It’s not the bridge rectifier, but it’s an artifact of the operation of the switchmode power supply. Similar effects are often described as 'coil whine '.
The switching operation varies in duty cycle and frequency depending on load, and isn’t absolutely stable so oscillates a little bit. This switching supply is often in the audio range; typically between about 5kHz and 200kHz depending on design and load.
Changing current and magnetic field causes the physical components (particularly transformers/inductors) to change size and shape, and this vibration causes audible noise. At some conditions, it will resonate at an audible frequency and be loud. At other conditions, it might not resonate and/or the frequency is outside the audible range, so it’s silent.
Mains transformers do the same, causing the characteristic 50/60Hz hum. You’ll also hear the same out of cellphone chargers.