Hi Zack!   As you may already know, this problem hinges on the Doppler effect, where a shifted frequency f' is observed when a source of absolute frequency f is sounded while the source and observer are in relative motion toward or away from each other:   f' = [(v ± vobs)/(v(-/+)vs)]f   where   v...

Hi Zack!   In addition to Arturo's fine solution, you can also approach this as a conservation of mechanical energy problem (since gravity is the only force doing work in the problem, and gravity is conservative).   Initially, the mechanical energy of this system, meaning...

Hi Pia!   I think the solution in the video you linked to is incorrect.  There should be a third imaging considered, because the light physically returns through the lens.  The person in the video is treating the system as if it were two lenses, but mirrors and lenses are...

Hi Gustavo!   Gauss' law combined with a symmetry argument can show the electric field at the exact center of a uniform sphere of charge is zero.  The same applies in this case, since the off-axis cavities are placed symmetrically around the center.   It can be shown...

Hi Ab!   This problem is a little tricky, because the usual condition about rolling on the ground without slipping does not appear to apply (I will assume, however, that the rope comes off the disk without slipping; otherwise, all bets are off and the problem gets a *lot* more difficult...

Hi Porcia!   You should have a table in whatever textbook or class material you have for something called the "temperature coefficient of resistivity (or resistance)," usually symbolized α.  You can also probably find it online.  That coefficient is usually...

Hi Arun!   A board swinging about its end is what is called a "physical pendulum."  In a simple pendulum, the mass is all concentrated at the end of the support, and the rest of the support is considered to have insignificant mass.  In a physical pendulum, though,...

Hi Muhammad!   (a) We are meant to treat this situation as a mass (the climber and equipment) on the end of a spring (the rope).  For that, there is a formula for the frequency of oscillation (f).   f  = (1/2π)√(k/m)   where   f = frequency...

Hi Arifur!   A singularity is a point with a mass density approaching infinity in the limit.  It occurs when all the mass of an object is gravitationally collapsed (under its own weight) to (in the limit) a single point.  This happens with some supermassive stars (I think...

Hi Tom!   As long as the cavity is fully inside the metal sphere, it does not matter for this question whether it is off center.  Metal being a conductor, it is not allowed to have any standing net electric fields inside of it.  Conceptually, this means the electric field...

Hi Ben!   It may be better to ask this as a math question, since you are looking to convert your PDE into an ODE along some characteristic curve that you have to discover.  This is, admittedly, not my area of expertise, but I can see what I can find out with a little research....

Hi Amy!   These multi-loop problems pretty much always boil down to getting enough equations to solve for all the unknowns that show up as you try to get to your solution.   Kirchhoff's laws are heavily employed here.  What I will do is set up the equations that I...

Hi Karen!   This is a very clever question, and I hope I do not lead you astray.   The key here is that as the cart rolls in the horizontal direction, and the clay balls drop into it, horizontal momentum is conserved (if it were not, we would have to be given more information...

Hi Snehankit!   I would be ready to fully answer this question, except that I am not sure where this "one resistance" is with respect to the bulbs and the battery.  I would need to know where that extra resistance is, as that would affect the result.  Is there any...

When I wrote my previous comments, I did what I warn my students against doing all the time: over-complicating the problem. I was gearing up to do a full angle of deviation of the ray through the prism. But all they ask for is what happens at side AC. And they give you the index of refraction of...

Hi Gg!   See my answer to you other question for some definitions of sound intensity and sound intensity level.  These are two distinct, though related, quantities, and understanding that is key to answering this question.   The question here is really, by what factor...

Hello Gg!   Decibels (dB) -- a measure of sound intensity level -- is a logarithmic unit, linking sound intensity I (given in watts per meter squared) to the human's average ability to hear "just-noticeable differences" in sound when they change by a factor of 10 in intensity...

Hi James!   The relationship you can use for this is an approximation based on the Doppler effect:   Δλ/λ ≅ v/c   where   Δλ = (absolute value of) the shift in the spectral emission from its laboratory wavelength λ = the laboratory wavelength v...

Hi James!   Luminosity is defined by the Stefan-Boltzmann radiated power law:   L = σeAT4   where   σ = the Stefan-Boltzmann constant (whose often-used value is 5.67x10-8 W/m2·K4 e = emissivity of the object (usually equal 1 for a star) A...

Hi Claire!   This is basically a lot of equation hopping, so let's line them up! :)   a)  To get the resistivity ρ at 50 Celsius, given the resitstivity at 20 Celsisus, use:   ρ = ρo(1 + α(T - To))   where To = 20 Celsius   b)...