PH 105 Dr. Cecilia Vogel Lecture 6

OUTLINE  Natural or Normal Modes  Driving force  Resonance  Helmholtz resonator  Standing Waves  Strings and tubes  Longitudinal vs transverse waves

Superposition  When two disturbances (or waves)  are at the same place at the same time,  total disturbance is the sum of the two.  watch impulsive waves

Interference  Because of superposition,  Waves, when they meet  can add or interfere constructively  so the total is  periodic waves, when they meet  can cancel or interfere destructively  so the total is

Beats  Two waves with slightly different frequency (period) go in and out of phase

Interference  Waves from two source,  will have places where they interfere constructively  what does it sound like with sound?  what does it look like with light?  and other places where they interfere destructively  what does it sound like with sound?  what does it look like with light?  video

Normal Modes  A normal or natural mode is  a way the system behaves when left to move naturally.  How does a pendulum behave naturally?  How does mass on a spring behave naturally?  How does string vibrate naturally?  Some systems have multiple normal modes

Driving Force  You can apply a periodic driving force  a force that pushes the system periodically  Period of driving force =  Example: pushing a swing

Sympathetic Vibrations  A driving force will often cause the driven system to vibrate  with the same period as the driving force.  If the driving vibrator is vibrating naturally, these vibrations are called sympathetic vibrations.  Listen to the tuning fork;  listen again when on box  box driven by tuning fork.  both emit sound

Resonance  When the frequency of the driving force matches a natural frequency,  the driving force has  the vibrator is resonating  Why push a swing each time it swings?  Observe spring on and off resonance.

Helmholtz Resonator  A bottle with a neck is analogous to a mass on a spring.  the air in the neck is the mass which oscillates  the volume of air in the bottle acts as a spring  Called a Helmholtz resonator  f=resonant frequency  V = volume of bottle  bigger bottle, _____ r freq (pitch)  a = neck area, l = neck length  long, skinny neck, _____ freq

Closed Tube Resonances  If tube is closed at both ends  the pressure has no  there is a pressure antinode at ends  Observe slinky “pressure” hi & lo at fixed end  observe that a pressure antinode is a displacement (motion) node!

Closed Tube Resonances  How can there be antinodes at both ends?  If  etc  L =

Resonant Frequencies of Closed Tube  L = n /2  n = 1, 2, 3, 4, 5, ….  Since f = v  n shows there are many resonant frequencies 

Resonances of Open Tube  If tube is open at both ends, it has a pressure node at both ends  displacement __________  analysis is similar

Tube with One Closed End  If tube is closed at one end  there is a pressure _________ at that end  _______ at the other end

Closed Tube Resonances  How?  If  etc  L =   L =

Resonant Frequencies  L = n /4  n = 1, 3, 5, 7, 9…. (only odd!)  Since f = v  n odd

Standing Wave in String  String is generally fixed at both ends  node at  analysis like  L = n /2  n = 1, 2, 3, 4, 5, …. Were measured resonant frequencies integer times f 1 ?

Standing Wave in String  Combine  Can change resonant freq’s by changing 

Impedance and Resonance  A reflection can occur any time there is a change in impedance.  Acoustic Impedance means difficulty of air flow  observe wave machines  There can be resonance in each part of a complex tube: L1L1 L2L2 L3L3

Summary  Interference is the addition of waves at point where they meet  constructive interference  destructive interference  Normal modes are natural behavior  sometimes multiple natural frequencies  At resonance  driving frequency matches natural freq  driving force has a huge effect  Resonance of  Helmholtz resonator, open and closed tubes, strings