Hixee is correct in that the frequencies of the drives resonate with the natural vibrations of the track and train at certain speeds, this amplifies the sounds but is not the source. There are actually 2 distinct and seperate sounds produced by linear motors caused by 2 different systems.
Trax is leaning in the right direction and I will explain how the sounds are created.
To understand what is going on you first need to know the difference between the types of motors used as this affects how they are powered and therefore the sounds they produce.
A linear induction motor, or more accuratrely an asynchronous electromagnetic induction drive is the simplest and easiest to control as the stator mounted to the track produces a drive field that induces a driven field in a paramagnetic fin on the train, the train then rides this field down the length of the launch.
The sound this system makes is a high pitched whine like that produced by station drive wheels, the reason they sound the same is because they are driven by the exact same device.
Both rotary and linear induction motors can be driven by whats called an inverter, or what should be called a variable frequency drive. These things take an AC supply voltage, usually 415 volts from the mains, rectify it into DC and store the energy in a set of capacitors. The drive then feeds the motors with DC pulses at a contstant rate of 12KHz, this is the control frequency which gives off the distinct high pitch noise. Each pulse of the control frequency is of a slightly different voltage that range from +415v to -415v in order to create an imitation sine wave that the motor responds to just as if it were AC straight from the mains. What a VFD allows you to do is adjust the AC frequency to precisely control the speed that the motor will run.
For example, if you just wanted to move the train slowly then the output from the VFD would only need to be a constant 10Hz, this would move the train at a slow and constant speed.
When it comes to launching, the motors are ramped up gradually to whatever speed is needed. There really is no technical limit to how fast LIMs can accelerate, hit them with their maximum rated frequency straight away and anything strong enough to stay in once peice will accelerate in a fraction of a second. There are practical limits however, the immense current draw would incinerate the drive coils and their supply cables. If by some miracle that didn't happen though, you would probably rip the fins off the train.......
Anyway I digress.
The second type is the linear synchronous motor which is powered the same way as an induction motor through a VFD, the difference is how the stator on the track interacts with the train.
The 12KHz control frequency produces the same high pitched noise which resonates through all the active drive units and changes volume according to current draw. Instead of inducing a field in a fin, the train has ferromagnetic yokes which are exactly the same type used for regular magnetic braking. The yokes have 2 rows of around 10-20 permanent bar magnets depending on its length. Each individual magnet in a row is positioned vertically with respect to the track and their poles alternate along the length of the yoke.
The output frequency is synchronised to each individual magnet in each yoke and depending on the final speed, this frequency usually ends up quite higher than the 50Hz maximum for most induction motors.
As the train moves over the stators, the drive coils give the magnets tugs and pushes that are in step with each other, this gives an increasing engine-like sound in addition to the high pitch sound caused by the control frequency.
