"with what intensity" is correct and usable in written English.
It is typically used to suggest the magnitude of an action or emotion. For example, "They experienced love with what intensity!".
With what intensity did the tsunamis crash onto land?
When did the Chos first observe such episodes, how often and with what intensity?
Given how long, and with what intensity, she has been using that voice, that is a major statement, metaphorical though it may be.
The data help determine how often an area might be flooded, and with what intensity; that, in turn, guides engineers and architects in building bridges, roads and communities.
We also need to know "how much?", "'with what frequency?" and "with what intensity?".
The indicator of score damage of the dwelling corresponds to the responses of the head of the household to the question "What part (roof, walls and/or ground) of this house was damaged by the earthquake and with what intensity (0=no damage to 3=totally destroyed)." The final indicator of score damage is the sum of these three variables and ranges from 0 = no damage to 9 = complete destruction.12.
The maximum platform displacements with the proposed three ddifferent kinds of controllers are all smaller than that with the passive system no matter what intensity or seismic waveform is.
Through their daily social experiences, children learn what acceptable emotion expressions are and with what kind of intensity they should be expressed [ 55].
A rebel commander nicknamed Matoshi said villages outside Tetovo had been bombarded overnight with what he called catastrophic intensity by helicopter gunships and artillery.
They now have to live with what happened, and the intensity of that kiss can't be denied by either party.
Furthermore, both toxicity rates and delivered dose and dose intensity are consistent with what is already reported for the same regimen (Buzzoni et al, 1991).
