The electric current through the machine windings creates attracting and repelling force between wires due to the magnetic field created by each wire in the stator. Due to the high frequency switching on the input source voltage (details will follow below), the current through the machine windings will also have a high frequency ripple on top of the normal low frequency wave. Each switching instance creates a mechanical impulse on the machine windings (think of it as an impluse on a piano wires)... high frequency impulses then sound like a beep.
The beep sound indicates that the source powering the BLDC machine uses a controlled output voltage with high frequency modulation.The output voltage by the source can be either sinusoidal or square wave; As long as the amplitude is controlled for current/speed control, then there is a high frequency modulation in effect.
The reason the sound is like a high pitch beep is that most commertial inverters usually operate in a range between 5KHz to 30KHz switching frequency, which happens to be near the upper bound of human hearing threshold.
In an experimental inverter setup, you can eliminate the noise by using a high frequency inverter operating above 50KHz.
That is not beep sound, frictional noise due to the coenergy occur in the machine. Due to the cogging torque and commutation torque, it occurs in the machine. Beep sound will occur in the inverter side due to the frequency and current range
Beep sound can be occur due to high drive frequency of BLDC motor driver. In this case the rotor can not follow the coil magnetic filed so it stars to vibrate in that frequency which will produce sound in motor. Also noise can be made by driver but it is not in your case.
To produce sound two elements is need. First is the signal .Second transducer to convert electrical energy to mechanical. In case of BLDC making beep sound. This signal (waveform) is generated by its ESC and the Speaker is motor itself.
For a BLDB( out runner) the inner part is the is the stator with windings and rotor carry sets of permanent magnets which vibrate rotor to produce sound on a signal to stator of BLDC .You can see the it analogy with generic speaker with electromagnet and diaphragm as vibrating element.
Now the question arise is why ESC is giving such signal to BLDC to produce beep?
Answer is simple. It is given the status indication and mode on which the BLDC is operating currently. The Every beep by BLDC has meaning. This meaning is set by the ESC manufacture. One of the example of this beep meaning is define in the attached datasheet of a turnigy ESC.
You may also hear a particular Beep sequence while arming BLDC. The Beep you may have heard is the beep-----
Which indicate startup. The next beep Sequence may indicate the battery type attach to ESC.