Oscillations and Waves Physics 100 Chapt 8 Equilibrium

Oscillations and Waves Physics 100 Chapt 8

Equilibrium (Fnet = 0)

Examples of unstable Equilibrium

Examples of Stable equilibrium

Destabilizing forces NF = 0 net W

Destabilizing forces N Fnet = away from equil W

Destabilizing forces Fnet = away from equil N W destabilizing forces always push the system further away from equilibrium

restoring forces N Fnet = 0 W

restoring forces N Fnet = toward equil. W

restoring forces Fnet N = toward equil. W Restoring forces always push the system back toward equilibrium

Pendulum N W

Mass on a spring

Displacement vs time Displaced systems oscillate around stable equil. points amplitude Equil. point period (=T)

Simple harmonic motion Pure Sine-like curve T Equil. point T= period = time for 1 complete oscillation f = frequency = # of oscillations/time = 1/T

Masses on springs Animations courtesy of Dr. Dan Russell, Kettering University

Not all oscillations are nice Sine curves A Equil. point T f=1/T

Natural frequency f= (1/2 p) g/l f= (1/2 p) k/m

Driven oscillators natural freq. = f 0 f = 0. 4 f 0 f = 1. 1 f 0 f = 1. 6 f 0

Resonance (f=f 0)

Waves Animations courtesy of Dr. Dan Russell, Kettering University

Wave in a string Animations courtesy of Dr. Dan Russell, Kettering University

Pulsed Sound Wave

Harmonic sound wave

Harmonic sound wave

Harmonic wave Shake end of string up & down with SHM period = T Wave speed wavelength =v =l distance time =v= = V=fl or f=V/ l wavelength period l = = fl T but 1/T=f

Reflection (from a fixed end) Animations courtesy of Dr. Dan Russell, Kettering University

Reflection (from a loose end) Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves pulsed waves Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves Two waves in same direction with slightly different frequencies Wave 1 Wave 2 resultant wave “Beats” Animations courtesy of Dr. Dan Russell, Kettering University

Adding waves harmonic waves in opposite directions incident wave reflected wave resultant wave (standing wave) Animations courtesy of Dr. Dan Russell, Kettering University

Confined waves Only waves with wavelengths that just fit (all others cancel themselves out) in survive

Allowed frequencies l= 2 L f 0=V/l = V/2 L Fundamental tone l=L l=(2/3)L f 1=V/l = V/L=2 f 0 1 st overtone f 2=V/l=V/(2/3)L=3 f 0 2 nd overtone l=L/2 f 3=V/l=V/(1/2)L=4 f 0 3 rd overtone l=(2/5)L f 4=V/l=V/(2/5)L=5 f 0 4 th overtone

Ukuleles, etc L l 0 = L/2; f 0 = V/2 L l 1= L; f 1 = V/L =2 f 0 l 2= 2 L/3; f 2 = 3 f 0 l 3= L/2; f 3 = 4 f 0 Etc… (V depends on the Tension & thickness Of the string)

Doppler effect

Sound wave stationary source Wavelength same in all directions

Sound wave moving source Wavelength in forward direction is shorter (frequency is higher) Wavelength in backward direction is longer (frequency is higher)

Waves from a stationary source Wavelength same in all directions

Waves from a moving source v Wavelength in forward direction is shorter (frequency is higher) Wavelength in backward direction is longer (frequency is higher)

surf

long wav elen g ths Folsom prison blues s th g n ele v a o Sh w t r

Confined waves