What is the evidence that sound travels as1yjh+5no -7)q ;cl hsv c+pimk a wave?

What is the evidence that sout9p;.ulm7).bjw j zx(583y z+5x yy kxfcfl blnd is a form of energy?

Children sometimes play with a p/bt;y om7 +e)fjpv,t homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29).+; ppm yb, tovet/j)7f Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wayyp i ojp4g .v1yp8jd7+b /;;.xabzxqter, do you expect the frequency or wavelength to chang+xpj.dz .po741bgx jqa; vy/bi;8p yye?

What evidence can you give that the speed of sound in air k1zcll ktjy:bu 0y1-tx8) d* sdoes not depend significantly on frequenctyud : *jk-zsx1 c8yt b)l1l0ky?

The voice of a person who has inhaled heln; 5ea l2yzirz z( lxo-3cv2i-ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organxz,- kg .t 9ac 7ph ,iko+lvv70a/rjvp pipes?

Explain how a tube might be used as a filter to reduce6 e3p49r2erl04 3g+ f h9fmhbnhefcct the amplitude of sounds in various frequency ranges. (An exampleep 0h64fhetbe9r2+3g9n mlfchrc34 f is a car muffler.)

Why are the frets on a guitar jhhzvv3ow yro-f/j5(v p/ h) 2(Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridgej2 hhw-v5vyf 3(/o/zjhr )vop?

A noisy truck approaches you from behind a building. Initially you hear5t/ 0rg9ijc7hznayq5 it but cannot see it. When it emerges and you do see it, its7y 0ti5 qhg9ra5njzc/ sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference 2ipli +dk. uye/qs 6+lin space,” whereas beats canqks 2ul .6iipy+el+/ d be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the freeb :kyf2 v 2vjh*fxt82quency of the speakers were lowered, would the points D and C (where xe*fjvb8 2fkhy:t2 v2destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting thvd;9dz/ l 6qhgde)+ vue hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise 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 tu vd h/;+gl9e z6dv)qdhe sound levels reaching the ears?

Consider the two waves sh p /jkmp k1*nv.fj-6liown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component f.1im*pn/j-6kv lf kpj requencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer m 9dioj22ecnzcm+ +e -oud4kt 0ove in the same direction, wi +euocdc oej+9tz4km20 d2-nith the same velocity? Explain.

If a wind is blowing, will this alter the frequency ofa rmyb3;m t9a+ the sound heard by a person at ra3r+;mbmy ta 9est with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A x,w oi4hy:: hj *bpgk5monitor is blowing a whistle in front j:p:h ,wogi5yb4 h*xkof 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 t fq 7uk rtrh .0zbxah7r7b-()ghe length of a lake by listening for the echo of her shout reflected by a cliff at the far exh bu r()0 z.-hfqa7gkb77rtrnd 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 be iji7g0 sea:v3low the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How dj7 0ei:a i3sgveep 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths rgq tb(l*5gzu/soj7e(:kto et 6l o6; in 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 o67y p8.i1m0c (+akxve c95hdl ynrixk f tuna on a foggy day. Without warning, an engine backfire occurs onhy 8+c i7vaiy1lr9e 5xd (mk.xp06nc k another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the sj )ry)9 2qdede/0ovotop of a cliff. The splash it makes when striking the water beloq2)d)y vo9ore /djs 0ew is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, se(fn u3dg 0j7moes a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1(g70j3 numd of.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-secoly6a.q isdjl*q sw0dqff *)*.nd rule” for estimating the distance frdia*0jqyql*fdl 6 *.q.s s)wfom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound bz)pxko0g0w(at the pain level 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 of a sound whose intensity issoazao a1, j9,nlow;;c b;; dm $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a snfpsdq2s-.5pi: mz 1sa6t b+yound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if onlq+fb :1 .2pa sznpi-6tmds 5ysy one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallynq/sv+p n/v)k noisy jet engines is experiencing a n+/qv) k/pvsnsound level bordering on pain, 120 dB. What sound level 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-noise ratim(gj sy:uu2tn: ,hk 1ck8n0ldo of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiuts0gjmd uk :,:h 8ncy 2(knl1es 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 person speaking in normal cod+ )zikqp te251bm3 f2;zw ilpnversation. Use Table 12–2. Assume the sound spreads roughly uniformly over d2iwmplzk3f5tzq;+e)1 i 2p ba 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 strikes an eardrum whose i),aw9io i8t1 mg:y/ np)oiqg6d4vb v:(qexyarea 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 y 9 mmbjz8s;auca5 t75rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in zc m 758symbj; 5auta9turn 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 l;* u+ djt4qijloudspeaker on tujdl*i4 +tq j;he 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 typically detect a differezr- k g2gl31n,rpzxqlq( k/w)k.g x0mnce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Seer,z1qr3l0qzg -k.pxg (wk m)nl gx/ k2 Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by 1 h.n(lsa 9s(3hzio uxwhat factor will the intensity increase? Increase (oi1zlsn .hxhu3 (9asby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicbbomus2o;m q .f) a (3pg;f.nwe the frequency of the other. What is the ratio);uom;f ba2qm. 3b(o fgsn.wp of their intensities?   

  What would be the sound level (in dB) of a i rma9vvx *+*gsound wave in air that corresponds to a displac*vav xmr 9*gi+ement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100 r+rcssqff 1t+w+)h2bt fxg+4 -Hz tone that has a 50-dB sound level? (See+ffr+b+ sch)xtst+rg21 4f q w Fig. 12–6.)    dB

What are the lowest and highest frequencies that an e+k- ply 026cbw d(;yce,of bsyar can detect when the sound level is 30 dB? 6oyd 0cfscb ( epky+b-wy,;l2 (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the rcbk-ent3z .2 fatio of highest -e3fc2 kzntb.to lowest intensity 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 fuh3n-jp 9ivge wa8z.p:ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pivj .h9-e ang:w pz38placed?    N

  An organ pipe is 112 cm longyf dg)cx6exx-4qla11. What are the fundamental and first three audible overtyfa dx6-g4) x1xq1cleones if the pipe is
(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 p wf/rj4ef9 l.expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed itrf .fl94p jw/e was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a vmrpgd(al (z(oz* bdxm07 j,9 pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes(mp (,zda0 *rzogmj9d(7lbvx required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frp y 02mpb9 (q8nil .i*iethmj6equency of 540 Hz as its third harmonic. What will qm lmy 9ejp8p(.iti*0hi6bn2 be its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar si14v12p zngr atj7v2ttring is 0.73 m long and is tuned to play E above middle C (3t1 t27p1a24vv injr gz30 Hz).
(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 Hz) when on 1o/n9a 1j i ssv;.7i1wszc:;thhbh the tem h7a. 1sc;oiv:stjw; zhb1 1ns9h/noiperature is 21 $^{\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 20 7+(dud3:ey )cm vfqvz$^{\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 tti9l: ,dua p1msv 7r8dhe hole be that must be uncovered to play D aba8 19dtmrli 7udv:,psove middle C at 294 Hz?    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 264 Hz, 440 Hz, and 616 H-ewwnv7d5qezp8 1+h nz, but not at any other frequencies in between. (a) Show why this is an opep15-nqw7z edehv8n+wn or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 mzl*.osek(1ry, x;yx r9 6kms i long is open at both ends. It resonates at two successive harmonics of s6er(;xkz,y1.o y9* lm xksri frequencies 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 c7 ,f smr rffoxnpc 6q i:3y+(/ebs++y$^{\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 a4 c sv :xzjnn3: ll1/n*lb0wlt(d5qn xre present within the audible range for a 2.14-m-long organ pipe at5ll xz/jl 04*bxncn3:1 ndn(lvq :swt 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxot8su hy0lawsy9dht( a: /,*uimately 2.5 cm long. It is open to the outside and is closed at the other end by the eardruso9(whlhtu:ya8 */ady, s0t um. Estimate the frequencies (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 every 2.0 s when 8c-gzen 7 m;cat-mwq- trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strin mz- qcte ;mgc-8a-7wng? ±    Hz

  What is the beat freq0yxomy5wy si2:/ ntk/ uency if middle C (262 Hz) 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 whistlb1h bw.uljn-n((udygw.b dyd.p 2q5)e operates at 23.5 kHz, while another (brand X) operates at an unknown 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.l( dg1..qd w-bn(hw. 2pjuynbd5yub )    kHz

  A guitar string produces 4 bea(x ;n1fzx (m;5ui 6jalkeqz9fts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuniek5nma (f(z; 6x iufj1lq9x;z ng fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu9w2s3hd7oag l-v l-qqned to the same frequency, 294 Hz. The tension in one string is then decreh wvl d-9la23oq s-gq7ased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plavn ipkpmp+1td( e653oy middle C (262 Hz), but one is at 5.0°C and15dkpetpov in 6(p3m+ the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forkp3 itn5,nja77ei ej *n 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 frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sound7i*nt3e7pjjna5e i n,ed together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands :ubw; xu28gf y3.00 m from one speaker and 3.50 m fruy ug ;8fxw2:bom 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 vibrating acb4-c1jmd(io t 132 Hz, but a piano tuner hears three beats every 2.0 s whe(1b4dcij -mcon they are played 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 wr2zim ,*:zfbeavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? b*2if,emr zz:(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f-gu9y.xgn kc: ire engine’s siren is 1550 Hz when at rest. Wugg-x:.ykcn 9hat frequency 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 do yox/1b e+i7zxwl)l nmgf )d9rb9hw i19w u detect if a fire engine whose siren emits at 1550 Hz mmzii+9b r1wh g)ned7lw 19/bwlxx f9)oves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftzt y pp;9xf643 gbtz3n in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you movin xp; n6zgzt433py 9btfg toward it at 15 m/s Are the two frequencies exactly 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 on8yl,,vpji cb) e is at rest and the other is moving toward the first at 15 m/s the dr)b,i jl,v c8pyiver 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 sound rh4e/kp zgg31waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is 4z1h/rgk3 e gpthe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As ittvq4mz 2 el;0+isq q iv7ulc35 flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What f2 qq3eilitl47 s vv;z5u +cm0qrequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doaj4sroo -xv:qm 54:x rppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tonm - q5rjro4s:v:xx4ao e while at rest in the railway 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 to measure blood-flow speeds. Supr1* )1xpdq 7s5 cns hndl71xxipose the devich*7ir ds15sx)1nxx7pdnq c1le emits sound at 3.5 MHz, and the speed of sound in human tissue 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 k7p i*r9) mwux+(tpj;tafc o+waves of frequency $2.25 \times10^{ 6}$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 oji 7oc;w: krjsigz;i:i-c,0 cf frequency 570 Hz. When the wind velocity is 12 m/s fri sic0jci,; :7z; gocr:ijk-w om the north, what frequency will observers 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 20 1 fjfs9,yoy2w 6cgrrf x;m i9 xwo)s+5$^{\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 Maxl p4m:. bt:dwch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpxlt 4d:p :mwb.lane’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 aau vbj(99- zoc planet where the speed of sound is only about -b cuzova(99j35 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. Determine the+/ pui6o2 tvyn+e-jua shock wave angle it produce ayjnto2 vp6/euu+-+is
(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 fj/1czvw)rt,n(dq;0gh- y rm$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flyidy t (3x(gac1yng faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 ka1(3cgdy(t xy m. See Fig. 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 devic(ez a97w us6j.ggeo0 ye that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed t6eu(7 ejg.ags0zw oy9o work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there l) cwj0.45yky)q s;fe m;up qkin the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called af9.orb 2 ,(w issa)efugvs(+z sewer pipe symphony. It consists of many plastic)2 ,zg(i(sssv9 .aro+bufe fw pipes of various lengths, 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 m from a peukao,v )n44vmy 6 zsz6rson makes a sound close to the threshold of human hearing (0 dB)sz6ony)zk6mu ,v4v a4 . What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when aqf bebxo+ 2oz* p-;dynah6a/k*,hj;w n 82-dB sound and an 87-dB sound are hearo;z6,+b xd;oyew**aaq phnk2 jfb-/hd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in +qkkv-3gp+ gn,ctr5z the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it + gk3+-tpn5vzr g ,kqcradiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ldy(s,spep tc/0- cw1bmmekyf(*e81 output drops by 10 dB at 15 kHz. What is the power output in wattsee-l/ep(d * 0 fctmw8bkpsyy,1c ms(1 at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devin8ds2 -rxk29rw6ea,zq 8i kprces over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, ni2kerrxp8s8 aq 9wzk r6d-2 ,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 distance of 30 m from a jet airplane engine?    W

  In audio and communications: 9,tiy:,7fj j bwurkg 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 ggf9dxmf) y87 frequency 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 wcz d nzkj)2efko8*:umd-c.g2ith a fundamental fr- : fzden2 *)odmg2 j.kc8cukzequency of 440 Hz and a mass per unit length 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 tube filled with wat,mx 9m7o 6znd7wwj9am er (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above 9m97j w7 am dnxwm,oz6the 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 strw1 lkb 1y +z9sh69gcgding of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the stry 1+swdkgb z9 gc9hl16ing if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to redl 4nxudz,vp (+ -aekzsc: mz4s +/xm-sonate as one 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 the 500–1000-Hz range coo,oqggml4ze)w*9sqf,v s55 n) kj*j j ming 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 j )w*ql*sf,o4z g g9sv5n)oj mqje5k,level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424- l djpd9:/c2xeHz whistles. One train is stationary. The conductor on the stationary traindcxdp2lje/ 9: hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you i)a1it,- kea 9(ggq 0ryiny(p+ 4ckqsv s 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume er+(9n ycka( qq)1agks 4,iyt0i-pvg constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening tc8ji /ij *kjn)dlafl.br93w pr79* mdo the difference in pitch of the9wj9*ncrl/pjii8 )d .3dmfj l r*7ka b engine noise between approaching and receding cars. 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, 8qaej3 ui4pjj;1-:/ k noluoy6r zx 8 5cc6srgproduce a beat frequency of 11 Hz. The shorter one isuja6o lc4py: g exk ;8jcszjo-6/rqu n3i r518 2.40 m long. How long is the other?    m

Two loudspeakers are at opposit;;2- rpixvkt te ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If ttkx-;;it vr2phe 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 him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 k2 jw;g4zr*vs m/s what beat frequency would you expect if 5.50-MHzkzwvg;r4*s j 2 ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed 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 towar74lnjon(r 6c)rfy l ov2af0 4rd 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 mot0lfo2c)6or(4rnrny v a7 jfl4h?    kHz

  A bat emits a series of high frequency sound pulses as it approac3rqc6o rn1/6 glgp4 uz oakcy-3x8 9jches a moth. The pulses are approximately 70.0 ms apcl9uxg6po648yj nr3ao1 qcrk3 c / -zgart, 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 to send signals from one Alpinenu /+0gj*d amy4 atue) 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 alpent/ *)0y+4mja ugduaen horn 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 tube.

  Room acoustics for stereo listening can be compromised by the presence fw 7lk)vvjgyja q,6+9of standing waves, which can cause acoustic “dead spots” at the locations of t)qjk9yf7 g a6l,jwvv+ he pressure nodes. 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 “s;,(iwif9. dfgesw lc3inging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rd(,w.gi93fl;csf e wiod is stroked with the other hand. With a little practice, the rod can be made 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 hearin1 h6aavopa x3da ,3kn(g for the human ear at a frequency of about 1000 Hz isa3(ak3xahnd, p6v1o a $I_0$ = $1 \times10^{12 } W / m^2$ 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 Machy 2;3g+myd6 tp0v) xearx+ephfr1;tb 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pl xfy++ptrpr2 ;10d m3)age bxy6ev;thane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15-9 emt zc rnyx;hmw74g-;4wfw $^{\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