Oscillations and Waves UHM（振荡和海浪嗯）.pptVIP

Oscillations and Waves Physics 100 Chapt 8 Equilibrium (Fnet = 0) Examples of unstable Equilibrium Examples of Stable equilibrium Destabilizing forces Destabilizing forces Destabilizing forces restoring forces restoring forces restoring forces Pendulum Mass on a spring Displacement vs time Simple harmonic motion Masses on springs Not all oscillations are nice Sine curves Natural frequency Driven oscillators Resonance (f=f0) Waves Wave in a string Pulsed Sound Wave Harmonic sound wave Harmonic sound wave Harmonic wave Reflection (from a fixed end) Reflection (from a loose end) Adding waves Adding waves Adding waves Confined waves Allowed frequencies Ukuleles, etc Doppler effect Sound wave moving source Waves from a stationary source surf Folsom prison blues Confined waves l=(2/3)L f0=V/l = V/2L f1=V/l = V/L=2f0 l= 2L l=L l=(2/5)L l=L/2 f2=V/l=V/(2/3)L=3f0 f3=V/l=V/(1/2)L=4f0 f4=V/l=V/(2/5)L=5f0 Fundamental tone 1st overtone 3rd overtone 4th overtone 2nd overtone L l0 = L/2; f0 = V/2L l1= L; f1 = V/L =2f0 l2= 2L/3; f2 = 3f0 l3= L/2; f3 = 4f0 Etc… (V depends on the Tension thickness Of the string) Wavelength same in all directions Sound wave stationary source Wavelength in backward direction is longer (frequency is higher) Wavelength in forward direction is shorter (frequency is higher) * W N Fnet = 0 W N Fnet = away from equil W N Fnet = away from equil destabilizing forces always push the system further away from equilibrium W N Fnet = 0 W N Fnet = toward equil. W N Fnet = toward equil. Restoring forces always push the system back toward equilibrium N W amplitude period (=T) Displaced systems oscillate around stable equil. points Equil. point Equil. point T T= period = time for 1 complete oscillation f = frequency = # of oscillations/time = 1/T Pure Sine-like curve Animations courtesy of Dr. Dan Russell, Kettering University A T Equil. point f=1/T f= (1/2p)?g/l f= (1/2p)?k/m f = 0.4f0 f = 1.1f0 f = 1.6f0 natural freq. = f0 Animations courtesy of Dr. Dan