how do i measure Sones?

Also you have to factor in the size of the room for makeup air, to help keep the steam down. 110 CFM may not sound a lot. But the larger the turbine and duct, the faster it can pull out the steam from the space.

"One sone is roughly equal to the sound of a refrigerator running. Normal conversations take place at about 4 sones, and light traffic rates up to around 8. Use sones to compare units, but be aware that the higher the CFM, the higher the sone rating is likely to be."

So figure that at 3/10's less than 1 Sone, you are talking about a pretty quiet unit at about 26.245 Phons.

"The loudness of N = 1 sone is equivalent to 40 phons, which is the loudness level
of LN = 40 dB of a sine wave (sinusoid) with a frequency of f = 1000 Hz."

"For loudness level LN < 40 phons: loudness L in sones = (LN / 40)2.86 − 0.005 LN in phons.

For loudness N < 1 sone: loudness level LN in phons = 40 × (N + 0.0005)0.35 N in sones.

According to Stanley Smith Stevens' definition, 1 sone is equivalent to 40 phons, which is defined as the loudness level of a pure 1 kHz tone at LN = 40 dBSPL, but only (!) for a sine wave of 1 kHz and not for broadband noise.

There is no "dBA" curve given as threshold of human hearing. "dBA" has absolutely noting to do with sone, or with phons, or sound pressure level in dB.

60 phons means "as loud as a pure 1000 Hz tone with a level of 60 dB.""

This should help to place that fan in a better scale. It is a little above a whisper. Of course a room like a bathroom with a lot of surfaces, is going to amplify the sound.

There are free db meter apps for both iOS and Android OS. They do at least give you some reference at a C weight, what you are looking at.