Review Section I.

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Presentation transcript:

Review Section I

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

Wave Types Longitudinal Waves Transverse Waves

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

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

Waveform – amplitude vs. time Impulsive Sound Waveform – amplitude vs. time

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

Superposition 

Decaying Sound Frequency (f) Initial Amplitude (Amax) Halving Time (T½)

Damped Sinusoidal Motion By experiment we get Or, in symbols

Halving Time Notice – the larger the mass, the slower it vibrates and the longer it takes for the oscillations to die away

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.

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 = 1046.5 Hz Q = 2810 Hz R = 3906 Hz S = 5494 Hz

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

Harmonics 1st 2nd Sum

Plucked strings The frequencies are very nearly whole numbers fn = nf1

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

Bell Harmonics

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