PH 105 Dr. Cecilia Vogel Lecture 7

OUTLINE  Standing Waves in Tubes  open vs closed  end correction  Modes  fundamental  harmonics  partials  overtones

Resonance  Resonance occurs  when the frequency of the driving force matches a natural frequency of the driven system,  & the driving force has a large effect on the driven system.

Resonance Examples  Recall  for a string fixed at both ends  or a tube with both ends open  or a tube with both ends closed  f 1 = fn=fn=  n =

Longitudinal vs Transverse  Note:  These images are GRAPHS of pressure in tube  They do NOT show air molecule motion  Sound waves are longitudinal waves  means the motion of the medium (air) and the motion of the wave (sound) are along the same axis  String waves are transverse waves  means the motion of the medium (string) and the motion of the wave are perpendicular

Traveling vs Standing  traveling waves  means the disturbance moves through the medium at the wave speed.  standing waves  means the nodes and antinodes remain fixed, do not move through the medium.  standing waves  can be thought of as two traveling waves  traveling in opposite directions  and interfering: constructively at ________, destructively at _____

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

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

Pitch of Tube  Pitch often reflects  compare pitch of open vs closed tube  listen to pitch to determine freq, f 1.

Example  Calculate three lowest resonant freq’s for tube with both ends open  f 1 =  f 2 =  f 3 =  Calculate three lowest resonant freq’s for tube with one end open  f 1 =  f 3 =  f 5 =

Example  Calculate length of tube with both ends open  f 1 = v /2 L  L=  Calculate length of tube with one end open  f 1 = v /4 L  L=

End Correction  Actual length is smaller than calculated  because pressure doesn’t equilibrate  pressure varies  as if tube were  For  add an ______________ to the actual length  add  r is

Fundamental  Pitch is often determined by the lowest resonant frequency of a system:  this is called the  behavior is  If only one frequency involved in a sound, it’s called a

Partials  Many systems have several resonant frequencies.  The sound they make is made up of many  The different frequencies that make up a sound are called  They are numbered from  The 1 st partial is the

Harmonics  In some  such as  the frequencies of the partials are multiples of the   If this is true,  the partials are called

Overtones  The lowest freq partial is the  All other partials are called  “over,”  the 1 st overtone is

String Example  __________, ___ partial, ___ harmonic ( _ times f 1 )  ___ overtone, ___ partial, ___ harmonic ( _ times f 1 )

Tube Example (one end open)  ___________, ___ partial, ___ harmonic  ___ overtone, ___ partial, ___ harmonic ( _ times f 1 )  ___ overtone, ___ partial, ___ harmonic ( _ times f 1 )

Summary  Comparing open and closed pipes  longitudinal vs transverse  traveling vs standing waves  Single freq  pure tone  complex tone made of partials  overtones are partials, excluding fundamental  harmonics are partials that have freq=integer*fundamental frequency