What is the evidence that 6hiz.hzjeebm+(k f ray 2;+j78 zngb(sound travels as a wave?

What is the evidence that sound 3 u.26q2f)x xjlacvpv is a form of energy?

Children sometimes play with a homemade “telephone” by attacc2j)nb9;9e)7n (vg mhoajac*x i zbu 3qfgw4 2hing 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). Explaingjmq4nxzu)g*a nb(3jic 72)c9fhaeb2w vo;9 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 frfp+x;l u +a (d4 c:ov 4t:pi(evj251p rzlpgrnequency or wavel5:+:tpfvr+a2 cl z4n1 prp4evlo; (d(xpjg ui ength to change?

What evidence can you give that the speed of sound in air dyad f lwbm x2h52)9py1c*rdr6 oes not depend significantly on fre d1f2awr)6yy9b h 5cml*xr dp2quency?

The voice of a person who has inhaled helium sounds very high-pitchef /uqpcd/,7jwp mrb2-d. Why?

How will the air temperature in a room affect the pitch of organ pip.* r 8yp(rt;htbchhd 5es?

Explain how a tube might be used as a filter to reduce the ampu/(o7s eb7x ; sqx2 ;xolrb3jplitude of sounds in various frequency ranges. (An example is a car mufflee(xl3ojpu;x2 b/ s 7s7;oxbqrr.)

Why are the frets on a guitar (Fig. 1yr 6l+,ux5o8x y n:eia1 y)off2–30) spaced closer together as you move up the fingerboard tfor)+y,nx x:l81 efyy6 i5auooward the bridge?

A noisy truck approaches you from behind a building. Initially you hear ivxjsa .ery*-1 t 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 11–15 on dje -avr*1y x.siffraction.]

Standing waves can be said to be due to “interfh;bv)kje ri+ *erence in space,” whereas beats can be said to be berjv;+k* i)hdue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spkg d71os(p2)/qgq li feakers were lowered, would the points D and C (where destructive and constructivfgki1do 2g (s)7ql/qpe interference occur) move farther apart or closer together?

Traditional methods of protecting c9vnw: f rj+az.kdc7f+,.s; xvkml f) the 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 electronicallym)sw af..; n,+:kldzvj rx9f fc7cvk+, 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. Each wave can be thought v zn:cl(92zgydr5w4h 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), 4:n9zgvrh w2 zd5cyl( are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directio8fad ,y;hh 4q /*q1juj ixfc2gn, with the same velocity? Explaijqhg4i /fjq ;cfd18x ah,y*2u n.

If a wind is blowing, will this alter the frequency of the soup , j,h9ol5viwb+fbi o)eh ;4cnd heard by a person at rest w+i ,o5chepi)fhv ;obl9 4 bjw,ith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mos 3qpt-6+ap1gbebl -ation on a swing. A monitor is blowing a 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 3tpbal-s+g61 - ba qepthe whistle? Explain your reasoning.

  A hiker determines the lengfk)-s 2 emm8 ae-p1bo:t6o np adc0o3fth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echokd8 ot 2a0:)fofnc6abm1m-- seepp3o 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 waterline. )odlrh5b bajn.t. 6k :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 kdrh.baon6 tj b)l.:5sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air 9kp9 ivng- ;3 nfe;r8jf5ssua 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 foggyni 4 *qa(1jul k)kuu-z day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How m 1 nkz quuajlu)i4*k-(uch time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top oaoo1af*4 m n p.0: ut8ckme7dpf a cliff. The splash it makes when striking the water below is heard 3.5 s later. 7mot a :8ec1npofda 0p mk*u4.How high is the cliff?    m

  A person, with his ear to the ground, sees a hu1irvx-b4z*u2uf t(9xxbhfyn e, c.1 qge 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 1.1 s apart. How far away did the impact occur? See Table ucy* u9ztx 4 fh(.ivn- xbf,1r2e1qxb12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one k;fr 3d(k;wwumbv;/ge ,cow8n,jw g 8mile of distance by the “5-second rule” for estimating the distance,dcw w f(8bw;jk;/ ;wnrv 8gg3ku,oem from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ar )nob- be-enpsj :m; 6amd**v sound 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 isf0hob789h4kxci u +:vx8 w*-g9yji7rmumxey $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta5drfiwy2od l -lj*:dpbz:wy 4:j zq/-neously at a certain pid fdlrql2y4- w:wz*5d:p/zbj oyj:-lace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance froc n7ts-vxoz e:;yo76v k7 nluu.ka t-9m an airplane with four equally noisy jet engines is exptan6n lk-9;oytusezvocv xk.7 u:-77eriencing a sound 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 rqco4bwsd+49:fb zy fk6zoy 0*a. 1; xd,fdp yhatio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal andwofyx; z kqad9 1zo y06sfpbd4,+yc:4hdbf. * 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 convx6vcw.fvr*r y6 2v 0lqersation. Use Table 1262xr. vwyfl *v 6rvqc0–2. Assume the sound spreads roughly uniformly 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 strik ps c+bz4n1)5f(6pemo /yqvdwes 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, wc5 uvb5;a(zuit .ebui6 4lsz if:0se0 hile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poiucu i0b uzztevis :sf;45b6 a5(0eli.nt 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 ngi4, m- ,dphp2.8 m in front of a loudspeaker on the sp4pim,g , -hdntage.
(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 difference in sound level of 2.0 dBord :dw3h,j5+4m-nnrsw) io v. What is the ratio of the r) doj nwws v,r4+m 3-ni:5ohdamplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trmp/b *8lk3ztm) cee /qipled, (a) by what factor will the intensityepqm/bze *t 8lm)kc/3 increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one h 627v4d f7zsb ( zkfn.(2kpcpoqb4 gpeas twice the frequency of the other. What is 6znp. bkdvkp s2g( of7cbfe2z(44p7qthe ratio of their intensities?   

  What would be the sound level (in dBt -; waw5 6kw7xpyvce(; hqi2be8e+jr) of a sound wave in air that corresponds to a displacement amphe6( wr; etq5j;+pbx ivy8c wake2-w7litude 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-Hz to5pi j;gqeug3xvi 983 p0pep2 n51nzgm ne that has a 50-dB soun3pj; gex50 pm 5zq1pi ei nv3p9u8g2ngd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencie *(9tsc;bduvbulyr5*/rhh c;s that an ear can detect when the sound level is 30 dB? (See Fig. h;b*hvs ru;(bctrdc9*/lu y5 12–6.)

  Your auditory system can accommodate a huge range of sound levelfkxab: u1,yty(1 s 0its. What is the ratio of highest to lowesybst1:x(af, 0uk i1 tyt intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin h;p9l m/-/6:oeyk .adk)clgt qb qt8d kas a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and ic/ep/)gta .kk8mt- qy:9dbkl 6dq o;lt has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental andoefr-t5w(n4 7o x.r*jjx w be, first three audible overtones if the pipe is n. w4j(5oewx7orftre, *j-bx
(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 exiimb 0mnh /0-ypect from blowing across the top of an empty soda bottle that is 18 cm deep, mbhm i0n/0y-i 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 a pipe organ with open-tube pipes spanning the range of h2;z bs,wmgf2zdbot/ 3uman hearing (20 Hz to 20 kHz), what would be the rang;g z btoz2mws3 2/bdf,e 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 harmonic. W/a1wjra+p2/b hczs4t hat will be its fundamental frequency if it is fingered at a length of only 60%wz cbtr/jh24/psa+1a of its original length?   Hz

  An unfingered guitar string is 0.73 m lo9lq g2k0 2ergl lkcoy). o/vb,ng and is tuned to play E above middle C (330 k9 0)oe.glq ly,/ og2b2kc rlvHz).
(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 thaky ne(ub-z-i .z uvu js2.79gq+gcab+t emits middle C (262 Hz) when tczg9u.u7 +-2. vjq euyk z s+(abnib-ghe temperature 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 y :vn4* hov8p *hyq1sk$^{\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 mm- bc wf x:+)x,xrn,n5r)kt t12–10 should the hole be that kttbwxfc)xx) :-+r ,r 5,mmnn must be uncovered to play D above 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 61z nvdl+sr4ol p:al res6uz/n6/ hqj* 6m83l/a6 Hz, but not at any other frequencies in between. (a) Show why this is an open oqe*zl43jrsd zln6 rpa/6n/6v:ah mu l lso8 +/r a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tt gqad,)ffr/u45 m /qpo4 ,nspwo successive harmonics of frequencies 275 Hz and 330 Hz. What is tag nrfp5 p,/sd /fq)4qo,um4
(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 :x9t9 h5h .g.i+y-kmrgdcmv kkqam,:$^{\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 thewrxmwp a 0f88-6m6off audible range for a 2.14-m-long organ pipewm8p6fof8 6wx-rfam 0 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the1r)ut mp91 rf8z+bd hun3ng)r outside and is closed at the other end by the eardrum. Estimate the frequencies (in gn9u)hntmu bf)1r rr 13z+d p8the 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 v1jzg3l+t pe(trying to adjust two strings, one of which is sounding 440 Hz.3(ezjv1+p g lt How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (*8d-ohv ,umki( amvm-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 whistle operates at 23.5 kHz, while another (brand X) operates a 0ld3 at;0 j(3xcv s-da3cspoat an unknown frequency. If neither whistle can be heard by humans when played separately, but a0s;at c33s 0djv(da3 l-xo cpa 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 a- wqb kkvmmy.wt(3;2c 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequemv c3by q;-.mw( tk2wkncy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in x/ metb/o all2h z-h09one string is then decreased by 2.0%. Whaoahm 9llht 0-/2e bzx/t 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 ident.gsw(ex lar0g.: n8z rical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at a:r x.nglgrw 8s.z0(e25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fod-4sp *nc at:99gp x( sty(jvhrks, A, B, and C. Fork 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 C49x(*pdva tpgtjc(h-n:s s9 y 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 apart. A person stands 3.00 m from one speavoxvc(0kikir 75f4y 1 ker and 3.50 r(iv71vf4k5 ocki0xym from 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 at 132 Hz, but a pl;d8yaw 9j:u)) lv3nb4:gfp nex(t kf iano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of t3wfvxflbt( 8 9 euj) :ya);pldn4kn g:he 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 wavellj:e k calqws/;y 68p;ji8g3fengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 8wjp;6eq:3 k;aif j8/c lgsyl$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1gwh 0,4.s trzw.mglrl:.o: eh550 Hz when at rest. What freq.r.0lgw o:eh w z.mtl4:, srhguency 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 you detect c0-jj fm xyw*.if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/sj0.f cyx*m w-j
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towa h eefw7)dll1n1: mgr- tsk-.erd you at 15 m/s versus you moving toward it at 15 m/s Are the esfn ehg-l7m-t :.dw rle )1k1two 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 witle) vd mleb8ixyo8(/;3d3 abq h the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz d e33qbi(y)/x8;o mleald 8bv. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waemvig,5b ujf 0hy) ;,qves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequen;umfv5,)hqyi g, 0ej bcy?    $ \times10^{ 4}$ Hz

  A bat flies toward a :c07xg5 i69kczkfpj tc( jr/bybm4v 0wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.v b0y6ki:t70mpk9j rc g4 cjzxcb/f(50 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat2sqzlf mz),k 1y j3:ng train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway statioyz qsj 1,)z3kg2:lm nfn. 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 to7zhcfl; wsc r7tm9,0y measure blood-flow speeds. Suppose the device 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 bloodl m9sw7hz; cty07 fr,c is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultpuc8 m/pk.mmzzm12 l 5rasonic 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 of frequency 570 Hz. When the wind velocity is 12.ulll9 4puz59.kmhek*ak0ekj,io u/ m/s from the north, what frequency wil zl0io.4 jh9 m5lup/9eulu.ek,akkk*l 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 movisfu9f/sw/ pc 3jq0)esfn68p l ng on land if its speed at 20 $^{\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 speed of sound is 310 m/s (ajsr+/w3 d dm7bkyh4s*) What is the angle th ymb3 7*/d+ rdhwss4jke shock wave makes with the direction 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 play7 u y08 tr6c*mrhhm8hbzaj*/)2 gx6yrbiw 3jnet where the speed of sound is oy 7h*m*6 /2 hi6jz trhabywb8ru8)0jrcxy3mg nly about 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. Determine thezv2hztt3u-;h 3v:zxmjo. 6 aa shock wave angle i:xmh z ajuz vo32t;z.6t -a3hvt 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 o(uj8cmb 8:f(q:qokpyck (-thfh ;k/$/theta$ 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 exjw h*wb n+v px3lu77e(actly 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 p+7*hbjvx (3 w7wenlu. 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 xo bct;j.w1 5;rk+hdh sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxhhw.; x5cb; 1+jdrkotimum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how man7c3sb i /9h75cfuufuwy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p g8 lsrkx(f *n4iyols)x+l 0,cipe symphony. It consists of many plastic pipes of various leil nsol(+r *x) y,fclsk 8g40xngths, 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 fy,ant/ren85uv pa 6u6 c8d yi6rom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoese/ p 86nutai6r5,acvd6n u8yy?    dB

  What is the resultant sound level when an 82-dB sound and an 87xtp k83- m.s,b:(0alng s jjwv-dB sound are heard simvwx.- :ssmgj(k n ,ltj8ab03p ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.:a5g8kaca (li What is the acoustic power output (W) of the speaker, assuming g5 c:a l8kia(ait radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pdf. 64 zv3sgioapl.z1ower output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHgp1ozvi. 36dfl 4za.sz?    dB

  Workers around jet aircraft typically wear protective devi 1jtlt8,jz /hfs: d 5sk;ql/pyces over their ears. Assume that the sound level of a jet airplane engine, at a distance jtfh5dp/zls kys1;, jl t:/8qof 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 distance of 30 m from a jet airplane engine?    W

  In audio and communications syste(f ixoem:y p4q7v3 jd)vd 4d;af3x8kbms, 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 fre+he+/ sb 52 7zaxc4qt3hmuucy quency 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 beahu5dw8zt cy *50h16-p esblxtween fixed points with a fundamental frequency*xlzw0d b 1atsyc5eh 6p58u-h 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 watemvzlp ok3y 0:mmb3f/ 5r (Fig. 12–35). The water level is allowed to drop slowly. As vmkb mlf:yo0 53mz/ 3pit 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 aseskgw 8x2v3bmq otl,+5kifvc+eyv6s 7 )d8; tube that is open at one end and also 75 cm long. How much tension should be in the string if it iw 5d,mxoyc78 tsf+6v;v gveb3eksl+s8 iq2k)s to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full 9gxb jhik65 *rloop ($\frac{1}{2}\lambda$) 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 tonectx;*rh rh5,c in the 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 le 5ch*ctx, ;hrrvel 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-Hz whistles. One train is stationary. The condo0 c(t ppdxf9w:9zhk0uctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traio 9p0:d0hzw9cpx(kft n?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After itm4rfu8k 9 p(hf passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? kh( u8m9prf4f   m/s

  At a race track, you can estimaeqb 8g -c90+ i2kqjksrte the speed of cars just by listening to the difference in pitch of the 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 go gj k0iqqr2-s+bce8k9ing?    m/s

  Two open organ pipes,h omfnhp i km7/.6/h5zgfu; )q sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long iq/5 nfh/koh) gmpz6;u mh7.ifs the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves po*pu 8-pmj) g(/ htkp 1kfnf3hast a stationary observer at 10 m/s as shown in Fig. 12–37. If tthkf) pgo(ku8/p1fnpj- 3 m*hhe 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 no .ac4w/e:fmoiegii:3 rmally 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 i4m:/og3caf.iw ei:e 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,gi ,)fm .v z4i(y3ogkcba w0i/s while the moth is flying toward the bat at speed 53vcwibk),g.f, mgy(i i ao4z0 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it approavvlo /a/95axb b*e/jugo d(t0ut:-lc ches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be d5-/tl(cxuval ou j/ve 9/t oadg0b*:betected 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 v)nk u :en/zmq1-y(:+wvibn pcz; / 7(fdhahtsend signals from one Alpine village to another. Since lower frequency sounds are less susceptible to i: n/bvn(f-(m 1+thzaicuwvh pez)y 7q/n:kd;ntensity 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 tube.

  Room acoustics for stereo listening can be compromised by the pres euk h5 a.4,gfs7: qpxb8o9uojence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m ,okbu:.9g apx4j8q7fohs 5ue 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 a long, sl74 i3kkze; :.j 6o8kuapro swtender 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 made to “sing,” or emit a clear, loud, ringiwpkt7 eo6z .isro8:;4ja3 kk ung 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 at a frequency of j s;8v teq .xha4aw)t8abouq8a 8swj h)a;te xv.4tt 1000 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 observ8tvjqsk l/0pg.z(( /-8 4mrfzcbffrber on the ground hears the sonic boom 1.5 min after the plane passes directly overhe sbz0f(ctqf/pz l 8k/gmfrjvb84. r(-ad. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iszdt6h 5 mv 8uvjs2.iwbil:i 80 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