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Adv Physics

Adv Physics. Chapter 14 Sections 2 & 3. Natural Frequency. Frequency at which an object will vibrate if disturbed ex – every pendulum has a T of vibration (if you change the length the T changes) - every time you strike a 260 Hz tuning

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Adv Physics

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  1. Adv Physics Chapter 14 Sections 2 & 3

  2. Natural Frequency • Frequency at which an object will vibrate if disturbed ex – every pendulum has a T of vibration (if you change the length the T changes) - every time you strike a 260 Hz tuning fork it vibrates at 260 Hz

  3. Forced Vibration • Object is forced to vibrate at a particular frequency due to an outside force ex – can force a swing to oscillate at any frequency you want if you hold it - if you hold a 330 Hz tuning fork against a desk the desk vibrates at 330 Hz

  4. Resonance • Dramatic increase in the amplitude of a vibration when the frequency of the outside force matches the natural frequency of the object ex – if time pushes on a swing its amplitude increases - Tacoma Narrows Bridge - 1989 California earthquake and overpass - foot soldiers break step at bridges

  5. Standing Wave • Wave that appears to oscillate but not travel as a result of interference between a wave and its reflection - if sent and reflected wave are in phase you get constructive interference and a wave pattern - if sent and reflected wave are out of phase you get destructive interference and no wave pattern

  6. Standing Waves on a String • Only certain frequencies produce standing waves fn = n ( v/2L ) where n = 1,2,3,…. v – speed of wave f - frequency L – length of string n – harmonic #

  7. Standing Waves in Open Tube • Frequencies that produce standing waves in an open ended pipe are given by fn = n ( v/2L ) where n = 1,2,3,…. v – speed of wave f - frequency L – length of pipe n – harmonic #

  8. Standing Wave in Closed Pipe • Frequencies that produce standing waves in a pipe closed at one end are given by fn = n ( v/4L ) where n = 1,3,5,…. v – speed of wave f - frequency L – length of pipe n – harmonic #

  9. Sample Problem The speed of a wave on the heaviest string of an electric guitar is 207 m/s when it is stretched to a tension of 226 N. This string produces the musical note E when vibrating along its entire length in a standing wave at the fundamental frequency of 164.8 Hz. A) Find the length of the string. B) A guitar player wants the string to vibrate at a fundamental frequency of 329.6 Hz, as it must if the musical note E is to be sounded one octave higher in pitch. To accomplish this, he presses the string against the proper fret and then plucks the string. Find the new length of the string.

  10. Sample Problem When all the holes are closed on a standard flute, the lowest note it can sound is a middle C, whose fundamental frequency is 261.6 Hz. A) The air temperature is 20 C and the speed of sound is 343 m/s. Assuming the flute is a cylindrical tube open at both ends, determine the length of the tube. B) A flautist can alter the length of the flute by adjusting the extent to which the head joint is inserted into the main stem of the instrument. If the air temperature rises to 32 C, to what length must a flute be adjusted to play a middle C?

  11. Sample Problem The E string on a guitar has a length of 66 cm. The string’s fundamental frequency is 165 Hz. Pressing the string against one of the frets along the neck of the guitar effectively shortens the length of the string. What length will give the E string a frequency of 262 Hz (middle C)?

  12. Sample Problem Given that most people cannot hear sounds outside the frequency range 50 Hz to 10000 Hz, what are reasonable minimum and maximum lengths for musical wind instruments, which are open at both ends?

  13. Timbre • Distinctive quality of a sound that is the result of the mixture of harmonics of varying intensity

  14. Beats • Repetitive variation in loudness heard when 2 waves of slightly different frequencies interfere constructively and destructively • Beat frequency – number of loud/soft repetitions per second fB = f1 – f2 - humans can hear fB less than or equal to 10 Hz

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