The usual places sound comes from in electronic circuits is inductors and ceramic capacitors.
The cross product of current and magnetic field is a force. Forces always work on two things, which in the case of a inductor are the core and individual segments of wire that make up the windings. At the right frequency, this can make the winding vibrate a bit, which you hear as sound.
Ceramic capacitors exhibit piezo-electric effect to varying degrees. The more efficient ceramics capacitance-wise are also more susceptible to this. If I remember right, barium titanate is particularly good at this since the titanium atom in the lattice changes between two energy states, which also cause it to change its apparent size. Yes, the ceramic is actually shrinking and growing very slightly as a function of voltage.
I just recently had a problem with this in prototypes of a new product. A power supply capacitor was subjected to 5-10 kHz ripple, which causes the whole board to make a annoying whining sound. I test five different models from different manufacturers, but all the ones that had sufficient capacitance had the noise problem. I have now reluctantly switched to a aluminum electrolytic for that part.
In your case your switching frequency of 1.5 MHz is way too high to be audible, so it can't be the switching frequency directly. Most likely your power supply is meta-stable and you are hearing the control fluctuations. There may not be much output ripple at the audible frequency, but you can probably see a little difference in the duty cycle at that frequency. At very low currents the control loop may be causing bursts of pulses with some dead time between bursts, which could have a strong component in the audible range. At higher currents the system is probably running in continuous mode and is more naturally damped, which is why the control response in the audible range decreases.
Also look at the current draw of whatever the power supply is driving. That may be in the audible range, forcing the power supply control response into the audible range too.
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Best Answer
If the maximum load current is 3A, then you know one thing - the inductor saturation current has to be above this value. 3A flowing in your load is also the average current flowing in the inductor and providing the regulator doesn't enter discontinuous mode, the peak inductor current won't get above 6 amps.
(source: tantosonline.com)
The above picture shows an inductor in "continuous mode" and also when it enters discontinuous mode.
It's probably a good idea/rule of thumb to make the ripple p-p current about the same as the full-load average current (as an approximation to best practise) and this means the peak inductor current will be 4.5 amps on full load.
For decent efficiency you should choose and inductor that is probably rated twice this value for saturation current. Another rule of thumb.
As for the flyback diode I'd probably choose a 5A device off the top of my head and without going into the details of the device because it's too much to expect!