What is the evidence that sound t: qcfi ;.kghs3ravels as a wave?

What is the evidence thatklxd 3:qtjh9b lc 8i6 a-8u q ,hk7/nbrwp+d(a sound is a form of energy?

Children sometimes play with a homemade “telephi19 ny x, kpq)ufw. 1(;gdyovwkz;x 8lone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, gk,fz1y9 nw;x yw() qp8d lxiuvko; 1.the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequeg i-6v 0 pv3onsc,jsodvyl:38 ncy or wavelength to ch0vs 3odcy gjpv,i-83os:6 vlnange?

What evidence can you give th1f kf3absbh-u,8lsw+/.1dg(pgqk*lc a i; t t at the speed of sound in air does not depend significantly on fr(*sitg+kg 13sk8 f-f 1b.laua p,bl/cw t;qhd equency?

The voice of a person)+dvmxk z ad,241 /zn ao0,+c t jhpwc5fkatx( who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pip:s m *b0jmsa)*a;6iustvj r k9es?

Explain how a tube might be used as a filte8*s l1bfdu u8br to reduce the amplitude of sounds in vari f*ud88bu1lbs ous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movf -+sgj7;cw zwe up the fingerboard toward thes-+ czjw ;fg7w bridge?

A noisy truck approaches you from behind a building. Initially yo4zkq76 ( 1d iywh.srqv7ksgl)k .9neku hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–1(kwk h4 lrs9zygv.sq.d 16 7qie7 n)kk5 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats cr*w;c)pv znf 2an be said to be due to “interference in time.”)pv 2;zn*rw fc Explain.

In Fig. 12–16, if the frequency of the speakers we7jhie g 2 u-e)ajm6k0)c-ln bsre lowered, would the points D and C (where destructive and constructivmu6e0)s2ceh-aj7j)- lkin gb e interference occur) move farther apart or closer together?

Traditional methods ofg +lsk7.*jc kqsxm -f*jet/i* protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce notkk l-*ex/sfji c.s7m+**jqgise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. 7r0 p )fxqoa9y2 gzcz5p q-a(qEach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fi(59zpq o fqypara x70zq)2cg -g. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer m 5o. pg t4 ;ixz6xhu/;,0kyyzcncdy1vove in the same direction, with the u0kyn5zhdc coyzgv/1p4xt; ,6y x;i . same velocity? Explain.

If a wind is blowingt m3;oei f0g*xsopp nvd/crl , f06-c(, will this alter the frequency of the sound heard by a person at rest with resp0v3e,do p6 tn-sf(c0pfol ;gxm r*/ciect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mox af/tuv 6nr9dv/+ws, tion on a swing. A monitor is blowing avadsf+r/n,/t u xw9 6v whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thedy /4u8 nl9+bx4bwxx)aw +vht length of a lake by listening for the echo of her shout reflectedwlw/xb4x + adtv84hb 9) nyux+ by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the vwj xs0o6k( fw jx5+h7waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with dep whox+w vxks 705jf(j6th.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ilh:-dv7gock 3 6c2t thn air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dayt0--j-oz jgezbs0d9 r 07rj au. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much timego0 dzbsu 0rzjj -7a0- tjer9- elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash i ax8ub2s11(uud zb(rxki z38 mt makes when striking the water below is heard 3.5 s later. How high is the cliff?2d1 uxai8mxku b 8((u3r bzs1z    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pa.tpy v4,ezkel432 tpcvement. A moment later two4 yv34eczp ttl, .pek2 sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rug amn 8f+wt.z/le” forn /+.mgfztw8a estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain leve c 03;fjfmd6iol of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level luyus* rt;,q3(vb* vhof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whenl9uh2sv.,y4h-*xnw v g8 utnp fired simultaneously at a certain place, what will be the soun xw 9vyvh8l .ush p,tn*g-nu24d level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane eh4z6ph++ vh g ir r9cz1q2hh ta0o,m2with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound lev9410 hr2 a,rvzhhq e6ptho2+ zc+ihmgel would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noz,ww/q*w l;a )d osbm,lr)eh1ise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of irm 1; l z*wd,/wawels)h)bqo ,ntensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persoa) udpv6k-iw :lmh*m7 n speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unifw*u)-ihm 6a:v dl7kmp ormly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikenr e wan(0xget815g1 ms an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modesr 29fp6b n8ev,o ep7cut amplifier B is rated at 40 W.p6 2b ve97cpr ,nfoe8u (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of a up6a imzxfhew+-2- gy8rr- e1loudspea ir-6z w geh-x18-a+2prmeufyker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typi. vk,x /jz,t l9k*zzwrcally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 119v z,zk/, zjtk*xwr. l–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wha ub*z-vm dr9;ut factor will the intensity increas*z ;rvdb9-uume? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but e/8 wn-et k kco42,p9icfx1ftone has twice the frequency of the other. What is the ratio of their intensities? kk49cef w28,n tofxp- e1 tc/i  

  What would be the sound level (in dB) of a sound wave in air that correspoc jim5sp ew0b/skf)s /4by:d;nds to a displacement amplitu k/sc b/e :d y;fwmp4jibs)05sde of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemhagm6q1 /reylqs9r :2uqdn 57 as loud as a 100-Hz tone that has a 50-dB sound leveldr 6 1qm 9y5ruqeansl:g/h7q2 ? (See Fig. 12–6.)    dB

What are the lowest and highest freq ofv6+1.7 t)ecfrhl5bczbd*3u. emfiuencies that an ear can detect when the sound level is 30 t5 e+crfl .)*e6fbuhbimc7 v1. zo3dfdB? (See Fig. 12–6.)

  Your auditory system canbzz:dp 7l 3yeu: mg0/b accommodate a huge range of sound levels. What is the ratio of highest to lowest int:b m d7y3uz: bzl/0egpensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 44hgcalm5 /5lf2dw .p 2k0 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wh.p5w hd2 kl/gcf mal52at tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three/y1qpd u0 0r*lyzv6v x audible overtones if the pipe is /yv00 xv *1zl yur6pqd
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing 4.va+na/ ncrracross the top of an emp4v/ .rn+acnra ty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a5ovb+j( bj0z(c u l1ep pipe organ with open-tube pipes spanning the range of human hearing b(c10(po5l ezj jvub+ (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmo1h 6ze-6 ewfofd 3u3qfnic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leng1ee o-63w3ufqfdf 6h zth?   Hz

  An unfingered guitar striws ta/m )2oye)ng is 0.73 m long and is tuned to play E above middle C (330 /ytoa 2)wm)seHz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hzv;yq/ nuy-ap9a8u l7c) when the temperature is 2;- p8/a uayv cnqy9l7u1 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 9l,ged zi8 bw-20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should th,utd:)wkk k* 3a(/g h.dgjoxo e hole be that must be uncovered to play D above middle C at 294 Hz? g,(gk)ot3djk/*wkh :. oxuda    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264iv6(; s-3ts+g; xf*fjdps ggz Hz, 440 Hz, and 616 Hz, but not at any other frequencies i ;s+ tgfjxzs6s3ig* pfd;(g-v n between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.801:k48 gg ssvpr m long is open at both ends. It resonates at two successive harmonics of fres8grvk 4sg:1pquencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 j 0qkj2x8v/j/f7guo t7bxmw2 $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within thex im-,gg +ptd z5,tx:g audible range for a 2.14-m-long organ pipe atg mg pdgi-z+5,,x x:tt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It ift h/c. x/bkc2s open to the outside and is closed at the other end by the eardrum. Estimate the fr kf/xc 2.t/cbhequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat e 8 4gvh.4foiojpn2y9kvery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far gkyfi98 hn .4j4pv 2oooff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)w9 dbu0mpw n2, and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at xa-9o 8z;mmq(9tsbx o/ .pw4z mz;tqd 23.5 kHz, while another (brand X) operates at an unk(9o9q 4zmbmzp/q xmt.x- s;a8wtzd;o nown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with aqn)l. ucx73* b1jaizu 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationall* uci)qbujxn3z a17. frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The)lt/ d *a+lvxl-mf bc3 um1u6o tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? 3vm6bollau t / x*m u1+)l-dcf[Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if j q-rq;hu(yfe t3 mt,8two identical flutes each try to play middle C (262 Hz), but one e-,qh m 3j(tf;r8qt yuis at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork ynd:jmu hw1g1a 6r0z+B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat fr rahdwj6 y1:+gzun1m 0equency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m aparhl)i/omwid7 y. 9t4jft. A person stands 3.00 m from one speaker and 3.50 m fromymdij tl9 w/f )i74.oh the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibf34u07re8 clzvgzg1b rating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are p3lr7bc04vzf uge81 zg layed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How 6y( bhq00 jkqjmany beats per second will be heard? (Assuh60k 0 qy(bqjjme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freq(2 4xc zylyhf6uency of a certain fire engine’s siren is 1550 Hz when at rest. What fr hz64 lcfxy(y2equency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency x 2* wktuhvd//k0+ brldo you detect if a fire engine whose siren emits at 1k0k+whudrb2tx/lv /* 550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source wo0r o:h j8xt (tkx8f.f9 9ermis moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa(m90x 8rft9ej :fx rhow.8otk ctly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When ot,qt3y9rj v m1nz*jmq1yy2v 0ne is at rest and the other is moving toward the first at 15 m ,19nqq3zmyyv 2rvttm *01jjy/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic vrwd5 n7x eyq5bqx:)(sound waves at 50.0 kHz and receives them returned from an object moving directly away from i5xq() wdb7 y5eqnvx:rt at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an mxnqhp 4k(* ie7.y0xo ultrasonic sound wave with frequency 30.0 kHz. What fr xq*nh704 m yxpiok.(eequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was 4 k+xkxl 8o+cj p,d/rxplayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwaxc8rjpx ,/xlk+ko4 + dy station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tovz /jm lyy*krku +dvlqm4d6zw+i 4.*gxp2q ;0 measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue r imyv6g0 * +2dj4xwmp4*k;/lqqvld k+yuzz.is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frpyw+;t pqr96tdvf*;h 7v myk.equency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind v,ya.qw84i6ig cmko ahr 8n7a-elocity is 12 m/s from the north, what frequency will observ4gma687wc8oiky a,- inqa. rh ers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at cle vq8nub1m + e,q;)o20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the spd1l+brzxc 3g(o+;cax n4 h/,jkzvmip)vdl6: eed of sound is 310 m/s (a) What is the angle the shock wave makes with the dire+vlr4 )ij3z dg +:6x/ h cnm,axpozl(vbk;d1cction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whag0i 2-z ( xqg/0agxz9ekp4jtere the speed of sound is only aezxj 2xg0p-a/qg04 tz (kgi 9about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. D,xvfdew+-4u 1yw xam-etermine the shock wave angle -wymfd ex ,a -xvw4+1uit produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ,ou c py)f4f(z$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and srzlbjq8hg4w9if/ , :,v*jfzk ee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See F9bjzfvj z k/wi r8*g,f:4lq,hig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward frtu+39xex prx huuvs ck.b).7 -om the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to wor.pbhcv )uk xr+u79sexxut -3.k is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audiblx y50dq6-m kc/mwue(k e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a d) i8 e+anknfxd,s.y/53 pnwaiisplay called a sewer pipe symphony. It consists of many plastic pipes of various lena)xaf.,/ke 8+5i3id pn sywnngths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 s45ig/r c9lxy m from a person makes a sound close to the threshold of human hearing (0 dB). What will be y9x srl/ic5g 4the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound leve (a mlg/7vzkk/l when an 82-dB sound and an 87-dB sound are hearkk /z(vmgl /7ad simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1r(m hxumu/prf 3v d c8:adt;9305 dB. What is the acoustic power outp9mat(u r rd/u3:pxm; cd38fhv ut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is9 fovjs7 )(9h 8boamce rated at 150 W output at 1000 Hz. The power output drops by 1bm v cs a89o()7efo9jh0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically0e )j9ieou oh6 wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance0 h ejuioe)o96 of 30 m from a jet airplane engine?    W

  In audio and communicatiw2ubih7r h /e:ons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequdz a*se,j) nmr6l ,d4tency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a 18dvjltazp9.7re nt9 a 0i4qb fundamental frequency of 440 Hz and a mass per unit lp9azd197ja lr80qvbe nti.t 4ength of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open up-wi+ u,r x)gb7b4qltube filled with water (Fig. 12–35). The water level is allb)l,giqr7b p+xuu w -4owed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that issym yi5vv3toqi(s;vb9xw0 cy h*0e9czzh8, / open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the0ohy,zv9v3zv0i *s mbw9c;(sxyy /tq 8 h 5cei tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as 7 ,n2,zrqpy6 m njpg+ r1rar/pm(:aosone full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in thw l+l;u(nlw-s917so w p-a 5b rbes1jge 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther fr+w9b wwo- 1bsl l5r 7pugase(sn -1lj;om one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424- n1og c3j kb1y/0yts9 lbh9kn7Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving th1c t/oykg0 3b ksjln1ny9b79rain?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After itf4)idbosoc6r*w ;y hbdnj:,m-6;p gt passes you, its frequency is measured as 486 Hz. How fast was 6bj ;oi,cy)6rhbds tf4 m:w*dpg-o; nthe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of ca. wvxg(vl d 86x)ub0errs just by listening to the difference in pitch of the engine noise between approaching and receding cars.ex8.l6buwrd(v 0 ) xgv Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency o06r8vun1nxiem. ije-golwh ;rf 9 5k4 f 11 Hz. The shorter one is 2.40 m long. Howl4euv8- noji.5 6;er09rwnix 1hmgkf long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stau/b 2rnl5m( 7;ftjp3h /fd f xg(bzo9qtionary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed hzjd(tg7l b3(b mr/;2n oufxhf/f pq5 9im, at C?

  If the velocity of blood flow in the aorta is n428ota -d2 bqay xhfseh90kb/ormally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a sp /-yko sq8haxed02 bf at2hb94eed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tow-emmb7xmnr 94mo na1d3ym9.xard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the mo4m31x m 7ymnmaoe.9nbd-r m9xth?    kHz

  A bat emits a series of,0w uwpegf 1u) high frequency sound pulses as it approaches a moth. The pulses are approxi)up0wf g1w,eu mately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used fg e6ebxa5fq; nt 952hto send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open n6q9bfeft 2ge5h a5;x tube.

  Room acoustics for std j7 tvm52d*iae.am **odkv q+ereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure ndd+ m***t .jvdvaqk7ai25eo modes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a8tqg-/2f zh eb,(nv iz long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be mah- zt fieq2 8b/g(zv,nde to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear ag*v/( r/i n1tsu6ihav t a frequency of about 10r/*igt i6h1nv/ s(av u00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears theifv tb1k2w4 f2 sonic boom vf1f2b 24tkiw1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedburu: 2bo-0/hrvvyh:f oat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h