Physics 116 Lecture 7 Decibels, and Doppler Effect Sound Level meter Oct 10, 2011 (www.extech.com) R. J. Wilkes Email: ph116@u.washington.edu
Announcements • � Exam 1 is one week away! Next Monday, 10/17 • � All multiple choice, similar to HW problems • � YOU must bring a standard mark-sense (bubble) sheet • � Closed book/notes, formula page provided • � You provide: bubble sheet, pencils, calculator, brain • � Covers material in Ch.13 and 14 (through Thursday’s class) • � Damped/driven oscillators will NOT be on test • � Friday’s class: review, and example test questions • � Clickers: • � Registration page is open: see link on home page if you did not get an email (to your @u address) about this, tell me after class Bring your clicker every day many more quizzes than needed – don’t worry if you miss a few
Lecture Schedule (up to exam 1) Today 3
Sound intensity • � Intensity = energy per unit time per unit area = power/unit area So [ ] = physical units • � For a point source, sound power P is spread over an expanding sphere – � So intensity drops off as 1/R 2 • � proportional to surface area of sphere of radius R : A=4 ! R 2 • � For a given sound source (amount of power P emitted), • � Loudness = perceived intensity - “logarithmic” human perception – � If we think one sound is twice as loud as another, it probably has 10X higher intensity – � Similar perception scale for light intensities – � Threshold of hearing (avg person can just hear) – � Threshold of pain (avg person can’t stand it!) – � Our ears handle 13 orders of magnitude! – � Makes sense to describe sound on a logarithmic scale: use decibels (dB) 4
Examples and applications • � One person talking to another produces, at 1m distance, How far away can you be and still (just barely) hear her words? To hear and understand, assume sound intensity must be : Seems like too long a distance! What’s wrong? This assumes there is no background noise to cover the whispery sound level at 100 m - i.e., you must be in a soundproof, totally silent room! (in practical terms: background noise must be below the threshold of hearing) Exercise for you: suppose background noise intensity is So we would need voice intensity to be larger, say: Now how close would you have to be? 5
Decibels for ratios over a large range of magnitudes • � Decibels are used to describe any quantity expressed as a ratio when a log scale is needed – � Originated at Bell Laboratories (bel = unit for base-10 ratios, after Alexander Graham Bell ) – bel is “too large” for most applications – � Commonly used in many engineering and applied science fields • � For intensities (power ratios) – � For acoustics, we use threshold of hearing as the reference level – � So a sound intensity at the threshold of hearing is 0 dB – � Sound at the threshold of pain has 6
Decibels for ratios over a large range of magnitudes • � Note: dB are used for ratios of two kinds of physical quantities – � Power-like quantities (intensity of sound, power in E-M waves) – � Amplitude-like quantities (sound pressure levels, electric field amplitude in E-M waves) “~” means “proportional to” • � For such quantities, power ~ amplitude 2 What does that always mean? • � Usually, we measure power, not amplitude – � dB definition 10log(ratio) is based on power or intensity • � So, when we use dB for an amplitude-like quantity, we insert a factor of 2 in the log10 (=squaring the ratio); factor is 20 instead of 10 • � This gives amplitude ratios the same dB relationships as their corresponding intensity/power ratios 7
Decibel levels for sound intensity (and sound pressure) http://www.sengpielaudio.com/TableOfSoundPressureLevels.htm Factor of 10 increase in intensity = addition of 10 to dB level Factor of 10 increase in pressure = addition of 20 to dB level 8
Decibels : examples • � The sound intensity (at 1m) of one person clapping is • � What level does this produce on a dB meter? • � If 100 people at a concert clap, what dB level do you expect? • � How many people would it take to make the clapping “deafening”? 10 million clappers: quite a stadium needed! 9
Doppler effect: If sound source and observer are in relative motion, observed frequency will differ from source’s frequency • � Sound waves require a material medium to propagate • � Recall: Galilean relativity – � If two coordinate systems differ only by a constant v, not by an acceleration, we can simply add velocity vectors to get apparent v in either – � Standard example: rowboat in a river that is flowing with speed v • � rower has speed u relative to water, • � water has speed v relative to earth, • � so rower’s speed relative to earth is u + v u is + if same direction as river (rowing downstream), negative if opposite (upstream) • � Coordinate system of medium (air, water, etc) is “special” for sound waves – � Sound waves have speed c, and f and " are related by • � For an observer moving relative to medium with speed u, apparent propagation speed c’ will be different: (sign depends on relative direction of u ) – � Wavelength cannot change – it’s a constant length in the medium, and same length in moving coordinate system (motion does not change lengths) – � Observed frequency has to change, to match apparent speed and fixed wavelength: 10
Doppler effect: • � So if observer is moving (speed u ) relative to source at rest in medium, then apparent frequency f’ is: + sign if u is toward source, Minus sign if away from source • � However, if source is moving (speed u ) relative to observer at rest in medium, then – � Frequency remains constant (same time interval between wavefront emissions) – � But source now chases its own waves (or runs away from them): wavelength in the medium is shorter or longer • � Wave speed = c • � Time between successive peaks = T • � Distance between peaks = cT – uT = wavelength • � Frequency of wave in medium (and for observer): minus sign if toward observer, + sign if away from observer. Notice: different f for observers on opposite sides of the source! Notice the central role of the medium in both cases 11
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