1. Review
Section I

2. Picture of a Transverse Wave
WAVE DESCRIPTION
Picture of a Transverse Wave
Crest
Wavelength l
A - Amplitude A
Trough

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. Waveform – amplitude vs. time
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. Not simply related to the fundamental
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 = 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
1st
2nd
Sum

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 Masses Normal Modes
½ wavelength
1 wavelength
1½ wavelengths
2 wavelengths
Lowest mode shows ½-wavelength
Each mode is ½-wavelength different from its neighbors