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Ch 16 Wave Motion - I

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Wave Motion Gun 1zWsXFNshttp://www.youtube.com/watch?v=ty- 1zWsXFNs Wave Motion Gun music

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Hum…. –What mathematical functions are their own derivatives?

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Outline The wave equation for waves on a string –Les Paul starburst, ukelele, fiddle, warshtub bass, sitar Basic shapes of waves Adding waves –AM radio waves –Standing Waves Fourier decomposition Review Questions

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The wave equation m a x = T cos 2 – T cos 1 m a y = T sin 2 – T sin 1 m a x = T 1 – T 1 m a y = T 2 – T 1 m a y = T ( 2 – 1 ) m a x = 0 mm

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The wave equation m a y = T ( 2 – 1 )

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The wave equation mm

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Basic Solutions to the Wave Equation

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What’s the fartherest a point can get away from y=0 ? Where is sin() maximum? How fast does this maximum location travel? Which direction (left/right) does the wave travel? Over what difference in phase does a sin() repeat? How long does it take a particular point to go down & up? Over what distance does a sin() repeat?

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Superposition of Waves

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Two waves same direction, same f, same, but init phase difference

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new amplitude traveling part If = 0, then max new amplitude = 2A same f same If = , then new amplitude = 0 complete cancellation

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Two waves opposite direction, same f, same, no phase difference no traveling part STANDING WAVE

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Two waves opposite direction, same f, same, no phase difference nodes no traveling part STANDING WAVE

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Standing Waves = L = 2L/4 = 2L/3

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Standing Waves fundamental

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Fourier Decomposition, or, What about waves that aren’t purely sine waves? Flute oboe

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Fourier Decomposition, or, What about waves that aren’t purely sine waves? traveling waves standing waves

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Review

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The graph shows the vertical displacement as a function of time at one location in a medium through which a wave is traveling. What is the amplitude of the wave? a) 1 m b) 2 m c) 4 m d) 6 m e) 8 m

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The graph shows the vertical displacement as a function of time at one location in a medium through which a wave is traveling. What is the period of the wave? a) 0.5 s b) 1.0 s c) 1.5 s d) 2.0 s e) 4.0 s

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Which one of the following factors is important in determining the speed of waves on a string? a) amplitude b) frequency c) length of the string d) mass per unit length e) speed of the particles that compose the string

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Consider the three waves described by the equations below. Which wave(s) is moving in the negative x direction? a) A only b) B only c) C only d) A and B e) B and C

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The equation for a certain wave is y = 4.0 sin [2 (2.5t x)] where y and x are measured in meters and t is measured in seconds. What is the magnitude and direction of the velocity of this wave? a) 1.8 m/s in the +x direction b) 1.8 m/s in the x direction c) 18 m/s in the x direction d) 7.2 m/s in the +x direction e) 0.35 m/s in the x direction

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Which one of the following correctly describes a wave described by y = 2.0 sin(3.0x 2.0t) where y and x are measured in meters and t is measured in seconds? a) The wave is traveling in the +x direction with a frequency 6 Hz and a wavelength 3 m. b) The wave is traveling in the x direction with a frequency 4 Hz and a wavelength /3 m. c) The wave is traveling in the +x direction with a frequency Hz and a wavelength 3 m. d) The wave is traveling in the x direction with a frequency 4 Hz and a wavelength m. e) The wave is traveling in the +x direction with a frequency 6 Hz and a wavelength /3 m.

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A wave is described by the equation y = sin (3.0x 6.0t), where the distances are in meters and time is measured in seconds. Using the wave equation, determine the speed of this wave? a) 0.50 m/s b) 0.75 m/s c) 1.0 m/s d) 2.0 m/s e) 4.0 m/s

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What is the frequency of a standing wave with a wave speed of 12 m/s as it travels on a 4.0-m string fixed at both ends? a) 2.5 Hz b) 5.0 Hz c) 10.0 Hz d) 15.0 Hz e) 20.0 Hz

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Which one of the following statements explains why a piano and a guitar playing the same musical note sound different? a) The fundamental frequency is different for each instrument. b) The two instruments have the same fundamental frequency, but different harmonic frequencies. c) The two instruments have the same harmonic frequencies, but different fundamental frequencies. d) The two instruments have the same fundamental frequency and the same harmonic frequencies, but the amounts of each of the harmonics is different for the two instruments..

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When a wire under tension oscillates in its third harmonic mode, how many wavelengths are observed? a) 1/3 b) 1/2 c) 2/3 d) 3/2 e) 2

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