What is the evidence that+kovzxn m. *,d 5aicj8 sound travels as a wave?

What is the evidence that sound is a fo c3k kzd5 a.j;7ylx pgu;-4nk ig5riz7rm of energy?

Children sometimes play with a homemade “telp1 v hjcj1(n*2-x uz bvukwm5:ephone” by attaching a string to the bottoms of two paper cups. When the string xz51- ku2ujc(:whjb n*1pv v mis 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, do you expect the fre* pqi3k nmq3kfv(b,5kquency or wavelengt3qpkfmknb 3vq ,i(5k *h to change?

What evidence can you give that the speed of sound in m2e,lgwwkpc8:t1 oq c(4 v i0cair does not depend significantly on 8, kowl:ec m c04tqpv i2w(1cgfrequency?

The voice of a person who has il uu )/j;o+s eh2 zdo,alf l3hl*ae-2tnhaled helium sounds very high-pitched. Why?

How will the air temperaturemzwlt zf obmc4q )0q o hedjlg:il+f7 81*/4)s in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter tn p, ckgub9b56o reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflerbug5c,k6pnb9 .)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo1sy4k klk0-fsl-mv5 u u move up --0kymslfkl5s4uv 1kthe fingerboard toward the bridge?

A noisy truck approaches you from behind a o.30ousbyd 6ncun(pqk4- 0sx building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “bqo.u0(s43nsko dybpnc 6-0x urighter” — 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 in space,”mm *aaq t9tdqt2k,)3z whereas beats can be said to be due to “interference i 3,tm9qq mazt k)dt*2an time.” Explain.

In Fig. 12–16, if the frequency ofz g(p-pn g ,z(fdn.9p)k+hawf the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fawn(f) h+ z-apd(.gp9p,z gnkfrther apart or closer together?

Traditional methods of protecting the hearing of people sk5vhvk g1z:p*mnj;* u9s/l vwho work in areas with very high noise lv9*ngm* s1j/skvp ulk:z5; vhevels 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 the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–3 )fp67a +ky)0b abrfqt1. 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, (fpaqyb)br+fak7 6 )t0 a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the z9d /okb+,ttg3d b+o* sm.rap source and observer move in the same direction, withd/+pdt r.t b9 b+zgam,3o*oks the same velocity? Explain.

If a wind is blowing, will this alteo9cuxe d xhsy ,1vw5+8r the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength oh xeoc1x8, 95wu+y dsvr velocity changed?

Figure 12–32 shows various positions of a child in motion on a swix, +bbc6l k p).jblj.sng. 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 the whist,bj .l+ ks.b6c)pjxlble? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echosq75z7xs8g 4 xzo eq0v of her shout reflected by a cliff s q78oxs7v ez50gq4 xzat the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the ecusl*u 74rf86px6 r5w8jzh bdmho of the sound reflected from the ocean floor directly below 28s7 jm56p wbzhd48lu6r*frx u.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 wavelengths in air at 2sajj .y; 7dtw lct,w(n.c v/s20 $^{\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. Wi;r.st55lrdjob j2o 16 3nu mqnto y)8athout warning, an engine backfire occurs o8ryjtqumo25135n. b dj6tlr ) oao;snn 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 saim )tz s: mjm)mk;,:upf1,z it makes when striking the water below is hemm:zm;,1 mkf)zautjs s,) ip: ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gro 1ay bfq (0+xfpiu mck6yzj466und, sees 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 concretef qk 6+xyzuy 6b(p416jm0cf ai, 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 dis)ck6 p1u/ a liql6m9)7vp irvttance by the “5-second rule” for estimating the m976t/aipvk 1qlir )v)u pl6c distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levearj it8 utrr92cnf1b* kzqk8 wr9*,w*q- 3prel 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 intenw1kcgc:nf8n (+u)e vgsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firexi61-fe/x6pce uzoa tksr6b5 r820a d nc4+e ad simultaneously at a certain place, 5z8ro6xx+b6s a -pknc 0 tciu2a/6ad4eefr1ewhat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance p7;-okht cin3(p6mww8p (r qa1 ic2ie from an airplane with four equally noisy jet engines is exper8o6(-k;p12 ihiri3wa(cct pm pnw qe7iencing 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 signaw,k,a4 3qgxual-to-noise ratio of 58 dB, 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? ,q3au4xkwag, 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakingv) il.j9e1we u in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centere)i v u9ewe.1ljd 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 anti)a58/c9rbbx o k3w z 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 modest e f1a uuzh492xamplifier B is rated at 40 W. (a) Estimate tu zah249 uf1xehe sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in frono7s)2dt49 v0 tnun:t8ffaq hrt of a l) 4untt8d7 :2rn0qtof afsv h9oudspeaker 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 diffryi 0 4-dvvg jst;9fw.erence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–yvv;f 9w d04-irsg tj.9.]$\approx$   

  If the amplitude of a sound wa4 s:;jfai x,j fmeq5wr08gg ;eve is tripled, (a) by what factor will the intensitiwj4fxfq ;r5;, e0m: sa8 ejggy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amp1azbrae;qxt2h( 5 g z(litudes, but one has twice the frequency of the other. What is the ratio of their intensities? (xqz2g1 aaze5 rt;b(h  

  What would be the sound level (in dB) of a sound wave in air that /t5 xad;g (dpxcorresponds to a displacement amplitude of vibrating air molecules oft/dg(x;5 apx d 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as-b,6bbn dfp lt5 8x6 knj7grj+ a 100-Hz tone that has a 50-dB sound leve8r+bk65n pbljjfgxdb,76t-n l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear nki( -1)cszwkcan detect when the sound level is 30 dsc(kw)kni- 1zB? (See Fig. 12–6.)

  Your auditory system can .c /ms+kt lvq nykoe2r 5t469faccommodate a huge range of sound levels. What is the ratio of highest to lowest inten6kyn42rl qvcstote9k/fm 5+. sity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440x r b21 mcahgx,/6ja7pimwo/8 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Un axxmiphow7c/ aj, mrb62/8g1 der what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firv2zs+lj/. i : hx2z/u-qpndwust three audible overtones if the pipe is hjsd.l/zz:/2qxp2u+uvi - wn
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of ad/tbywesx* 9*oid,:jn empty soda bottle that is 18 cm deep, if you assumed its:by9edxdwtj*, */ i o was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build b5. tfmhr.f2.. h l)jljuz xz /+snw(va pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range..zux.nhblw/r)fvs(ml+.5fzh t2 jj 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 hx4g* wv yi3xf-zde5 cz;7 5zxparmonic. What will be its fundamental frequency if it 4xx*vzpgf5 -zcze ixy5w7;d 3is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playec3c*;b vyzkq/: hi s) E above middle C (he k) zv3/y:q bccs;i*330 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 ofmombx))tq686p:u ue q an open organ pipe that emits middle C (262 Hz) when the temperature x6 )q8mtebu:uopm6)qis 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 2z t 9./m0i98qc-rzwjhpxxv mxed/* .x0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouth/lte-*f z dxd-3 puvy,piece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hzp /vytel-*xfd u3d-,z?    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 Hzygk*g7yrt vpk (sd:7b-7qsv2 , 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cykgv7qtd-y72k*gs p 7 bs(:vrlosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80+ku8ju0mjpr z e 7*tfyyps:02y 8q a)e m long is open at both ends. It resonates at two successive harmonics of frequencies 2* 0zaytjpus ke fp0mq :78e)u2jy 8y+r75 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 l ptq ll0 k*8j/lm*u.m$^{\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 tprfjn,4lg 49phe audible range for a 2.14-m-long organ pipfr npg,lpj44 9e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately,uy vk/ /atv. yla.-vrabq 92-uky-bs 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the freql . ky2v/ -v -a,/baaqu-bkvu.st9ryyuencies (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 2.7(2 ppwyprrc- 0 s when trying to adjust two strings, one of which is sounding 440 Hz. How f rwp( p-ryp2c7ar off in frequency is the other string? ±    Hz

  What is the beat frequency if mi) wrbtj3mj/jwh5c )e+ ddle 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 whistle operates at 23.5 kHz, while another (brand X) opegj/l 42:odqh .tnrp66-xib 9+hjk sitrates at an unknown frequency.rbs h2 6t4 njq+xjti9pd oglih/k-6:. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunin(a/5-deecy n zg fork and 9 beats/s when sounded with a 355-Hz tuning for-y /d5ec (znaek. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hjn *qkir1/o7fi ,6qyvz. The tension in one st6nq iq1 k y/v7ojfri*,ring is then decreased 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 py g1r,z.y kf8a(9rp 2fs+hq5bq p swn-lay middle C (262 Hz), but one is at 5.0°yhp5sq,p (1qaw r fbfk8r ynz+g-9s2. C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and3 8*vgsv4opyg C. Fork B has a frequency of 441 Hz; when A and B are sounded ts3vo*48v gpgyogether, 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 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 s*:bsw5 titfv 19k8x w3.00 m from one speaker and 3.50 m from the oktxf i*v8 s1ts:9w w5bther.
(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 pian,ht*r;ndzj1jdq.nzeuvc:7g2 /qmu .o 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 gn mzd/7ur.j;u 1 eq,tcq v*j2.nd:zh 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 waveleb8vyytiq+v +*jl j:4xngths 2.64 m and 2.76 m in air. How many beats per second will be4v*+bjy xl:yj 8 i+qvt heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155y z n- km ubu 3eh6w1bx(npoh1s;q1k0(0 Hz when at rest. What frequency dob 6z( hswm;0k1hqp3e 1(onukn xbu1y- 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 frequeu22iazvs e t i*:ck2lcf bimg,14q53yncy do you detect if a fire engine whose siren emits at i,2 :tcq5cu fe yb3smz 2ivg*2il 1a4k1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fr;jit3k79dcz p6d ym9v equency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the samejkti6 m79d 3cpyd9v ;z? 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 equip+pvhr01p1lzy g*+zmu z9 . qurped with the same single frequency horn. When one is at rest and the other is moving toward the first atr uhrplq1y1m+g 0*pzvz+z9u. 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 gi bn;l w7 q/w8.ul6dswaves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received soun. qwl8id;wu nl7/gs6bd frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the; li28hj,:gvc3gwj b w bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in tgbjvc,3;w glw8i: j2hhe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experime *xq8ijzu1pl2rajg 7 :nts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if t jzqa7r u8 i*:pl1jgx2he train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usew *jzcfm3 h:j+a(r; igs ultrasound waves to 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 blood * jga( zchi3wjfr;:m+is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasp dt2y 1kafm0,onic 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 s.f xce 3*es1dlound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at ree fd exsc31.l*st,
(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 7li 0u7l7aknsits 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 (a) What is /24zx g .;i9ikqosu(sc re3j hthe angle the shock wave makes with thorh i2 guk(x3sj i;s4z9cq/.e e 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*w (gfp a)ie9v the thin atmosphere of a planet where the speed of sound is only about 35 ef)( v*ga9iw pm/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. Determinkg mpl-kf8nd**+ * sose the shock wave angle it produdfknk* slgom8* *+s -pces
(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 9:j+lda 2+zs3pohg he$/theta$ 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 gsw 3yb3i5 f dr1io51hflying faster than the speed of sound. By the ti5ri13w1gyd 3b hsof 5ime you hear the sonic boom, 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 that sends 20,000-Hz spvs m9:tp idno 0+5u*qound pulses downward from the bpdt+5 smquiv9 n:*p o0ottom 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)?    s

  Approximately how many octaves are there in the human audible raqt .mvtt:f;m/nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has;ag z5rwvw z7+a m9bj; a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends95rw w;a+z7;jvgbz ma.
(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 frn7wlm:kjb/ .u)h 5sekom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sol57)ksknh.u: j/e mbw und level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8.vxw1k,(3df fg j4axf 2-dB sound and an 87-dB sound are hea vdgk .,fxwx3ff1 ja(4rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in tj oktf)-y bra8r*z;.wxcueqo+-wr 9p 177paihe open, is 105 dB. What is the acoustic power outpuz u -8kop7qep;c)o t-fw 7y .r1+ra9ajri*xwbt (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tj 9b91w.jzohshe power output drops by 10 dB at 15 kHz. What is thhs.zwb jo9j 19e power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices o z hg2dqx;y;0sver 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;dq2zsgy;xh 0 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 systems, th )*lv po9 ch)gzk 4gtkyfsjfpe/v/6*2e 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 frb 9.o4z gvsh,kequency 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 pziv6-6vwc) oh,-a mx yoints with a fundamental frequency of zx)- cyo-vivm66ah , w440 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 vertice1st )0lhis3 pal 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 frequeneh13tpsl)0s i cy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one eg/9 dv srkubr.l83z m7 1e,pexnd and also 75 cm long. How much tension shu1 8 . re37zvks9mbedg/pl x,rould be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obser3i 9x 30k yjow box4t0ozdpw37ved to resonate 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-Hw +d +legg5.qod:h1dxz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?x1.5de dgo ++g: qwdlh   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on th);d x9dfe18 kj fun(ite stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the8 9(ex1ti jkudn)f;df moving train?   m/s

  The frequency of a steam train whistle as itqjd ;n7 jmqpw6(-w:q7qsd3pw :dg no1 approaches you is 538 Hz. After it passes you, its frequency nndqw(d 7q36qod-j q1wgsmp pj7 :;: wis measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening t;w89mq 8 jxaezo 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 the9q; meawz8j8x straightaway. How fast is it going?    m/s

  Two open organ pipes, sou60zkc*v/ m )nycmn1q ending together, produce a beat frequency of 11 Hz. The shorter )y1n*qc v 0czk6mnme/one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a fnrmsq:9g w,l1whp g40q sn.6railroad car 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 frequ:qg fwmngnh61r9l .w,sqs 04pency 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 blgdx60dwut3u)q 6 yp3zt( yd j4ood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dire0(dwtx 3 ju3dg)pz ty 6y64udqcted 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 toward hlyg;nnnq4 9bbvwz;m p36x1 5the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detect6vlwgy45;q3xnhz 9m1n pb bn;ed by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of rubd.,jwtkf) 8u 06ve high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moj k)u.t ,0 u8vd6rebfwth 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 Alpine 8yx xm5k5,ec5lr n+ (un4bwir + a7gqjvillage to another. Since lower frequency sounds are less +bua xwy nlmk55 q5c7 ,x r+8i4j(erngsusceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence alrq* at+ w;v6of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m lal ; qv*+awrt6ong, 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,” involi 6twgez8/ eexhv/0+ vves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otheze0ev/he gvw/x8+i6t r 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 earv rl:n-+6taytr in.9x at a frequency of about 1+n6ryrtx9t:vl nai - .000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bobsr9hx.: mg, ;no dm 622ozqyqom 1.5 min after the plane passes directly overheadr, qobsqz6m9xg;d: y 2h onm.2. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo2-g v.fqr 9xmeat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h