Understanding Simple Harmonic Motion: Waveform, Amplitude, Frequency, Phase, and Damping -, Study notes of Speech-Language Pathology

Download Understanding Simple Harmonic Motion: Waveform, Amplitude, Frequency, Phase, and Damping - and more Study notes Speech-Language Pathology in PDF only on Docsity! 1 SPA 3011 Simple Harmonic Motion 2 The Waveform • Waveform shows change in some quantity as a function of time; e.g., ♦ Displacement (x) ♦ Velocity (c) ♦ Acceleration (a) ♦ Force (F) ♦ Pressure (p) ♦ Momentum, etc. (M) 5 Dimensions of a sine wave • Five dimensions of sine waves ♦ Amplitude ♦ Frequency ♦ Period ♦ Phase ♦ Wavelength 6 Amplitude • a. Instantaneous Amplitude (a) • b. Maximum Amplitude (A) • c. Peak-to-Peak Amplitude • d. Root-Mean- Square Amplitude (rms) 7 Concept of rms • Sampling the waveform: X1…X6 • Compute standard deviation, σ • rms is standard deviation of all instantaneous amplitudes • rms: the square root (r) of the mean (m) of the squared (s) deviations of instantaneous values 10 Determinants of Frequency • Frequency depends on properties of the source of sound • Natural Frequency: The frequency with which a system oscillates freely (fnat) – fnat = √ s /m 11 Dimensions of sine wave • (4) PHASE ♦ Four reference points: A, B, C, & D 12 ♦ At moment rotation begins, what is displacement in degrees for each of four points? A = 0 B = 90 C = 180 D = 270 Phase 15 Wavelength • Wavelength (λ) relates frequency and speed of sound • λ = distance traveled during one period λ = s / f 16 Wavelength • Examples ♦ In air: f = 1100 Hz, s = 340 m / s; λ = ? ♦ In air: f = 550 Hz, s = 340 m / s; λ = ? 17 Wavelength ♦ In water: f = 1100 Hz, s = 1360 m / s; λ = ? ♦ In water: f = 550 Hz, s = 1360 m / s; λ = ? 20 The Magnitude of Damping • Magnitude of displacement depends on force applied • Duration of vibration depends on magnitude of damping re: force applied 21 The Magnitude of Damping • In this figure, ♦ Panel A: lossless system ♦ Panel B: low-damped system ♦ Panel C: high-damped system 22 Examples of Damped Systems • Shock absorbers (nearly critically damped) • VU meter (nearly critically damped) • What would happen if they were nearly undamped?