Wave Motion

wave motion Transverse wave The mopagation of disturba- nces from aneport of the med- crust ium to other another by the Vibration of the particles Types of waves Iwave i) mechanical waves though Neecis a medium for Amplitude : The maximum gation. Eg : sound waves, propa- wa- displacement of particle ves column in shing , waves in an from mean position. ii) Non mechanical waves warelenger(7) The distance ium Eg EM waves. Doesn't require any med- b/w the particles having S- ame phase of vibration. Types of mechanical Frequency(s): The no. of waves in one second waves tsec n virations 1) Transverse wave particles vibrates perpencical f=2 t as to direction Of mapagation of wave. Timeperiod (T) :The finet Eg: wave in string, Enwa aken to complete one wave. n vibracions = t second ves. t ii) longitudinal wave T= n f= particles vibrates Parculel to propagation OR the wave. wave velocity(v) The displacement Eg : sound waves, naves-in phoye in one second sming etc For brave A

disp =a V = clisp y= f(bt1aa) time time =T V= Example for travelling wave: y=Asin (3)(++) V = fr (uxt 3t) mavelling wave / y=e progressive wave y= 4x+2t There will be energy trans- per. velocity of the wave :- V= coefficient oft y coefficient of x y V= b a x Y=1AA x X2 Differential equation of pr- and their time 't' ogressive wave The energy of the wave will d'y = V2 Dy 2 35) transper from one place 70 an- It ax2 other. such waves are tarar- elling waves. let 'y' be the displacem- Equation of progressive wave ent of particle from mean PO- (Harmonic wave) sition and 'x' be the wave displacement and t be the The pastic les in progressive time. harmonic wave is SHM And The particle displacement can all particles will vibrate lary with respect to wave di- with same amplitude. splacement and time. y=A sin (wt KK) so, y= f(x,9 y = Asin ( kcc cut) y= f (xit) if wave travels in tre x direction y = f (ax + bt) y = A sin(A-cut) or y = A sin

If wave travels -ve x direction y= A Sin y= Asin (wt +kx) Ksangular wavenumber K= 211 co = angalan velo- a City we = 2Rif V= w K if there will be initial phase () :- y= A sin (wt y=4 sin ( 3tt 2xt TI/4) A=4 Ce - 3 = "I/4 K=2