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PH109 Exam Review: Vibrations of Strings Guide

Join the exam review session covering homework, lab work, and study guide materials on string vibrations. Learn about changing frequencies based on tension, length, and mass per unit length of a string. Explore higher modes of string vibrations and standing waves, along with harmonics and partials. Don't miss demonstrations of the shape of string vibrations and the sound produced by different modes. Enhance your understanding of plucking a string and the resulting harmonics.

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PH109 Exam Review: Vibrations of Strings Guide

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  1. First exam: Monday October 8, 2001 12:05 lecture: Room 1300 Sterling 1:20 lecture: Room 125 OLD Biochem Bldg 420 Henry Mall (corner Univ Ave) the exam covers: Homework Lab through Strings Study Guide the material is covered in Ch. 2-4 in “The Science of Sights and Sounds” on reserve at Helen C. White and at Physics library • Review Sessions in Room 3335 Sterling • Emre 1-3 pm Saturday, October 6 • Santhosh 1-3 pm, Sunday, October 7 • Eva 3-5 pm Sunday, October 7

  2. PH 109 Lecture 8 10/1/2001 Strings, Pipes Vibration of Strings: Fundamental frequency f1 T : tension in N L: length in m r: mass per unit length in kg/m • changing the frequency: • change length (guitar, violin etc):shorter L higher pitch • change tension (tuning): higher T higher pitch • change mass per unit length: heavier string lower pitch

  3. Examples: (sent to class by e-mail include answers) 1. string frequency 300 Hz for T= 40 N. Find frequency for 50 N tension 2. 60 cm long string plays a certain tone. What length will produce a tone an octave higher (double the frequency)? 3. A cello string is 80 cm long and has a mass of 1.2 g. a) Find the mass per unit length. b) Find the tension required to obtain a frequency of 200 Hz.

  4. HIGHER MODES OF STRING • An oscillation is called a “MODE” if • each point makes simple harmonic motion • NODE: place where string does not move • ANTINODE (BELLY): largest amplitude of motion A first mode: freq. f1 “fundamental” N N N A N N N 2nd mode: freq. f2 = 2f1 “first overtone” A A A 3rd mode: freq. f3 = 3f “second overtone” N N N N A

  5. Standing Waves wave on string is reflected at both ends of the string RESULT: SUPERPOSITION of waves travelling in opposite directions makes “standing wave” 2 waves travelling in opposite directions (Quicktime Movie) 2 waves with superposition (Quicktime Movie) Only superposition (Quicktime Movie)

  6. Harmonics and Partials • The overtones are called “HARMONICS” if they their • frequencies are whole-number multiples of the fundamental • when a string is bowed or plucked, many modes oscillate • at the same time (shape of string: superposition of modes!) demos: shape of string; tone from different modes • musicians call the sound made by the different • modes the “PARTIALS” of the tone

  7. Plucked String example: pluck string at 1/4 point from end. which harmonics will be strong? which harmonics will be absent? Answer: 2ndharmonic has belly where string is plucked: STRONGEST 4thharmonic has NODE where string is plucked: ABSENT 8th harmonic ….ABSENT other harmonics: more or less present, depending how much amplitude they have at pt. where plucked.

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