Recent content by Nerrad

So for the first bit you're saying that the thickness of the mirror is equal to 5 times the wavelength of the light?

Homework Statement A double-slit experiment uses a helium-neon laser with a wavelength of 633 nm and a slit separation of 12mm. When a thin sheet of glass is placed in front of one of the slits, the interference pattern shifts by 5 fringes. When the experiment is repeated under water, the shift...

Is it simply due to the fact that ##u_{xx}-c^2u_{tt} \neq u_{x'x'}-c^2u_{t't'} ##, so that if ##u## satisfies the wave equation in ##x##,##t## coordinates, then it does not satisfy the same equation in the ##x'##,##t'## coordinates? Or do I deduce it mathematically?

I give up. Can you guide me through this. Please. Thanks

Can you give a little bit more hints than that please? Thanks

Homework Statement (a) Light waves satisfy the wave equation ##u_{tt}-c^2u_{xx}## where ##c## is the speed of light. Consider change of coordinates $$x'=x-Vt$$ $$t'=t$$ where V is a constant. Use the chain rule to show that ##u_x=u_{x'}## and ##u_{tt}=-Vu_{x'}+u_{t'}## Find ##u_{xx},u_{tt},##...

Oh so what you mean is that it doesn't matter what I set the incident amplitude as, because at the end I'm going to get a percentage/ratio of it? Kinda like how for probability it all adds up to 1?

Does it have something to do with ratio? To me it's quite vague

Homework Statement An interface is formed between a block of aluminium (density = ##2.70 \times 10^3 kg/m^3##, speed of sound =##6.40 \times 10^3m/s##) and a block of copper (density = ##8.96 \times 10^3 kg/m^3##, speed of sound =##4.76 \times 10^3m/s##). Longitudinal waves traveling through...

From the given BCs for ##u##, am I right in saying that BCs for ##v## is ##v(0,t)=v(a,t)=u(0,t)+C=2C##? Also by substituting ##u(x,t)=v(x,t)+C## into the PDE do you mean partially differentiate it then substitute in like $$v=u+C$$ $$...

Q: Suppose ##u(x,t)## satisfies the heat equation for ##0<x<a## with the usual initial condition ##u(x,0)=f(x)##, and the temperature given to be a non-zero constant C on the surfaces ##x=0## and ##x=a##. We have BCs ##u(0,t) = u(a,t) = C.## Our standard method for finding u doesn't work here...

Thanks guys I appreciate this a lot. :)

Then the distance to the centre of mass of the big is constantly changing as the small rock approaches the CoM?

So the angular momentum L = mvr which taking r as a=0.5, gives a result of L=50 which is apparently the right answer. But why would r be a if its rotating about point O?

So the angular momentum of the small rock about point O before the collision is its mass m * distance from point O * its angular velcoity about point O. But the angular velocity is constantly changing?