What is the evidence that sound travels as a wav*0g8 v9yumr3n w cy q3dp6vq/he?

What is the evidence that sound is a form ofkjdsxq 7o+(1k-lrq - x energy?

Children sometimes play with a homemade “telephone” by attaching a string to thfqeke9rqmr *.ybm4 (9e bottoms of two paper cups. When the stringme k9*m4(9yb. frreqq is stretched and a child speaks into one cup, 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,+u oq lye/ w(7bew9*e5ml pja+ do you expect the frequency or wavelength topuyq/j9+emwlaw (+5bo7*e l e change?

What evidence can you give that the speed of :ar ,,j1lx3;t x dnau2qyqw)f sound in air does not depend significantlfx 3 :n2lq,q)da1;wt,auyjr xy on frequency?

The voice of a person who has inhaled helium sound/fi1o5 48 3iapcdsff is very high-pitched. Why?

How will the air tempe7f02suo2je r drature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplituh d*hc/u9d6gjbf h p2d42ofari-vg-l7)go o:de of sounds in various frequency ranges. (An exampg*ov h f7d dag o2b :j)of2rcu--hlgd 4h9i/6ple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sp2 *ezfiv u;a3daced closer together as you move up the fingerboard toward z;2ai3ve*u d fthe bridge?

A noisy truck approaches you from behind a building. Initially you hear it bhigb,mz.n/n t ln5509wamvf9 ut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the f0hnn5/bnt9zm,9.5 al vmgwihigh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wher uro;sgf9xk(/ eas beats can be fx/ k9o(grs u;said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frei fpav:ocnr8):b5yl 9 quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move :ip vra895ocl)bn:y ffarther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with v,l55p4+w0jw9 a v h3ccwempe9bj:awdery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a re dmp:l5c a b,3e+w9c45j9pj0 wwvhaewlatively 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. Eac5 :g 6mpbssad-9-/ ztu3k97 aucaz vzvh wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fm gzuz:tv 7baz /sau-va9k cp3-s569 dig. 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 move in the pmofe.to9;i w.) 6pw+tfhao5;r 7zdad )xgo5same direction, ta h. gfd i;xmd w6t)o9 oo;7w.p )fo5z+pa5erwith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sbj)efa yh:p j(y.mf 24 b1kz-iound heard by a person at rest with respect to the source? Is temzb 1jfjk.f4)2yp i-by a( h:he wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moni9mg+e+ds/y totor is blowing a whistle in front of the child on the ground. At which position, At9md++ s/o egy through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the9-x u 9pwo 0fuitl 7s15,ywone length of a lake by listening for the echo of her shout reflected by a cnptw0u ,yfo 1 seo9ul9xi 5w-7liff 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 thajzw j2*:d kj c6m;wy9e waterline. He hears the echo of the sound reflected from the ocean floor diry 26jwj*m cdawk:j z;9ectly 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng (1 q,;ihc:cgezak52 .:hhezbb 9nybwhvh5k -ths 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 of tuna on a foggy day. 9w 5 zuda6( 0xrk8xw-tvqgpu0 Without warning, an engine xp0w qkrud- z8w9x(0a5 tv g6ubackfire occurs on 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 top of a cliff. The splash it mayv kqzjgr 32q7a6c7o+kes when striking the water below is heard 3.5 s later. How higr+ j726vgo zk7 y3aqqch is the cliff?    m

  A person, with his ear to the ground8m:q 0sy1l3uj otnb)l(j3 k ly, sees a huge stone strike the concrete pavement. A moment later two sounds aljll1mq0yn ( k33b8oty su)j:re 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-secoaxxalkhka11/o6 cfs6o4e y3 6nd rule” f146akf/3 1x6aya k6loe x schoor 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 ;.xe yeyen8ahn/:h7. fsnl d(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 soundmcd4,azkvu6xhy 6 7ox)) s:i.hdenn2 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta4ir fmafke leh52.g88neously at a certain place, what will be the soundh4k f 858aeg.2lei mfr level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an;p xwfwq.c q u4un2b99 airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 9n .bq;4uq 9 w2upcwfx120 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 ratio of 58 dB qszq1gv96dztjwy2l425az r) , whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 5w46vaqr12z 5 l)29gz jzqtsyd8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a cqh1h 2w:emg bm, yv56person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniform2qhec 5m: 1,ywgvb6hm ly 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 strikes an(7kaj6:crf mqlx; wtxuqe *:( 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 *6dk+q6psepma++ds rmodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point d skr6m6+ p q++ades*p3.5 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 )/ 2yv14.3(kz x3zg hi kkise5qdl atlloudspeaisq d.k/ (zg35 i2z31 vyk)ellhk 4txaker 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 typically detect a d )n zdos;2t 1 /rw 7+l*brr.qhbq9p4wl+h oyjiifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hirrt+q ybq+*lhpn2w dojwrs iol/ 17b.9); hz4nt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave -.ktu h d;hly,is tripled, (a) by what factor will the intensity ih dylt;k, .-uhncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, g sv)zc .yyx8w:h7l4)gtv9hibut one has twice the frequency of the other. What is the ratiox8 49 hyy7vvw)gsl) hig. tcz: of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cohrde/s rjb66 2rresponds to a displacement a/ redbs66 jr2hmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what 0c0dsq zcnkshq0 5x+e 1f/6xasound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12– nx/10a0esc5skqhdxc+ z06 qf6.)    dB

What are the lowest and highest frequencies that an ear ca .vle+ 0a5h4mexp2* jsyq z9kcn detect when the sound level is 3es4+ez j 2*ymhavqk.5lcxp0 90 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rkx9;*kzyy kftz pkz*jm5* 19 sange of sound levels. What is the rati*59z * ;zjpktxy 9kfkmkz1ys *o of highest 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 fundamental frequd m9 50xassl7a2e gur2ency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wr9s d x2m a7ls025aeughat tension must the string be placed?    N

  An organ pipe is 112 cm long.qfsz5nbic+9 eq6b -j6 What are the fundamental and first three audible ovi5fzebb+-q s6 nqj c69ertones 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 m*k k-bc nmgs)ee;.5 oexpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assums.; k megkbe )-o5nc*med 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 hum t ; eauqek(l+/y7tsq6an hearing (20 Hz to 20 kHz), what would +s7 t ka/q( eqle;t6yube 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 itf62tphvwx 10 us third harmonic. What will be its fundamental frequency if it is01pf 26wt huvx fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar strizqp/(mqlhp i 8(z27od,qi m2kng is 0.73 m long and is tuned to play E above middle C (3z7q /i h8,qkz po22(mi mdq(lp30 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) /gyu.ij;sfgh ,,rl .q when the iq.fh /,,gr; . sgjluytemperature 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;u9q;oo lhcb8 :an. p+f6li mn $^{\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 the hole be tha,g ds wz6y*udy-1 +c(8liprk mt must be ukd ls+6yi8m yzw ,-u(rc gd1*pncovered 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 reyaux:w 9p/;pmsonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whyppxy9m/wa u:; 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 1.80 m lotd p7-zk14 kq:hyhq2 sng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz 4qzk-27phqd t1khy: sand 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 jmkm m0e3 gt,s3.mf (gr9tnn*43cn eu$^{\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 the audible range for a 2.14-m-long orgat, v)kmxlyr2 /n pipe at ry/tmv2 ,kx )l20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 m sx,ip:9s)+ 2 eazj n+y2p-f5voayvvcm long. It is open to the outside and is closed at the other end by the eardrum. 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 grasv+2f9, n2:s- axayepim )5o+yvvj zpph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryivw6kv,z p)c0rng to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other cz), w6kpvr0v string? ±    Hz

  What is the beat frequency if middle C (2 +cddt.ilc i9*62 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 /g6gze9kmtlz y;, h4 jX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but zel, g hz;96j/4kmgyta shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producq5dm /a0 u;jxfes 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the s5d ;fqj0 uaxm/tring? Explain your reasoning.    Hz

  Two violin strings are tuned to t5 :jm,rt1d +jayk3vw6l .gogwhe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11r:gaj+tw5gw yvd1 oljm3 . ,6k–13.]    Hz

  How many beats will be heard if two ident7m;ymegmorg .)cj ++n ical flutes each try to play middle C (262 Hz), but ej++mmm ry;o).gcn7 g one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqv tg8)nds.x4g-x tp7u uency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is x t8spv.u7tgn- xg)4dheard. 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 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 person6is3 n(4b xmh8vm 5icemk0x6 f stands 3.00 m from one speaker and 3.50 m from the othe i n5s3exm i8cb 0f6(vxmh6km4r.
(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 vibratih-h ostfyr.,.ng at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibra f.h,s.hy otr-ting 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 many be9626a ru8zqzdqkkgd :ats per second wi6:6zd qg9k raq2uz8dkll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fir jh1pnz.o t zm)+gj7;re engine’s siren is 1550 Hz when at rest. What frequorgz;pjn+. m t1hj 7)zency 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 if a fa.p .jhxc5 lugmm45d/qd2cq0dso//rire engine whose siren emits at 1550 Hz moves at a socd/sd 0.2x mmqh/d5jlp4rq /. a gcu5peed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source isdjad/m0 0 s: p*ou5wlu moving toward you at 15 m/s versus yoump 0u0j/ uwdal*5 ods: moving 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 8um*0 q3n+xj5gjeh jrsame single frequency horn. When one is at rest and the otherj jr5+8x jn0qmgh 3u*e is moving toward the first at 15 m/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 sound waves at 50.0 kHz and receives them zgzf;rd(f*d3 r)3vsw9 fs.w lreturned from an object movin;d lrf 9.fw dzssrg)3 *f3zvw(g directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speeh;x.s9x ig)a sd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqh9g.; )xa xissuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playa bv,2 vayi /z.ua-ohdt gdw)/.n*g- wed on a moving flat trai)h vzav.-2wg ab/wa. /dig, t-ny* odun car at a frequency of 75 Hz, and a second identical tuba played the same tone 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 zm59tr*boz. n 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 theo.nb r9 mzt*5z 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 frequencyl- cq*; l) z1o2-zpt d6deuo )smzyck4i1q(k e $2.25 \times10^{ 6}$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 ofivjbo,/ 301p 3lwdv wu frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers31ijvuo bv,wl3 /w pd0 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 jwm5 nd9df7(6bv boo-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:5 4zf1,iv7m+3 zbt gw 7jvazmm(cb tg 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave mak4b majgmg mtzv: +773tiz5wzv1cb (,fes 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 planet where the snyr/k-5g 4o lkpeed of sound is only abgn4 rk y/olk5-out 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-bq1epitp j75 c2n75tko vn6p the shock wave angle it produc tp inqpe 2nt15-5 opbj7c7kv6es
(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 nmz i 6ege(o:*i u+0nd$/theta$ 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 k xql. 9knbm9k3m above the ground flying faster than the speed of sound. By the time you hear the sonic boon3.kb9 xqm9lkm, the plane has traveled a horizontal distance of 2.0 km. 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 device t8ssqkv:-y fv 2hat 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 to work is 200 m, what is the minimum time between pulses (in fresh water)? v8sf 2vk: sq-y   s

  Approximately how many octaves are there in the human audible rasye 475e f2)jmhqw3f te (uka7nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consistspoiv r ky)dwd7b(h6.xlf,/,v of many plastic pipes of various lengths, which are open on both eh( d ,r o 7ldwfi.),6kbpxy/vvnds.
(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 nq5btkbc2 r6;68ev-se c3u*a s3 qytr a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 suct3trcq c-*k6qsy6;8r aev2bu 3 b5sne h mosquitoes?    dB

  What is the resultant souu-o 20z4x n vycvr(ar2nd level when an 82-dB sound and an 87-dB sound are heard sv4(z c02 avyurn2xor -imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1in)y. mm9m+inp;u8oap4wm p0 05 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equai;mop 0nni+8)p4a uy mmmp.w9lly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpu +9wyv6 +sgzbbqinq+01n . lnk09j e km*wfn0ht drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? 0smnbw9 +wyh +690fnkzngn* .e qqi+klv0j b1   dB

  Workers around jet aircraft typically wear protective devices ove--j wk kh pwefbuzba 489d67g)r 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 distanceb)jge pf awzw-8b-d96 7uk h4k of 30 m from a jet airplane engine?    W

  In audio and communications syste vyst tthc* 7:bjx7/j6ms, 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 tunedxf0x3 qvt+x f8 to a 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 vio4w2puy , k3imtlin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a masu,3 4ikw2pymts 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 intoy7mqo8s+ 6 rke vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed 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 qmks87r 6oe+y of the tuning fork?   Hz

  A 75-cm-long guitar stringo(-;0g oxtpz-kzgv l+ 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 string if it is to 0tvloz(o-x+;g k-zg p 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 loop4-)*bwxe cw)ziv0 hh/ycr,cg ($\frac{1}{2}\lambda$) 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 coming from two soua uk0dm 19*aft7x(hj kxhs37brces. 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 sakt30x b7( fjh7ukd 1ah*sxm9ound 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-Hz whistles. One train is stationary. The 8v3n.(qe ;wjy nuf)nc conductor on the stationary train hears a 3.0-Hzcne 3wqf.)n8; (yvjun beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a st0m84 *ycirpu 7bh l, a*lbwl6xeam train whistle as it approaches you is 538 Hz. After it passes you, its frequency x7bh*c*payu8b mll4w ,r6 li0 is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can(w5ay*k hvj :qg4.aqs estimate 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 ta qg *: 4jawyv(sh.q5khe straightaway. How fast is it going?    m/s

  Two open organ pipes, soundl9 e jzzkiic k3,:(1jm:dhh(au ;k5pying together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the ohi: dzy5zu(m1ak:j; l hk3k,je ci(9pther?    m

Two loudspeakers are at opposite ends of a railroad cc sxyglv/l*)w-h . u5rar as it moves past a stationary 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 th*csxu ylhvr-)5 .w gl/ey have passed him, at C?

  If the velocity of blood flow in the aorta gi u5 px74j3xff.g 8skis normally 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 3xjg .58ki ug7ps4fxf 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 toward the bs/f yo7 fnrmv.s5j d e-6fz6y8at at dysrmy5e6so jn z/ ff 6v.-f78speed 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it approao+-p n0 zft+owd8rd6bches 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 detected by the bat so that the echo from one chirp returns before the next chirp is b 08p-wofo++rt6 dd znemitted?    m

The “alpenhorn” (Fig. 12+ad n3mq0-rsr5ha ffw (fn , .nak;-pd–38) was once used to 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 flfhdnq 5dwfr.-m,(+n;-0a3pfan akr s at) 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 of stanv;3 gdy fg:nc,rn-ztj g2a1t4ding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m l, 4j12dtg vz:y-c3 nr gtngfa;ong, 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, slender alumin .23f dlj;w xj,kvzm*fum rod held in the hand near the rod’s midpoint. The rod is stroked with the othek j;*2dj fm3f wl.,vxzr 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 hearing for the human lsx z0s.-k oy9ear at a frequency of about 1000 Hz .lsx0 oz9sk- yis $I_0$ = $1 \times10^{12 } W / m^2$ 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 2d0- wf3+ lx1t.h+ l69pjiebjf kmbwx5.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’+jdw bfltbfipxw6x+kj.-59 130 el hms altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ipi u(hi/ 9ci;ns 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