# PHYSICS 151 Notes for Online Lecture #26

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1 YSCS 5 Ntes fr Online Lecture #6 Acustics - earing Sund hen yu hear sething, there are tw priary characteristics yu ntice: hw lud the sund is, and the pitch f the sund. Ludness is related t the intensity f the sund itch is related t the frequency f the sund Because peple are srt f cplex, we can t say that these tw things are ttally unrelated t each ther; fr exaple, if the sae frequency is sunded, but at different intensities, yu ay perceive the t be different pitches. S there is se subjective cpnent pitch and ludness. eple can hear fr abut z t, z, with the upper range decreasing with age. e call frequencies abve, ultrasnic - eaning nly that they are sunds abve the range f ur hearing. Yu ay have heard this in ters f ultrasnic jewelry cleaners, r ultrasnic tthbrushes. hen yu think abut hw sund waves wrk. Dgs can hear uch higher frequencies up t abut 5, z, and bats, which eit ultrasnic waves t lcate fd and bject they d like t avid running int can hear up t, z. Ludness Ludness is related t the intensity f the wave. ntensity is the aunt f energy that passes thrugh a given area in a given tie. E At Thus intensity has units f /. The energy eitted per tie by a surce spreads ut ver a larger area s that we experience a diinishing intensity as we ve away fr the surce. r The intensity f a wave is prprtinal t the square f its aplitude. f we call the aplitude f the sund wave A, the intensity is given by: π vρf A CA The iprtant thing here t realize is that if yu have tw waves and ne is twice the aplitude f the ther, the intensities will differ by a factr f 4. The huan ear can hear a very brad range f intensities fr - / t / (althugh this wuld be painful.) Experientally, we find, thugh, that t prduce a sund that is twice as lud as anther sund, the luder sund has t have an aplitude abut x higher this indicates that what we hear as ludness is definitely nt the sae thing as the intensity. r this reasn, we use a quantity Lecture 6 age

2 called an intensity level, which is defined as and is re in line with what we hear as ludness. is defined as: ( in db ) lg where is a reference intensity, taken t be. x - /, which is theretically the lwest sund we can hear. S the lwest value fr ccurs when ; bg ( in db) lg ( in db) lg db f we find the sund level fr an intensity f x - / which is ties luder than ; ( in db) lg x ( in db) lg x J db S if the intensity increases ties, the intensity level changes fr t. hat if we lk at an intensity f - /? ( in db) lg x ( in db) lg x J db S anther increase f ties the previus level gets us anther db rise in intensity level. This cntinues t be true: every tie the intensity ges up by a factr f, the sund level rises by db. The threshld f pain is /, ( in db) lg ( in db) lg x J db S db actually eans re intensity than the threshld f hearing. Lecture 6 age

3 Surce db ntensity (/ ) Jet plane at 3 4 db Threshld f pain db Siren at 3 db x - Ordinary cnversatin 65 db 3 x -6 hisper db x - Threshld f hearing db x - f we want t cpare tw sund levels, say and, we can write ( in db) lg ( in db) lg lg lg Recall that lg (a) - lg (b) lg (a/b) lg lg lg lg L N M lg O Q Lecture 6 age 3

4 EXAMLE 6-: The specificatins f stere equipent ften cite a signal-t-nise rati. A signal-t-nise rati f 6 db eans that the signal has an intensity level 6 db higher than that f the nise. hat des this figure ean abut the intensities f the tw sunds? nw use: if x lg (y) then y x This eans that is a illin ties lg 6dB lg 6 lg 6 EXAMLE 6-: A 5 db sund waves strikes an eardru whse area is 5. x -5. (a) w uch energy is absrbed by the eardru per secnd? (b) At this rate, hw lng wuld it take yur eardru t receive a ttal energy f J? lg lg lg + lg lg 5 [ ] ( ) + lg 7 wer ntensity * Area 7 5 ( 5x ) 5 energy J tie s 6,35years pwer 5 Lecture 6 age 4

5 EXAMLE 6-3: At a recent rck cncert, a db eter registered 3 db when placed.5 in frnt f the ludspeaker n stage. (a) hat was the pwer utput f the speaker? 3 lg 3 lg lg 3 lg + lg r ( r ) 4 π (.5) 785 (b) w far away wuld the intensity level be a reasnable 9 db? 9 lg 3 9 lg lg lg + 3 lg r 785 r 5 3 Lecture 6 age 5

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