Darren Tarshis, a physics teacher in Hayward, CA, has some physical optics questions:
Imagine that red light with a wavelength of 600 nm passes from air to a chunk of, say, diamond. In the diamond, I know the speed slows, which causes the wavelength to shorten (because the frequency remains constant). In the diamond, would the light have a different color because of its new wavelength?
I always teach my students that for a sound wave, pitch is determined by the wavelength/frequency, and for a light wave, color is determined by the wavelength/frequency. But I'm starting to think this may be incorrect, and the pitch is actually determined by frequency only, not wavelength, and color is determined by wavelength only, not frequency.
Yup. Frequency determines color and pitch. The red light stays red even in diamond.
As a quick example: My voice is baritone. Imagine that you are in the pool with your ears just under water, and I am standing on deck talking to you. When the sound waves from my voice enter the water, they start moving about 4 times faster. The frequency doesn't change -- frequency of a wave NEVER changes when the wave changes materials -- so the wavelength increases by a factor of four as well. If pitch were determined by wavelength, then my voice would sound not only soprano, but squeaky soprano.
Similarly, have you ever stood underwater and looked up at the trees overhanging the pool? The leaves of the trees still look green, even though the light speed (and thus the wavelength) has decreased by 25%.
I also propose a fanciful biological rationale for pitch being related to frequency only. The eardrum vibrates in response to incoming sound waves. It is the rate of vibration -- the frequency -- that can be measured by the ear and converted to a frequency. But how would an ear measure wavelength? With a meterstick? With a teeny weeny tape measure that an invisible goblin sticks out of the ear to measure the peak-to-peak distance of the incoming sound wave?
As long as the sound wave is in room temperature air, or as long as the light wave is in a vacuum (or air), then wavelength and frequency can be used to desribe color and pitch interchangably. That's why it's perfectly okay to say that red light is about 700 nm, and violet is about 400 nm. Those wavelength values must change when the light enters diamond, but the frequency of a given color will never change.