eguruchela

List of formulas related to Periodic Motion

Wavelength

$$ \lambda = \frac{v}{f} = vT$$

Wavelength

Function Wave At Some Points

$$ => O : u_o = Acos \omega t $$ $$ => u_M = Acos[2 \pi(\frac{t}{T} - \frac{x}{\lambda})] $$ $$ => N : u_N = Acos[2 \pi(\frac{t}{T} + \frac{x}{\lambda})] $$

Wave Interference

S1,S2: 2 sources of wave having same phase; M: a random point

$$ \omega = \frac{v}{R} $$ $$ \text{Function at point M} $$ $$ u = 2A[cos \frac{\pi(d_2 - d_1)}{\lambda}] cos 2 \pi (ft - \frac{d_2 + d_1}{\lambda}) $$ $$ \text{Phase difference} $$ $$ \Delta \phi = \frac{2 \pi}{\lambda}(d_1 - d_2) $$ $$ \text{Constructive Points} $$ $$ d_2 - d_1 = k \lambda $$ $$ \text{Constructive Points} $$ $$ d_2 - d_1 = (k + \frac{1}{2})\lambda $$