Review

1
Review

• Section I

2
WAVE DESCRIPTION
Picture of a Transverse Wave
3
Wave Types

• Longitudinal Waves
• Transverse Waves

4
Fundamentals

• Wavelength (l)
• Period (T)
• Frequency (f 1/T)
• Amplitude (A)
• Speed (v distance/time) lf

5
Oscillation Categories

• Natural Frequency
• The set of frequencies an object emits when
  struck
• Forced Vibration
• Causing a vibration at a frequency other than a
  natural frequency
• Resonance
• Causing a vibration at a natural frequency
• Amplitude increases

6
Impulsive Sound
Waveform amplitude vs. time
7
Impulsive Sound

• Halving Time
• Method of striking makes a difference
• Hard vs. soft hammer
• The position of striking makes a difference
• Tuning fork sounds difference when struck at the
  end compared to striking at the center

8
Superposition
?
9
Decaying Sound

• Frequency (f)
• Initial Amplitude (Amax)
• Halving Time (T½)

10
Damped Sinusoidal Motion

• By experiment we get

Or, in symbols
11
Halving Time
Notice the larger the mass, the slower it
vibrates and the longer it takes for the
oscillations to die away
12
VIBRATION OF A PENDULUM

• What does the period (T) depend upon?
• Length of the pendulum (l).
• Acceleration due to gravity (g).
• Period does not depend upon the bob mass.

13
Frequencies for bars
Not simply related to the fundamental

• Observed
• P/P 1.000
• Q/P 2.68
• R/P 3.73
• S/P 5.25

• P 1046.5 Hz
• Q 2810 Hz
• R 3906 Hz
• S 5494 Hz

14
Clock Chimes and Bells

• Trained listeners often disagree as to the pitch
  assignment
• Due to the fact that several identifiable
  harmonic series may be present

15
Harmonics
16
Plucked strings

• The frequencies are very nearly whole numbers

fn nf1
17
Assigned Pitch

• Our ears assign pitches based on any whole number
  sequences they can find.
• Assigned pitch is the lowest frequency that gives
  harmonics

18
Bell Harmonics
19
Model with Many MassesNormal Modes
½ wavelength
1 wavelength
1½ wavelengths
2 wavelengths

• Lowest mode shows ½-wavelength
• Each mode is ½-wavelength different from its
  neighbors