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I need help understanding how one wavelength can have multiple peaks / cyles within a given time, lets say one second, and another will have less cyles within that second (longer wavelengths). Can someone explain frequency to me and how it affects amplitude, intensity of light, and the number of photons?
The frequency is how many times a wave cycle passes in one second. If the wavelength is shorter, you would get a higher frequency. It takes a wave with a longer wavelength more time to get through which is why see the lower frequency. Understanding the photoelectric effect will help draw the connection between frequency in waves and the number of photons. Increasing the frequency when it comes to viewing light as particles is difficult to explain as frequency is typically associated with waves but the closest explanation I can give is like increasing the number of photons that pass in a second whereas increasing the intensity would be increasing the energy of each individual particle. This is why increasing the frequency of light didn't remove any electrons if the intensity wasn't high enough since no individual photon had the energy to remove an electron.
To speak specifically to the part about how the number of peaks can vary within a given amount of time between different wavelengths, I think you answered that within your question. The way I interpreted that, wavelength isn't so much about following the line up and down but rather the width of the entire wave to shorter wavelengths would be able to fit more into a certain time span than longer ones. Also the shorter the wavelength (i.e. the less wide) the higher the frequency, and the longer, the lower respectively. I'm sorry if I am totally off base with that, and for not answering the whole question but I hope this helps at least a little bit!
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