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Lecture23 - PHYSICS 149: Lecture 23 Chapter 11: Waves 11.5...

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PHYSICS 149: Lecture 23 • Chapter 11: Waves – 11.5 Mathematical Description of a Wave – 11.6 Graphing Waves – 11.7 Principle of Superposition – 11.8 Reflection and Refraction Lecture 23 Purdue University, Physics 149 1
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Lecture 23 Purdue University, Physics 149 2 Simple Harmonic Motion • Occurs when having linear restoring force F= -kx – x(t) = [A] cos( ω t) – v(t) = -[A ω ] sin( ω t) – a(t) = -[A ω 2 ] cos( ω t) • Springs –F = -kx –U = ½ k x 2
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Lecture 23 Purdue University, Physics 149 3 • Longitudinal: The medium oscillates in the same direction as the wave is moving. – Sound – Slinky • Transverse: The medium oscillates perpendicular to the direction the wave is moving. – Water (more or less) – Slinky Types of Waves energy transport energy transport
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Lecture 23 Purdue University, Physics 149 4 Waves on a String
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Speed of Transverse Waves • The speed of a transverse wave on a string is where • The speed of a transverse wave depends on mechanical properties of the wave medium. More restoring force makes faster waves; more inertia makes slower waves. No! F : tension m : mass of string L : length of string μ : mass density Lecture 23 5 Purdue University, Physics 149
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Periodic Waves • A periodic wave is a wave that repeats the same pattern over and over. Period T : the time for a single point to repeat itself (that is, the time for a single point to move from crest Æ equilibrium Æ trough Æ equilibrium Æ crest). Or, the time for a pulse to move from a crest to the next crest. Frequency f : the number of cycles (for a single point) per unit time Wavelength λ : the distance from a crest to the next crest Amplitude A : the maximum displacement of a single point from its equilibrium position amplitude: A Lecture 23 6 Purdue University, Physics 149
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Example: Speed on a String • A 2 m long string has a mass of m = 6.40 g. What is the speed of transverse waves on this string when its tension is 90.0 N? Linear mass density: μ = m / L = (6.40 × 10 -3 kg) / (2 m) = 3.20 × 10 -3 kg/m Speed of transverse waves: v = sqrt( F / ) = sqrt[ (90.0 N) / (3.20 × 10 -3 kg/m) ] = 168 m/s Lecture 23 7 Purdue University, Physics 149
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Harmonic Waves • Harmonic waves: a special kind of periodic wave in which the disturbance is sinusoidal (either a sine or cosine function). • In a harmonic transverse wave on a string, every point on
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This note was uploaded on 04/23/2011 for the course PHYS 149 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture23 - PHYSICS 149: Lecture 23 Chapter 11: Waves 11.5...

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