1 Phys 125 Winter 2007 Lecture #25 Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu Sound Waves FINAL EXAM • Friday December 14, 7:30-9:30 pm • Room assignments have changed • You are allowed four note cards or one 8.5 X 11” sheet (both sides) for this exam. Typewritten is OK. • There are 25 questions: 5-8 cover new material. • Practice exams and solutions are posted on CTools • Extra time arrangements are posted on CTools 2 Final Exam Room Assignments Dr. Andrew Tomasch 012, 018, 019: Angell Aud B Dr. Arthur Cole 010, 016, 017: Angell Aud D Dr. Konstantin Bobkov 009, 011: Angell Aud C Dr. Salin Cheng-Bernstein 003, 004, 005, 006, 007: Angell Aud A 008: Angell Aud B Be sure to locate your room before the exam! Final Exam Review Session • Wednesday afternoon December 12, 2:00 – 4:00 pm • Room 296 Dennison • Bring problems to work from practice exams, previous exams, assigned book problems, etc. 3 My Final Exam Office Hours • Tuesday December 11, 2:00 – 3:00 pm (regular hours) • Thursday December 13, 1:00 – 4:00 pm (extra hours) • Bring problems to work from practice exams, previous exams, assigned book problems, etc. Waves • Two types of waves: a) Transverse b) Longitudinal kT fv ωλ λ === For periodic waves Demonstration: waves on a slinky 4 Sound: A Pressure Wave • Condensation ≡ region of increased pressure • Rarefaction ≡ region of decreased pressure • A pure tone is an harmonic (sine or cosine) sound wave with a single frequency • The energy of a sound wave propagates as an elastic disturbance through the air • Individual air molecules do not travel with the wave • A given molecule vibrates back and forth about a fixed location • When we speak of sound, we mean frequencies within the range of human hearing: 20 Hz < f < 20,000 Hz Sound Waves Propagate in Air Demo: range of hearing Ultrasonic: f > 20,000 Hz Example: bats echo locate objects with f > 60,000 Hz Infrasonic: f < 20 Hz Example: Whales Demo: no sound in vacuum 5 Sound Intensity • Human ears are sensitive to an astonishing dynamic range of sound intensities → many orders of magnitude ≡ Powers of 10 Power Area I ≡ If the source is emitting sound uniformly in all directions, then the sound waves disperse like ripples on a pond losing intensity with increasing distance Power ≡ Energy / Time Units: W/m 2 21 I I< • If the source is emitting sound isotropically (uniformly in all directions) all the emitted energy passes through every sphere of radius r centered upon the source: Spherical Waves 2 () 4 source P Ir rπ = The Surface Area of a Sphere is 4πr 2 Units: W/m 2 Caution Qwizdom Ahead 6 Concept Test #1 Suppose you are standing a distance D away from a speaker that is radiating sound isotropically. You walk away from the speaker until the intensity of sound is reduced by a factor of four. About how far from the speaker are you now (neglecting any reflections from the ground)? A. 10D B. 4 D C. 3D D. 2D 2 444 4 4 4 44 22 new old22 new old 22 2 new old old new old 22 old new new old new 2 22old old old new new old2 old new new old PPP II I DDD IDDIP IDPDID IID ID DDD πππ π π =⇒= = ==⇒= =⇒ = ⇒ = == Intensity Level β • The loudness of a sound is characterized by the intensity level ≡ β : – I 0 is a reference intensity corresponding to the threshold of human hearing: I 0 ≡ 10 -12 W/m 2 – Sound with an intensity ten times that of the faintest sound you can hear (I 0 ) has an intensity level of: 10 0 10log I I β ⎛⎞ ≡ ⎜⎟ ⎝⎠ Units: dB dB 10 10 log10 0 0 10 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = I I β ( ) 10 0 10II β = The decibel scale is logarithmic and divides one factor of 10 into ten incremental factors of 10 0.1 , each of which corresponds to one point on the decibel scale 7 10 0.9 = 7.9439 10 1.0 = 10.00010 10 0.8 = 6.3108 10 0.7 = 5.0127 10 0.6 = 3.9816 10 0.5 = 3.1625 10 0.4 = 2.5124 10 0.3 = 1.9953 10 0.2 = 1.5852 10 0.1 = 1.2581 10 0.0 = 1.0000 I/I 0 Intensity Level β (dB) Intensity Level β 10 0 10 I I β = The decibel scale is logarithmic and divides one factor of 10 into ten incremental factors of 10 0.1 , each of which corresponds to one point on the decibel scale Properties of Logarithms yxy x 10 log10 =⇔= 10 10 10 log ( ) log logABAB= + 10 10 10 log log log A A B B ⎛⎞ =− ⎜⎟ ⎝⎠ 10 10 log log N A NA= Caution Qwizdom Ahead 8 Concept Test #2 A certain sound has an intensity 100,000 times greater than the faintest sound you can hear. Its intensity level is: A. 50 dB B. 60 dB C. 500 dB D. 100,000 dB 5 10 00 5 10 10log 10 10log (10 ) 50 dB II II β β ⎛⎞⎛⎞ == ⎜⎟⎜⎟ ⎝⎠⎝⎠ ⇒= = An increase by a factor of 10 N in intensity corresponds to adding 10×N to the intensity level β. dB ≡ decibel The Speed of Sound 19554 (5962 m/s) Steel 18504 (5641 m/s) Glass 4993 (1522 m/s) Seawater (20 o C) 4862 (1482 m/s) Fresh water (20 o C) 1125 (343 m/s) Air (20 o C) 1086 (331 m/s) Air (0 o C) Speed (ft/s) Substance restoring force parameter inertia parameter v = ρ Y v = Sound Speed in a Solid atm sound air P v γ ρ = γ≡ ratio of specific heat capacity at constant pressure to specific heat capacity at constant volume for air Sound Speed in Air solid liquid gas vv v>> Demo: speed of sound 9 Doppler Effect: Moving Source • For a moving source: – The emitted wave immediately speeds off with v ≈ 343 m/s (20 o C) – If the source is stationary the wavelength is λ = v/f – If the source is moving toward the observer each successive wave is emitted from a point closer to the observer than the previous one – The observed wavelength is shorter than the emitted wavelength→ higher f 1 source observed source source sound f ff v v => − 1 source observed source source sound f ff v v =< +Source moving toward you Source moving away from you Demo: Doppler whistle Doppler Effect: Moving Observer 1 observer observed s s sound v ff f v ⎛⎞ =+ > ⎜⎟ ⎝⎠ 1 observer observed s s sound v ff f v ⎛⎞ =− < ⎜⎟ ⎝⎠ Observer Moving Toward a Stationary Source Observer Moving Away From a Stationary Source s source frequencyf ≡ 10 1 1 observer sound observed s source sound v v ff v v ⎛⎞ ± ⎜⎟ = ⎜⎟ ⎝⎠ ∓ In the Numerator: (+) ≡ moving toward (-) ≡ moving away In the Denominator: (-) ≡ moving toward (+) ≡ moving away Doppler Effect: Moving Source and/or Observer This single formula covers all possible cases Top Symbol → Toward Today’s Homework • Wiley Plus Homework 13 is due Wednesday December 12 • Assigned Conceptual Questions & Problems from Textbook • Print tomorrow’s discussion worksheet • Review worksheets not covered in class • Prepare for the Final Exam by reviewing problems missed on Exam #3 and previous exams atomasch Microsoft PowerPoint - p125_25_f07.ppt