In terms of physics, Sound waves (including infra and ultra) are not as intense as many other wavelengths. Light is more intese than sound!! Sound waves are not dense enough to cause harm any more than normal light (UV is the highest level of light and that is what the damage starts at) If you shone an extremely bright light on your belly I think you would have as much chance of injuring the baby as you would putting a doppler on. There is very little risk identified because there is very little risk!! An Xray which is the way twins used to be determined is more harmful than an US so I am happy to have US and doppler as often as I need / want to.
Sound waves can also cause glass to shatter, and beach whales

Light doesn't travel as intensely through the stomach wall and uterus, either.

Ultrasound has a thermal affect on tissue and penetrates internally to that tissue - that's why it is used in physiotherapy, not simply as an imaging tool. There have been concerns raised about the effect of this stimulation particularly on the development of the foetal nervous system.

I have looked long and hard for good longitudinal studies or good, large double blind studies done on the safety of ultrasound exposure, and have not found convincing evidence for its safety. Bearing that in mind, my own preference is to keep it for strictly clinically necessary examinations. For a woman who is extremely anxious about her pregnancy (and stress is a known risk factor for pregnancy) this may indeed qualify as a clinical necessity. I'd also however strongly recommend other methods for managing that anxiety and stress.