VIBRATING SYSTEMS. example. Springs obey Hooke s Law. Terminology. L 21 Vibration and Waves [ 2 ]

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1 L 1 Vibration and Waves [ ] Vibrations (oscillations) resonance pendulu springs haronic otion Waves echanical waves sound waves usical instruents VIBRATING SYSTEMS Mass and spring on air trac Mass hanging on spring Pendulu Torsional oscillator All vibrating systes have one thing in coon restoring force 1 Springs obey Hooe s Law exaple spring force (N) Elastic liit aount of stretching or copressing () the strength of a spring is easured by how uch force it provides for a given aount of stretch we call this quantity, the spring constant in N/ agnitude of spring force = aount of stretch F spring = x 3 A ass of g is hung fro a spring that has a spring constant = 100 N/. By how uch will it stretch? The downward weight of the ass is balanced by the upward force of the spring. w = g = x g 10 /s = (100 N/) x 0 N = 100 N/ x x = 0. or 0 c x g x X=0 4 siple haronic oscillator ass and spring on a frictionless surface spring that can be stretched or copressed equilibriu position is the spring constant, which easures the stiffness of the spring in Newtons per eter A 0 A frictionless surface 5 Terinology AMPLITUDE A: axiu displaceent fro equilibriu (starting position) PERIOD T: tie for one coplete cycle FREQUENCY f : nuber of coplete cycles per unit tie; one cycle per second = 1 Hertz (Hz) 1 1 f, T T f 6 1

2 follow the ass position vs. tie Period (T) and frequency (f ) of the ass-spring syste + A -A position tie T 1 1 f T T T T 7 8 Period and frequency of the pendulu Energy in the siple haronic oscillator L L 1 1 g T f g T L PE KE PE A stretched or copressed spring has elastic Potential Energy F restoring Tension g The period depends on L and g The period does not depend on the ass, KE+PE KE+PE E total = KE + PE = constant L 1 For L = 1, T s g 10 / s 9 The pendulu is driven by Gravitational potential energy GPE KE KE+GPE KE+GPE GPE 10 Waves vibrations that ove What is a wave? A disturbance that oves (propagates) through a ediu Due to the elastic nature of aterials The people wave you stand up and sit down, then the person next to you does the sae, and so on, so the disturbance goes all around the stadiu (World s record) the standing and sitting is the disturbance notice that the people ove up and down but the disturbance goes sideways Waves are a eans to transport energy fro one place to another without transporting atter Electroagnetic waves (light, x-rays, UV rays, icrowaves, theral radiation) are disturbances that propagate through the electroagnetic field, even in vacuu (e.g. light fro the Sun taes about 8 inutes to get to earth) 11 1

3 Wave Classification Classification based on the ediu Mechanical waves: a disturbance that propagates through a ediu waves on strings waves in water (ocean waves, ripples on a lae) sound waves pressure waves in air Electroagnetic waves (no ediu) Classification based on how the ediu oves transverse longitudinal 13 Transverse wave on a string jiggle the end of the string to create a disturbance the disturbance oves down the string as it passes, the string oves up and then down the string otion in vertical but the wave oves in the horizontal (perpendicular) direction transverse wave this is a single pulse wave (non-repetitive) the wave in the football stadiu is a transverse wave 14 Longitudinal waves instead of jiggling the spring up and down, you jiggle it in and out the coils of the spring ove along the sae direction (horizontal) as the wave This produces a longitudinal wave Sound waves are longitudinal waves 15 Speed of a wave on a string The speed of the wave oving to the right is not the sae as the speed of the string oving up and down. (It could be, but that would be a coincidence!) The wave speed is deterined by: the tension in the string ore tension higher speed the ass per unit length of the string (whether it s a heavy rope or a light rope) thicer rope lower speed 16 Haronic waves eep jiggling the end of the string up and down produces a continuous wavetrain S N SOUND WAVES longitudinal pressure disturbances in a gas the air olecules jiggle bac and forth in the sae direction as the wave Sound waves cannot propagate in a vacuu DEMO 17 SPEAKER 18 3

4 Sound a longitudinal wave I can t hear you! Sound is a disturbance in a gas (air) In vacuu, there are no sound waves there is no sound in outer space 19 vacuu pup 0 The pressure of the sound wave aes our eardru vibrate Huans can hear sounds between about 30 Hz and 0,000 Hz Sound below 30 Hz is called infrasound Sound above 0,000 Hz is called ultrasound The Huan Ear The eardru is a very sensitive ebrane capable of responding to displaceents on the order of the size of an ato! Our sense of hearing is uch ore sensitive than our sense of sight 1 The speed of sound Sound pressure waves in a solid, liquid or gas The speed of sound v s Air at 0 C: 343 /s = 767 ph 1/5 ile/sec Water at 0 C: 1500 /s copper: 5000 /s Depends on density and teperature 5 second rule for thunder and lightning 3 Why do I sound funny when I breath heliu? The speed of sound depends on the ass of the olecules in the gas Sound travels twice as fast in heliu, because Heliu is lighter than air The higher sound speed results in sounds of higher pitch (frequency) 4 4

5 Acoustic resonance tuning for resonance shattering the glass 5 5