simple linear transformation of coordinates on a sin wave

[granpa]

1. The problem statement, all variables and given/known data let x=ksin(t). let k<1. let x'=x. let t'=t-kx. solve for x' as a function of t'. (this question has to do with relativity and deBroglie waves)


2. Relevant equations
given above.


3. The attempt at a solution
since t=t'+kx therefore x'=ksin(t'+kx). but I need x' as a function of t' only. I am ashamed to admit that such a simple linear problem has me stumped. if someone could give me a pointer I would be very glad.

[Elucidus]

1. The problem statement, all variables and given/known data let x=ksin(t). let k<1. let x'=x. let t'=t-kx. solve for x' as a function of t'. (this question has to do with relativity and deBroglie waves)


2. Relevant equations
given above.


3. The attempt at a solution
since t=t'+kx therefore x'=ksin(t'+kx). but I need x' as a function of t' only. I am ashamed to admit that such a simple linear problem has me stumped. if someone could give me a pointer I would be very glad.

I am not so sure this is "such a simple linear problem." The issue is that despite the equation t' = t - kx seeming linear, it leads to x' = ksin(t' + kx'), where x' is both inside and outside a trig function (and definitely not a linear problem). This sort of situation often leads to intractable transcendental solutions. This problems seems peculiar. How is the exercise actually stated in the text?

--Elucidus

[granpa]

its not a textbook. it comes from this website:

http://74.125.155.132/search?q=cache:_E2ld07CK4gJ:www.calphysics.org/mass.html+%22Compton+frequency%22+electron&cd=1&hl=en&ct=clnk&gl=us

in the left hand panel it reads:
If you combine the E=mc2 and the E=hf equations (where f is frequency), you arrive at the Compton frequency. de Broglie's conjecture was that the Compton frequency reflected, in the case of the electron (quarks were not yet discovered), some kind of fundamental intrinsic oscillation or circulation of charge associated with the electron... One can easily show that if the electron really does oscillate at the Compton frequency in its own rest frame, when you view the electron from a moving frame a beat frequency becomes superimposed on this oscillation due to a Doppler shift. It turns out that this beat frequency proves to be exactly the de Broglie wavelength of a moving electron.