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Ambulance sirens are notoriously out of tune.
Beamforming (in acoustics) is a technique that uses an array of microphones to detect a sound from a single direction, but this does not bear much relevance to the idea at hand.
If you knew the speed of the vehicle and the exact location of a single
bystander, and detuned the siren accordingly, you could correct the Doppler effect for them. However, for anyone not standing very close to this bystander, the effect would be worsened, with the sound changing pitch twice. Unsatisfactory!
Proposed is an array of sirens atop the ambulance that, based only on vehicle speed, play carefully delayed versions of the klaxon sound. This would of course be implemented by some digital circuitry, but as an analogy to how it will work, consider the following.
If you placed a conveyor belt on the roof of an ambulance and drove it backwards at the right speed, the top would appear to be stationary relative to the ground. If a series of sirens were mounted on the conveyor, and only turned on when on the upper half, each one would appear as a stationary source of sound to all bystanders. The sirens hitting the end of the conveyor would fade away and then reappear at the front. The Doppler effect would be completely eliminated.
One advantage of emulating this set-up using a phase delayed siren array is that the end product would not look any more halfbaked than an ordinary ambulance, thus confusing and disorientating everyone.
Tune in next time (hoho) when we will attempt to correct the Doppler shift for moving bystanders. The current plan is to somehow stop them moving.
Artificial Doppler effect
//If you placed a conveyor belt on the roof of an ambulance and drove it backwards at the right speed// [pocmloc, Aug 07 2016]
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||Its about time someone put some effort into rectifying this sloppiness on the part of ambulance sirens. Well done.
||But imagine now an ambulance approaching a listener on the sidewalk (the ambulance is not actually on the sidewalk). A second listener is behind the first, but 2 blocks farther back from the road. I suspect the magnitude of the doppler effect will be greater for the listener who is closer than the one farther away because the distance to the close listener is changing more quickly (as a percentage) than that to the far listener. The sound wave compression and uncompression will be greater for the close listener and so the conveyor belt will not be able to correct for all listeners.
||I lack the math to prove this is true.
||In your example with the two listeners, one near the ambulance's
path, the other further away, you are correct, there is a difference in
the magnitude of the observed Doppler effect. This is because of
the difference in the amount of change in the path length.
||If you wanted to calculate it, you'd start by calculating the
hypotenuse of a right triangle, with the 'a' leg along the path of the
ambulance, 'b1' and 'b2' being the distances from that path to
respective observers, and 'c1' and 'c2' the paths the sound would
||Start out with a snapshot of the instant of a wave peak coming from
the approaching siren. It will have to travel the path to an observer.
The next peak (assuming the siren has moved) will come from a
different point a little bit farther along the line of the siren's motion,
so when you calculate the triangle, 'a' will be different, thus 'c' is
different, so the wave peak will have a shorter path to follow to
arrive at the observer - but c1 will change more than c2.
||However, in [mitxela]'s proposal, the siren is being held stationary
with respect to the ground, so the 'a' leg of the triangle doesn't
change. Therefore, even though the path lengths to the two
observers is different, c doesn't change; they are still held constant
for the duration of each siren's path across the top of the conveyor.
There will be some sort of a blip as you switch from one siren to
another, but it won't be a change in frequency.
||It would be very confusing, though. The frequencies used for sirens
are selected to be those at which human ears are most sensitive,
however they are also the ones at which humans have the most
difficulty triangulating. Making the Doppler not work like one would
expect, I assume, would make it even harder to figure out.
||The conveyor is not [mitxela]'s proposal, only the phase delayed array. <link>
||This is the incorrect approach. The correct approach is to
draw inspiration from rainbows. Each person views their
own personal rainbow. The prismatic effect that one person
sees is from a certain view of a certain set of raindrops at
that certain time, and a person standing next to that
person would see through an entirely different selection of
raindrops at that exact time, hence, the rainbow is their
own personal rainbow and inherently discrete from the first
||This would succeed, I think, in counteracting the
Doppler effect, but it would also produce the effect of
all of the sirens being out-of-phase with each other
regarding their high/low tone alternations, resulting in a
||"stop them moving"
You probably should not have said that. It is a sure
invitation for the Borg to make suggestions.
||// all of the sirens being out-of-phase with each other //
||That's actually an interesting point. I was going to say, "ah, but the computer will correct for it" but it would not be able to do that for all bystanders.
||However, since the length of an ambulance is only a few metres, the phase shifts would be around 1 millisecond.