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PowerPoint Slides
General Physics II Sound Sound... ...a longitudinal wave in air caused by a vibrating object. Large scale - swinging door creates macroscopic currents Small scale - tuning fork creates sound waves Page 1 Series of condensations (increased pressures) and rarefactions (decreased pressures) Range of Sound infrasonic frequencies < 20 Hz ultrasonic frequencies > 20,000 Hz human hearing range frequencies between 20 Hz and 20,000 Hz Page 2 Speed of Sound Liquids and Gases: B is bulk modulus, ρ is mass/volume Solids: Y is Young’s modulus vair varies with the air temperature: v= v= v air = 331 m s 1 + B ρ Y ρ TC 273 .15 Interference of Sound Waves Assume sources “a” and “b” are “coherent”. If observer is located ra and rb from the two sources, Source a Source b ra − rb = nλ for maximum ra − rb = (n + 1 2)λ for minimum ra rb f beat = f a − f b Observer Page 3 DOPPLER EFFECT • A change in the frequency experienced by an observer due to motion of either the observer or the source. "Wheeeeeeeeeeee…….Oooooooooooooo” Examples: moving cars and trains moving buzzer in a ball (in class demo) rotating whistle Higher frequency: Object approaching Lower frequency: Object receding STATIONARY MOVING SOUND-GENERATING OBJECT SOUND-GENERATING OBJECT Velocity, v A Waves are created at point source and radiate outward creating a wave front with the same frequency as that of the source. B Although the frequency of the sound generating object remains constant, wave fronts reach the observer at Point B more frequently than Point A. Page 4 http://www.kettering.edu/~drussell/Demos/doppler/doppler.html Doppler Effect, Moving Observer When not moving, f = v λ v + vo v When moving towards, ƒ ' = ƒ Fig 14.8, p. 435 Slide 12 Page 5 If observer moves away: v − vo ƒ' = ƒ v Fig 14.9, p. 436 Slide 13 The Source in Motion Approaching source: f'= f v v − vs Source leaving: f'= f v v + vs Page 6 Doppler Effect: Both Observer and Source Moving O Toward f'= f O Away v ± vo v m vs S Toward S Away Switch appropriate signs if observer or source moves away A train has a whistle with a frequency of a 1000 Hz, as measured when the both the train and observer are stationary. For a train moving in the positive x direction, which observer hears the highest frequency when the train is at position x=0. Observer A has velocity VA>0 and has position XA>0. Observer B has velocity VB>0 and has position XB<0. Observer C has velocity VC<0 and has position XC>0. Observer D has velocity VD<0 and has position XD<0. Page 7 Standing Waves Standing Waves: Resultant wave created by the interference of two waves traveling at the same frequency, amplitude and wavelength in opposite directions. Standing Waves have Nodes and Antinodes Nodes: Points in the standing wave where the two waves cancel – complete destructive interference– creating a stationary point! Antinodes Point in the standing wave, halfway between the nodes, at which the largest amplitude occurs. Standing Waves on a String Wavelength, λ λ2 = L Only certain frequencies of vibration produce standing waves for a given string length!!! λ3 = 2L/3 The wavelength of each of the standing waves depends on the string length, L λ1 = 2L λn = 2L/n λ4 = 2L/4 or ½ L Page 8 Only certain frequencies of vibration produce standing waves for a given string length!!! fn = n v/2L n = 1, 2, 3, … Where, v is the speed of waves on the vibrating string (NOT the speed of the resultant waves in air!!!!) L is the portion of the string that is vibrating Standing Waves on a String Frequency, f A N N f1 = v / λ1 A N A N N Fundamental Frequency or 1st Harmonic 2nd Harmonic f2 = 2 f1 A A N N N 3rd Harmonic N A A A N N f3 = 3 f1 A N A N f4 = 4f1 N Page 9 4th Harmonic Standing Waves in an Air Column A node for displacement is always an antinode for pressure and vice versa, as illustrated below. When the air is constrained to a node, the air motion will be alternately squeezing toward that point and expanding away from it, causing the pressure variation to be at a maximum. Tube Closed at One End Wavelength, λ Frequency, f λ1 = 4L f1 = v / λ1 Fundamental Frequency or 1st Harmonic λ3 = 4L/ 3 f3 = 3 f1 3rd Harmonic λ5 = 4L/5 f5 = 5 f1 5th Harmonic λn = 4L/n Page 10 fn = n v/4L n = 1, 3, 5,… Tube Open at Both Ends Wavelength, λ Frequency, f Fundamental f1 = v / λ1 Frequency or λ1 = 2L 1st Harmonic λ2 = L f2 = 2 f1 2nd Harmonic λ3 = 2L/3 f3 = 3 f1 3rd Harmonic λn = 2L/n fn = n v/2L n = 1, 2, 3, … End of Sound Lecture Page 11