Recent content by olivermsun

Well, is your wave propagating at all?

Maybe start with this question: if you write ##\omega## as a function of ##k##, what does ##\omega(k)## represent? (Think about light in a vacuum as an example.) Can you the phase velocity in the form ##v = v(\omega,k)##? Given that, what does ##v_g(\omega,k) =...

My point is that once light has been split by a prism, you do gain information about the wavelengths involved, contrary to what you said above.

If you see yellow going into a prism and yellow coming, then that should be distinct from yellow going in and red and green coming out.

Be as specific as you can, and I think you will see what’s going on. What exactly is the period of ##\cos t##? What do you know about the value of ##\cos t## at the beginning and end of a period? What about ##t## at the beginning and end of a period?

Look carefully at ##\cos(t)##. What's the period? Now what if I have ##\cos(2t)##. Now what's the period?

The atmosphere is typically temperature-stratified, so it can be said to have a lapse rate. The atmosphere's boundary conditions and the properties of "air" help determine what this lapse rate actually is at any given location and time. Your question is whether an isothermal "ocean" that is...

Are you envisioning that gravity imposes a different acceleration on faster particles than on slower particles?

Say a “unit” of greenhouse gas forcing temporarily decreases OLR and causes temperatures to rise. Eventually OLR has to catch up and counteract the earlier imbalance; else the system would keep warming indefinitely. In the real climate system, there are additional positive feedbacks that...

If the ASR from effective albedo, etc., decreases more than the OLR increases (a natural negative feedback due to the Stefan-Boltzmann relationship) then you still have a net positive energy imbalance, hence net warming.

One of the most interesting applications, as pointed to by pbuk's reference, is that we have been able to derive modern global bathymetry maps with global coverage from satellite altimeters.

I’ve never seen this notation, but to dispute its fairness I suppose you’d have to establish whether the textbook or study material introduced the notation. Accepting the notation for the moment, how does this change one’s interpretation of the solution snippet posted earlier?

Based on the solution snippet, your and Dr. Claude's first reaction seems right. There is some confusion about the notation ##\ln{x}##, which already implies "log to the base ##e##", making the subscript in ##\ln_e{x}## redundant. However if you can overlook the weird notation and pretend that...

If we can agree that your claims are irrelevant to this thread, then I agree that any conflict with your claims is also irrelevant. What is more relevant is what did the teacher mean when writing the problem? And what's the claimed solution?

Actually I did not claim that at all. (Go back and read the thread.)