TODO:

Aplicaitons: SHM Wave eqn Superposition / beats Interference…

consider the funciton psi of x : ѱ(x) = sin(kx), where k is some constant (wavenumber)

what is the wavelength of this wave? what is ѱ'(x) ? what is ѱ(x) ? what is ѱ'(x) ? see a pattern? bonus: what is the 1000 th derivative ѱ(x) ?

sin(kx)+sin(kx + d) = 0 for what values of d is the above equation true?

sin(kx)+sin(kx + c) = 2sin(kx) for what values of c is the above equation true?

sin(x)+cos(x) = Asin(x+B) what are the values of A and B ?

sin(x)+cos(x) = Ccos(x+D) what are the values of C and D ?

sin(x+a) = Esin(x) + Fcos(x) What are the values of E and F (expressed in terms of a) ?

Hint: the only thing you need to know to derive all of the above is the following three formulas:

(1) sin^2 x + cos^2 x + 1 (2) sin(a+b) = sin(a)cos(b) + sin(b)cos(a) (3) cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Eqns (2) and (3) come witha little mnemonic sin –> sico sico cos –> coco - sisi (the negative sign because it is not good to be a sissy)

If you know (1), (2), (3) you kick ass !