare animals.
Pink
noise requires a relatively high power to be noticeable, so let's apply a
notch filter at 4 kHz to make it more noticeable per power. We want our
noise to have a sense of urgency, so let's add 10 Hz tremolo. The result
sounds kind of like a steam train.
In some
cases, we also want the Doppler effect to be easily noticeable. We can do
that by adding some sine waves, say, 500 Hz and 750 Hz. Let's apply some
distortion to them to shift some energy to harmonics to slightly reduce ear
fatigue from narrow constant frequencies and avoid potential dead spots from
interference.
Finally, let's add 2 Hz
tremolo to reduce perceptual satiation. The result
sounds like this. That's using
heavy tremolo with offset phases on the sine waves; I'm not sure if that's
optimal, but it seems more "siren-like".
It's also possible to convey information with the numbers
chosen: for example, different vehicle types could use different sine wave
frequencies, and tremolo rate could vary depending on vehicle speed.
For a warning noise for slow-moving vehicles backing up,
there's no need to make it easy to perceive the Doppler effect. Also, people
hear them for longer, so the sine waves could become annoying. So, instead
of the sine waves, it's probably better to overlay a distinctive sound that
indicates the vehicle type, maybe something derived from a musical
instrument.