13%20Outline

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13 Outline

• vibrations, waves, resonance
• Homework
• 1, 2, 15, 30, 41, 45, 51, 64, 67, 101.

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vibrations

• Examples
• vibrating reed, mass on spring,
• drum, piano wire, string,
• most vibrations are sinusoidal in time,
• and called simple harmonic motions (shm)

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terminology

• x displacement
• A maximum displacement
• f frequency (cycles/s)
• angular frequency w (rad/s)
• k spring constant (N/m)

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sinusoidal nature of vibrations
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Kinematics of SHM

• position
• frequency
• angular frequency
• maximums

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Dynamics of SHM

• F -kx, a -kx/m
• E ½kx2 ½mv2.
• Ex k 10N/m, m 200grams, A 10cm.

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Waves

• traveling disturbance
• Transverse Longitudinal

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wave phenomena

• interference of waves
• Examples, noise cancellation headphones, standing
  waves
• reflection, refraction, and diffraction.

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Periodic Waves

• continuous, well defined amplitude (A), frequency
  (f), wavelength (l), and speed v fl.
• Example f 10 hertz, l 3 m.
• v (10/s)(3m) 30m/s.

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Waves on Strings

• Wave Velocity depends on
• tension in string (F) and,
• the mass per unit length of string.
• Example F36N, m/L0.010kg/m

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Standing Waves
waves in which the amplitude at a given location
does not vary with time. Due to wave interference.
Features

• Nodes (places with zero amplitude)
• Anti-nodes (places with maximum amplitude)

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Standing Wave Both Ends Fixed
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Standing Wave One End Fixed, One End Free
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summary

• many vibrations are simple harmonic
• one equation set describes all shm
• wave speed equations
• interference of waves standing waves
• reflection, refraction, diffraction.

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Main Results
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Nature of Sound Waves

• Longitudinal
• Oscillations are
• Condensations (higher pressure areas) and
• Rarefactions (lower pressure areas)
• Sound travels at about 343m/s at room temperature
  and normal atmospheric pressure

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Doppler Effect

• Frequency received is different than the Source
  frequency due to
• Source Motion,
• Receiver Motion or,
• a combination of Source and Receiver motions.

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Example of wavelength distortion due to source
motion
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values of A and f?
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Decibels

• intensity levelwhere Io 1.0x10-12 W/m2.
• Example Intensity of sound is 4.0x10-5 W/m2.
  Intensity level is

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Sound Intensity (I)

• Intensity power/area P/A watt/meter2
• Spherical Radiation I P/4pr2.
• Example Small speaker emits 1.0W of sound in all
  directions. Intensity 10m from the speaker is
  1.0/(4p102) W/m2.

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Frequency of Sound

• Audible Range 20Hz to 20,000Hz
• Infrasonic f lt 20Hz
• Ultrasonic f gt 20,000Hz

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sinusoidal nature of shm

• position of blue mass moving on spring turns out
  to be same as the horizontal position of an
  object in uniform circular motion.

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Simple Pendulum
small angles