For any individual fan, various rules have been proved, including one that air flow is proportional to motor speed. If I read the "Noise" rule correctly – and assuming fan revs are proportional to supply volts – then under-volting a 12v fan to 7v gives 11.7dB noise reduction, under-volting to 9v a 6.25dB drop.
This assumption is often untrue – some fans have a diode in series with the +12v input to guard the electronics against a reverse polarity connection. That will lose about 0.75v. Then the electronic switching system will have an inevitable voltage drop, perhaps 0.25v. So a fan connected to a 12v supply may only see 11v at the motor winding, and at 7v get only 6v.
So, in such cases, the noise reduction by 7-volting works out at 13dB, even better.
Less good, flow at 7v is more like 6/11 (55%) of flow at 12v, rather than 7/12 (58%).
| Variable | When Speed Changes |
| Air Flow | Varies directly with speed ratio CFM1 /CFM2 = RPM1 /RPM2 |
| Air Pressure | Varies with square of speed ratio P1 /P2 = (RPM1 /RPM2)2 |
| Power | Varies with cube of speed ratio W1 /W2 = (RPM1 /RPM2)3 |
| Noise | N2 = N1 + 50log10(RPM2 /RPM1) |
| Multiple fans | total dB = 10* log10[10(Fan#1/10) + 10(Fan#2/10) + ...] Where Fan#1 = Noise from Fan#1 (dBA) etc. |