This is for a music/physics crossover experiment. Almost everyone will be familiar with the Doppler Effect, even if they don't know the name. Imagine that a vehicle is blaring its a siren or otherwise making a noise with a distinct pitch. As the vehicle approaches you and then passes you, the note will appear to drop in pitch.
The apparent note will be higher in pitch than the "true" note when the vehicle approaches, and the apparent note will be lower in pitch than the "true" note when the vehicles recedes. (By "true" note, I mean the original frequency emitted, prior to any Doppler shift.) There will be a glissando as the car passes. The closer the vehicle passes you by (e.g., the closer you are standing to the side of the road as the vehicle passes), the more rapidly the glissando will occur.
It occurred to me that it should be possible to calculate the speed of the vehicle by the interval between the approaching and receding notes. So, I have performed some calculations and here are a couple of examples: if the perceived pitch drops by a (well tempered) minor third, then the vehicle was travelling at 106.8km/h (66.4mph). To produce a perceived drop equal to a major third, the vehicle must have been travelling at 142.1km/h (88.3mph).
Personally, with my skills, even an accuracy of 10km/h would be a challenge. Increasing the speed by only 10km/h would produce something I might recognize as "a slightly sharp minor third," but it might be difficult for me to discern precisely how sharp the interval is.
Here is my question: how close could musicians come to determining how sharp/flat an interval is, in cents? For example, would musicians be able to detect (by ear) that an interval is 10 cents above a minor third, or will their unaided ear be limited to detecting that the interval is, e.g., 100 cents above a minor third? I can distinguish how sharp/flat an interval is to a semitone, but I expect that good musicians could do rather better.
So, does anyone know how good/precise musicians are at judging interval intonation in this fashion?
- Perfect pitch is not required, just the ability to judge the interval.
- The temperature will have an effect on how much Doppler shift occurs in the perceived frequency. The values above assume 20C / 68F. Oddly, the air pressure does not have an effect. Humidity does in principle but it is very small.
- I am not expecting a musician to answer with a speed, but rather with a musical interval and, ideally, with a judgement (in cents) of how far off an interval is (e.g., "this is a minor third that is sharp by 100 cents").
- I am not expecting to make radar guns obsolete. The purpose is for fun and for education. Forget my proposed use for the moment.
- Whether the musician is a professional or a good amateur is not important. There may be some amateurs who are better at this than some professionals. I am also interested in how well piano tuners would be.