OK..... I've done a little research on the doppler effect, and I think it won't hurt us too badly. Here is quite a handy little tool
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/dopp.html#c4
I made a couple of assumptions here.
1. An icecream truck that is trying make sales will probably be driving somewhat slow.
2. Icecream trucks do not make their rounds when it is cold outside(actually for our purposes, this won't make much of a difference anyways)
Now here are some of the results.
WORSTE CASE SCENARIO
At 40C(104F) an approaching source travelling at 5Mph and emmiting a sound at a frequency of 2Khz will sound like 2013Hz
At 15C(59F) -----------------------------------35Mph------ will sound like 2096Hz which gives us a range of 83Hz+13Hz=96Hz, in other words, a bandwidth of 96Hz will cover speeds from 0 to 35Mph and temperatures from 59F to 104F (and actually temperature does not have a great affect 1-3Hz at most)
Realistic scenario
25C(77F)--------------20Mph---> 2052Hz
All of these calculations assume that the vehicle is coming directly at you, in which case, the given frequency (2052Hz at 20Mph) will not change until the vehicle hits you, at which time the frequency will abrubtly change to a lower tone as it leaves you. Anyways, my point is, if you are off to the side of the path of said vehicle, then as the vehicle comes into earshot you will here a frequency slightly lower than stated frequency per speed, and as the vehicle approaches, the frequency will drop and pass through 1F as the vehicle passes etc. etc.
From what I can see the pulses are lasting approx. 320ms. With the approaching vehicle, the apparent wavelength will shorten, causing the frequency to increase. I assume this will also shorten the apparent length of the pulse right? I hope at least some of this is helpful and relevant. I'm sure some simple math will help determine what the shortest pulse length to expect is. bye for now