p288_04_w11 - PAT 102/Physics 288/489 Winter 2011 Lecture 4...

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PAT 102/Physics 288/489 Winter 2011 Lecture 4 Vibrations
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The Nature of Waves Two Defining Features: – A wave is a traveling disturbance – A wave transports energy one place to another Most waves have a characteristic speed of propagation, often denoted v (for “velocity”) Sound waves are transmitted as pressure differences in air – The speed of sound is about v = 344 m/s at 20º C (but depends on temperature)
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Characterizing Sound Waves • Audible sounds may be speech, noise, music, etc – Basic property: loudness • Musical tones have additional properties – Loudness (intensity) • How loud or soft a note sounds – Pitch • The perceived frequency of the sound • Where the note is on a musical scale – Timbre • The “quality” or “tone color” of the sound • What sets apart different instruments – Duration • How long the note is played
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Musical Tones • What makes musical tones different from noise is a recognizable pitch • Created by vibrations – Periodic motion – ie motion that repeats itself on a regular basis • Musical tones can be created by e.g. – Vibrating strings – Vibrating air column inside an organ pipe – Vibrating drum head Frequency
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Frequency and Period • The rate of repetition of a vibration is know as its frequency f – The number of vibrations per second – Measured in cycles per second or hertz (Hz) • The length of time it takes to perform one complete oscillation is know as the period P (sometimes denoted T ) Basic relation: P = 1/ f or f = 1/ P
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• Lowest note: A 0 = 27.5 Hz • Highest note: C 8 = 4186 Hz • Range of human hearing is generally considered to be 20 Hz to 20 kHz • See inside back cover of the textbook for additional information – Mapping between notes and frequencies – Frequency range of instruments The Piano Keyboard Musical pitch is frequency A 0 C 8 Middle C: C 4 = 261.6 Hz Concert A: A 4 = 440 Hz Modern standard
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Periodic Waves A vibrating source generates a periodic wave The pattern of the disturbance is repeated in time over and over again ( periodically ) by the source of the wave The orange curve is a “snapshot” of the wave at time t = 0 The blue curve is a “snapshot” later in time A is a crest of the wave B is a trough of the wave This wave moves to the right
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Describing Periodic Waves Periodic waves are characterized by speed, frequency, period, wavelength and amplitude v the speed of the wave (how fast the wave travels) f frequency (number of complete oscillations or cycles per second) P period (one cycle P=1/f where f frequency ) ! wavelength (distance between two successive corresponding points on the wave) A amplitude (largest displacement from equilibrium)
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Requirements for Oscillations Why do objects vibrate? How do they vibrate?
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p288_04_w11 - PAT 102/Physics 288/489 Winter 2011 Lecture 4...

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