Re: Energy of light wave as function of wavelength vs. amplitude

David,

You ask a good question, and the answer wasn't definitively determined until very early in the 20th century. In fact, the relationship between energy and frequency (E=hv) that you mention was proposed by Max Planck around 1900 (which is why the constant, h, in the relationship is named after him). The reason this relationship took so long to figure out is because light acts both like a wave and a particle at the same time. When Planck suggested this relationship, he was referring to the particle nature of light. Thus, for a given "particle" (also known as a quanta or photon), the energy of the particle is only dependent on its wavelength.

But, as you say, light is also a wave, so it does have an amplitude. For light, amplitude refers to intensity or, if you like to think of it in terms of particles, the amount of particles that share the same wavelength. Trying to think of light in the same way as a sound wave is, consequently, a bit confusing. This is because sound is a mechanical wave, and requires a medium to travel through, but light is a non-mechanical wave and does not.

So to return to your original sound analogy, perhaps you could think of light in terms of having 100 G's as opposed to 1 G#. In that case, the 100 G's would have more energy than the 1 G#. But if you compare 1 G to 1 G# the G# would have more energy because it is vibrating faster. If you're a musician, you can easily hear the increased vibration of a high octave note compared to a low octave note. This change in vibration is essentially the change in energy Planck was trying to describe in the energy/frequency relationship.

Hope this helps,
Amber