Speaking of unusual ways to play music:
This is more in the spirit of this thread:
Impractical math problem: How long a section of various pieces of music would it be possible to play with any specific doppler-flute? Or the reverse, what are the minimum requirements of a d-flute able to play a specific tune?
How much does adding a second car change these math problems?
Let’s start with Mary had a little lamb.
This thread does remind me of a story I heard once from the early (and I mean early) days of home computers. At a computer hobbyist meeting, someone arrived with an Altair 8800, the state of the art at the time. He plugged it in, and because there was no means of removable storage he spent much of the meeting entering a program. Computers of that era being what they were, they had a tendency to interfere with the reception on radios that were nearby. Well, this programmer had discovered that he could control the interference based on the instructions that the computer was running. He finished his program, put a small transistor radio on top of his computer, started the program, et voilà.
The pitch range would be a function of the emitter’s max speed. Some years ago I made an Excel spreadsheet to calculate the relative pitch change, due to Doppler effect, for an emitter moving directly toward and then away from a receiver. I figured you could achieve a pitch range of one octave by moving toward and then away from a receiver at 254 MPH. You come close to this with the camera right next to the straightaway at the Indy 500, when the cars are zinging by at about 230 MPH; compare the apparent pitch as they approach the camera with the apparent pitch as they recede from the camera, and it’s two half-steps short of a full octave.
Also, not quite the same thing, but you might be interested to know that there’s already a musical instrument that makes deliberate use of the Doppler effect: the Leslie speaker. The sound is emitted from rotating speakers; by turning the rotation on/off, the player can create/suppress a sort of vibrato/tremolo effect. Used to good effect during the guitar solo on Another Brick In The Wall.
For the rail-o-phone, the trick would be to find the “average” tone of the piece to be played, and pick the fixed frequency on the car to be that average, such that the motion away for low notes would be matched by the motion towards for high notes. Or more likely, transposing the piece to be played to match the fixed tone on the car.
The track would still need to be insanely long, though. There aren’t many songs with less than a one-octave range, and songs often have a high or low note (or a set of them) maintained for several seconds. More practical would be to have two such systems side by side, so they can take turns playing the notes, and resetting with the speaker turned off.
That “Top Gear” segment was the first thing I thought of. I got a real kick out of that.
Oh, no, it’s much more than “just a matter of money.”
It’s literally Rockette science.
I like the cut of your jib, Mister! Above all, these machines need to have some “exciting” failure modes.
We could replace the elevators in a tall building with a rotating high speed bucket-wheel device alongside at ground level that flings each passenger upwards so their free-flight trajectory apexes just above the floor they’re going to. At which point a synchronized catcher’s mitt thingy slides out from the side of the building just under the person who plops down into the mitt and is safely pulled back into the building. Like the first half of a juggling routine. The [del]balls[/del] people are tossed up and are caught just aft/after apex.
A similar machine on the other side of the building is used for getting down. You jump off a platform and free fall to land in the bucket wheel’s bucket which is rotating at an appropriate speed for a soft docking at tangency. Then it brings you to a safe stop within a turn or two.
Ideally the whole thing has a steampunk feel where all control systems and sync systems between upper floors and the base station are cogs, bicycle chains, cams and gears. No visible lasers or computers. Even if we need to use hidden lasers and computers and such to make it actually work once in awhile.
And best of all, it has some very colorful failure modes.
As long as you like the color red. 
Bravo. 
Impossible Engineering Challenge
A thermostat my wife can operate
Well I think we still need an empirical answer instead of the theoretical one for, Aircraft on a treadmill
I’d like to build a computer model that accurately predicts the output of a pot still. All of the reactions are well known and are basically a mix of organic chemistry, thermodynamics, and fluid dynamics but aside from being able to design my pot stills to put out a particular flavor it doesn’t really add anything to an industry that’s had thousands of year of guess and check but I could make some great booze.
Remember the Spruce Goose?
Built from wood, eight engines, still the longest wingspan of any airplane that ever flew. And, it was a seaplane!
Why stop there? Why not replace those old, troublesome radial pistons with modern JETS?
How about GEnx turbofans, each pumping out 60,000+ pounds of thrust? Put eight of those puppies on the Goose (maximum gross takeoff weight 400,000 lbs.) and that baby will take off like it’s shot from a catapult.
Did someone mention exciting failure modes? How about the hull being torn to shreds as it zooms across Long Beach Harbor! Imagine the thrill of its plywood wings being ripped off the fuselage when the jet engines reverse thrust on touchdown!
WE HAVE THE TECHNOLOGY. WE HAVE THE TOOLS. ALL WE NEED IS THE WILL!