What is the relationship between hertz and cents?
The hertz and cents units do not have a relationship that can be expressed in terms of how many cents are in one hertz. The relationship between the two is complicated, so for now we'll only talk about the reason for that relationship. There is a phenomenon that makes two sounds with the same ratio of frequencies (expressed in hertz) to one another seem to the human ear to have the same interval. Here is an example of how this works out.
Next to a 200 Hz sound, 300 Hz (1.5 times 200 Hz) sounds like a perfect major fifth up.
Next to a 300 Hz sound, 450 Hz (1.5 times 300 Hz) sounds like a perfect fifth up.
This means that even though the difference in the frequencies is not the same in these two cases (the first is higher by 100 Hz, and the second is higher by 150 Hz), the difference between each of these sounds seems the same: a perfect fifth (the same as C and G). As we can see, what can be heard by human ears can't be expressed using simple addition and subtraction.
The cent was introduced as a unit that allows us to calculate and consider what we heard using a logarithm scale.
When we calculate using this logarithmic scale, we find that at the range of the note right in the middle of the B♭ clarinet (B, a' standing for the actual sound), 1 Hz is equal to roughly 4 cents. Here a'=442 Hz is 2 Hz higher than a'=440 Hz, meaning that it's about 8 cents higher.
We also find that at the range of the note an octave below B, 1 Hz is equal to roughly 8 cents, and at the octave above, 1 Hz is equal to roughly 2 cents.