Oscillations and Waves Physics 100 Chapt 8

Equilibrium (F net = 0)

Examples of unstable Equilibrium

Examples of Stable equilibrium

Destabilizing forces W N F net = 0

Destabilizing forces W N F net = away from equil

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

W N F net = 0 restoring forces

W N F net = toward equil. restoring forces

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

Pendulum N W

Mass on a spring

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

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

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

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

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

Driven oscillators f = 0.4f 0 f = 1.1f 0 f = 1.6f 0 natural freq. = 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 wave wavelength = Wave speed =v Wave speed = v = distance time wavelength period = = T = f but 1/T=f V=f  or f=V/  Shake end of string up & down with SHM period = T

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 Wave 1 Wave 2 resultant wave Two waves in same direction with slightly different frequencies “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 in survive (all others cancel themselves out)

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

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

Doppler effect

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) Sound wave moving source

Waves from a stationary source Wavelength same in all directions

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

surf

Folsom prison blues Short wavelengths long wavelengths

Confined waves