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...
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},##...
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 travelling through...
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...
Homework Statement
A small spherical rock of mass collides in space with a large spherical rock of mass as indicated in the diagram. After the collision the rocks stick together to form a single spherical object.
https://postimg.org/image/fltmg3bj5/
(New here so I've no clue how to upload...