Why does white light split into multiple wavelengths and how does resonance amplify sound?

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Bob Busby
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Excuse my noobness but I can't find answers to these from searching.

When lights interacts with a prism it splits off into multiple wavelengths. Doesn't that imply that the incoming light consists of multiple wavelengths? My question is, since the speed of light in a given medium is constant (c = frequency * wavelength) how can there many different frequencies?

Secondly, and this is a little vague, I noticed when I was in my bathroom and was running the fan, whenever I sang a certain note it was like I could hear the fan louder (as if my head were vibrating). I think this has to do with something called resonance but I don't know that topic very well. What is happening?

If you don't want to answer my questions at least direct to somewhere that I can read about them. Thanks!
 

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Bob Busby said:
When lights interacts with a prism it splits off into multiple wavelengths. Doesn't that imply that the incoming light consists of multiple wavelengths? My question is, since the speed of light in a given medium is constant (c = frequency * wavelength) how can there many different frequencies?

Because there are many different wavelengths.
 
But doesn't frequency determine wavelength or vice versa? I understand how there are infinite ways to make the product of the two = c but isn't there only one wavelength associated with one frequency?
 
Yes, each wavelength is associated with a frequency. However, since there are many wavelengths, there are many frequencies.