CHAPTER 17: PHYSICS OF HEARING

Transcription

1 Collg Physics Studnt s Manual Chaptr 7 CHPTER 7: PHYSCS OF HERNG 7. SPEED OF SOUND, FREQUENCY, ND WVELENGTH. Whn pokd y a spar, an opratic soprano lts out a - Hz shrik. What is its alngth i th spd o sound is 345 m/s? Us th quation λ, hr Hz and 345 m/s: λ 345 m/s Hz.88 m 7. Dolphins mak sounds in and atr. What is th ratio o th alngth o a sound in to its alngth in saatr? ssum tmpratur is. C. Th alngths o sounds in and atr ar dirnt caus th spd o sound is dirnt in and atr. W kno 54 saatr m/s (rom Tal 7.) and 343 m/s at. C rom Prolm 7.5, so rom th quation λ kno saatr λ saatr and λ, so can dtrmin th ratio o th alngths: saatr λ λ saatr λ λ saatr 343 m/s 54 m/s SOUND NTENSTY ND SOUND LEVEL 3. Th arning tag on a lan mor stats that it producs nois at a ll o 9. db. What is this in atts pr mtr squard? 5

2 Collg Physics Studnt s Manual Chaptr 7 β log (., hr W/m ) W/m 9./..6, so that 3 W/m / β, and (To calculat an xponnt that is not an intgr, us th y x - ky on your calculator.). Popl ith good haring can prci sounds as lo in ll as 8. db at a rquncy o 3 Hz. What is th intnsity o this sound in atts pr mtr squard? β log β /, so that (. W/m ) 8. / W/m 7. (a) Ear trumpts r nr ry common, ut thy did aid popl ith haring losss y gathring sound or a larg ara and concntrating it on th smallr ara o th ardrum. What dcil incras dos an ar trumpt produc i its sound gathring ara is 9 cm and th ara o th ardrum is.5 cm, ut th trumpt only has an icincy o 5.% in transmitting th sound to th ardrum? () Commnt on th usulnss o th dcil incras ound in part (a). P (a) Using th quation, s that or th sam por, (.5)(9 cm ) 5.% icincy: 9..5 cm, so or a β db log No, using th quation ( ) log log B log, s that: B, and rmmring that 6

3 Collg Physics Studnt s Manual Chaptr 7 t β β t log log log log(9) 9.54 db 9.5 db t () This incras o approximatly db incrass th sound o a normal conrsation to that o a loud radio or classroom lctur (s Tal 7.). For somon ho cannot har at all, this ill not hlpul, ut or somon ho is starting to los thir aility to har, it may hlp. Unortunatly, ar trumpts ar ry cumrsom, so n though thy could hlp, th inconninc maks thm rathr impractical. 7.4 DOPPLER EFFECT ND SONC BOOMS 33. spctator at a parad rcis an 888- Hz ton rom an oncoming trumptr ho is playing an 88- Hz not. t hat spd is th musician approaching i th spd o sound is 338 m/s? W can us th quation (ith th minus sign caus th sourc is s s approaching to dtrmin th spd o th musician (th sourc), gin 888 Hz, s 88 Hz, and 338 m/s : ( ) (338 m/s)(888 Hz 88 Hz) 888 Hz s s 3.5 m/s 7.5 SOUND NTERFERENCE ND RESONNCE: STNDNG WVES N R COLUMNS 39. What at rquncis ill prsnt: (a) th musical nots and C ar playd togthr (rquncis o and 64 Hz)? () D and F ar playd togthr (rquncis o 97 and 35 Hz)? (c) all our ar playd togthr? 7

4 Collg Physics Studnt s Manual Chaptr 7 (a) Using th quation B : B, &C 64 Hz Hz 44 Hz () B, D&F 35 Hz 97 Hz 55 Hz (c) W gt ats rom ry comination o rquncis, so in addition to th to ats ao, also ha: B,F& B,F&C B,D&C B,D& 35 Hz Hz 3 Hz; 35 Hz 64 Hz 88 Hz; 97 Hz 64 Hz 33 Hz; 97 Hz Hz 77 Hz 45. Ho long must a lut in ordr to ha a undamntal rquncy o 6 Hz (this rquncy corrsponds to middl C on th nly tmprd chromatic scal) on a day hn tmpratur is. C? t is opn at oth nds. W kno that th rquncy or a tu opn at oth nds is: n n or n,,3... L th undamntal rquncy ( ) n is 6 Hz, can dtrmin th lngth: L. W nd to dtrmin th spd o sound, rom th quation L T(K) ( 33m/s), sinc ar told th tmpratur: 73 K T (K) 93 K (33m/s) (33m/s) 34.9 m/s. 73 K 73 K 34.9 m/s Thror, L.654 m 65.4 cm. (6 Hz) 8

5 Collg Physics Studnt s Manual Chaptr 7 5. Calculat th irst orton in an ar canal, hich rsonats lik a.4- cm- long tu closd at on nd, y taking tmpratur to 37. C. s th ar particularly snsiti to such a rquncy? (Th rsonancs o th ar canal ar complicatd y its nonuniorm shap, hich shall ignor.) First, nd to dtrmin th spd o sound at 37. C, using th quation T (K) 3 K (33m/s) (33m/s) 35.7 m/s. 73 K 73 K Nxt, or tus closd at on nd: n n or n,3,5..., can dtrmin th 4L rquncy o th irst orton ( n 3) 35.7 m/s Hz. khz. 4(.4 m) Th ar is not particularly snsiti to this rquncy, so don t har ortons du to th ar canal. 7.6 HERNG 57. What ar th closst rquncis to 5 Hz that an arag prson can clarly distinguish as ing dirnt in rquncy rom 5 Hz? Th sounds ar not prsnt simultanously. W kno that can discriminat tn to sounds i thir rquncis dir y at last.3%, so th closst rquncis to 5 Hz that can distinguish ar (5Hz)(±.3) 498.5Hz and 5.5Hz. 9

6 Collg Physics Studnt s Manual Chaptr What is th approximat sound intnsity ll in dcils o a 6- Hz ton i it has a loudnss o phons? it has a loudnss o 7 phons? From Figur 7.36: a 6 Hz ton at a loudnss o phons has a sound ll o aout 3 db, hil a 6 Hz ton at a loudnss o 7 phons has a sound ll o aout 7 db. 69. prson has a haring thrshold db ao normal at Hz and 5 db ao normal at 4 Hz. Ho much mor intns must a - Hz ton than a 4- Hz ton i thy ar oth arly audil to this prson? From Figur 7.36, th phons lin is normal haring. So, this prson can arly har a Hz sound at db ao normal, rquiring a 47 db sound ll ( β ). For a 4 Hz sound, this prson rquirs 5 db ao normal, or a 43 db sound ll ( β ) to audil. So, th Hz ton must 4 db highr than th 4 Hz sound. To calculat th dirnc in intnsity, us th quation β β log log log and conrt th dirnc in dcils to a ratio o intnsitis. Sustituting in th alus rom ao gis: 4/ log 47 db 43 db 4 db, or.5 So th Hz ton must.5 tims mor intns than th 4 Hz sound to audil y this prson. 7.7 ULTRSOUND 77. (a) Calculat th minimum rquncy o ultrasound that ill allo you to s dtails as small as.5 mm in human tissu. () What is th cti dpth to hich this sound is cti as a diagnostic pro? 3

7 Collg Physics Studnt s Manual Chaptr 7 (a) From Tal 7., th spd o sound in tissu is 54 m/s, so using λ ind th minimum rquncy to rsol.5 mm dtails is: 54 m/s Hz 3 λ.5 m () W kno that th accptd rul o thum is that you can ctily scan to a dpth o aout 5λ into tissu, so th cti scan dpth is: 5λ ( m).5 m.5 cm, 83. diagnostic ultrasound cho is rlctd rom moing lood and rturns ith a rquncy 5 Hz highr than its original. MHz. What is th locity o th lood? (ssum that th rquncy o. MHz is accurat to sn signiicant igurs and 5 Hz is accurat to thr signiicant igurs.) This prolm rquirs to stps: () dtrmin th rquncy th lood rcis (hich is th rquncy that is rlctd), thn () dtrmin th rquncy that th scannr rcis. t irst, th lood is lik a moing rr, and th quation + s s gis th rquncy it rcis (ith th plus sign usd caus + th lood is approaching): s (hr lood locity). Nxt, this rquncy is rlctd rom th lood, hich no acts as a moing sourc. Th quation s (ith th minus sign usd caus th lood is still s approaching) gis th rquncy rcid y th scannr: ' + s s + Soling or th spd o lood gis: ' (54m/s)(5 Hz) 6 (. Hz + 5 Hz) +. s 6 ' + s Hz.9 m/s 3

8 Collg Physics Studnt s Manual Chaptr 7 Th lood s spd is 9. cm/s. 3