Adv Physics

1
Adv Physics

• Chapter 14
• Sections 2 3

2
Natural Frequency

• Frequency at which an object will vibrate if
  disturbed
• ex every pendulum has a T of vibration
• (if you change the length the T
• changes)
• - every time you strike a 260 Hz tuning
• fork it vibrates at 260 Hz

3
Forced Vibration

• Object is forced to vibrate at a particular
  frequency due to an outside force
• ex can force a swing to oscillate at any
• frequency you want if you hold it
• - if you hold a 330 Hz tuning fork
• against a desk the desk vibrates at
• 330 Hz

4
Resonance

• Dramatic increase in the amplitude of a vibration
  when the frequency of the outside force matches
  the natural frequency of the object
• ex if time pushes on a swing its
• amplitude increases
• - Tacoma Narrows Bridge
• - 1989 California earthquake and overpass
• - foot soldiers break step at bridges

5
Standing Wave

• Wave that appears to oscillate but not travel as
  a result of interference between a wave and its
  reflection
• - if sent and reflected wave are in phase you
  get constructive interference and a wave pattern
• - if sent and reflected wave are out of phase
  you get destructive interference and no wave
  pattern

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7
Standing Waves on a String

• Only certain frequencies produce standing waves
• fn n ( v/2L ) where n 1,2,3,.
• v speed of wave f - frequency
• L length of string n harmonic

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9
Standing Waves in Open Tube

• Frequencies that produce standing waves in an
  open ended pipe are given by
• fn n ( v/2L ) where n 1,2,3,.
• v speed of wave f - frequency
• L length of pipe n harmonic

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11
Standing Wave in Closed Pipe

• Frequencies that produce standing waves in a pipe
  closed at one end are given by
• fn n ( v/4L ) where n 1,3,5,.
• v speed of wave f - frequency
• L length of pipe n harmonic

12
Sample Problem

• The speed of a wave on the heaviest string of an
  electric guitar is 207 m/s when it is stretched
  to a tension of 226 N. This string produces the
  musical note E when vibrating along its entire
  length in a standing wave at the fundamental
  frequency of 164.8 Hz. A) Find the length of
  the string. B) A guitar player wants the string
  to vibrate at a fundamental frequency of 329.6
  Hz, as it must if the musical note E is to be
  sounded one octave higher in pitch. To
  accomplish this, he presses the string against
  the proper fret and then plucks the string. Find
  the new length of the string.

13
Sample Problem

• When all the holes are closed on a standard
  flute, the lowest note it can sound is a middle
  C, whose fundamental frequency is 261.6 Hz. A)
  The air temperature is 20 C and the speed of
  sound is 343 m/s. Assuming the flute is a
  cylindrical tube open at both ends, determine the
  length of the tube. B) A flautist can alter the
  length of the flute by adjusting the extent to
  which the head joint is inserted into the main
  stem of the instrument. If the air temperature
  rises to 32 C, to what length must a flute be
  adjusted to play a middle C?

14
Sample Problem

• The E string on a guitar has a length of 66 cm.
  The strings fundamental frequency is 165 Hz.
  Pressing the string against one of the frets
  along the neck of the guitar effectively shortens
  the length of the string. What length will give
  the E string a frequency of 262 Hz (middle C)?

15
Sample Problem

• Given that most people cannot hear sounds
  outside the frequency range 50 Hz to 10000 Hz,
  what are reasonable minimum and maximum lengths
  for musical wind instruments, which are open at
  both ends?

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17
Timbre

• Distinctive quality of a sound that is the result
  of the mixture of harmonics of varying intensity

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19
Beats

• Repetitive variation in loudness heard when 2
  waves of slightly different frequencies interfere
  constructively and destructively
• Beat frequency number of loud/soft repetitions
  per second
• fB f1 f2
• - humans can hear fB less than or equal to 10 Hz