What is the evidence that sound travels as age9,h0e sy b seo+)f 6q+veyh5 wave?

What is the evidence that sound is 1 (;ph:7w mimlcglx4d a form of energy?

Children sometimes play with a homemade “telephone” b4(poi m p, 3;zzgkangq0zjvba d +tbx2o4d8*,y attaching a string to the bottoms of two paper codz n0k3vgixt+(j b,z* aom ppaz,42bd 4g8q;ups. When the string 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, do you expect the frequency or wa7 4vtlxeuzhk06be12 eveleeu le0 vxztkeh71b264ngth to change?

What evidence can you give that the spw:lid*b l1k * c;s-ulteed of sound in air does not depend significansi*;- ubdw:1 c ll*ltktly on frequency?

The voice of a person who h:f1 yztqri0+ oas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ asq/vyhp cnso,sxn 7u uk;.l2jqo.b-n2 *;7 h pipes?

Explain how a tube might be used as a filter to reduc z)vxlw,t-n d46br2j ae the amplitude of sounds in variwt6z lxv)4d b2 an,-jrous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitarv;r6af 8spl; r8+oso( ne :yqee- mbq+ (Fig. 12–30) spaced closer together as you move up the fingerboard toward the 6arqf-;opm:snevy 8(oq+bs+8 re; le bridge?

A noisy truck approaches you from behind a building. Initially you hear wub70-h4f bj wit but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — 40f b-wu 7bjhwyou hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due-khjri. 9s;uwsiv1/mw 6 i8tm to “interference in space,” whereas beats can be said to be due to “interference in ti 69hwwrs-k/uim8ijv.s;m ti1me.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points a s)w)7 nyb.-c c6pgjvD and C (where destructive and constructive interference occur) move farther apart or closp)6vg n-7.sjybcwc )aer together?

Traditional methods of protecting the hearw.j bn*en+ gg;8n hxm4ing 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 e8g+ h4gew ;jnb.mnnx*lectronically, 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 wave x)mlotd73sy1*o7, dmfstq5 e6 mlrq1s shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightlo131dtlfqm) msr6 7 o*stedq7 x5,ml yy different frequencies, as in Fig. 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 same ditv+ 1ri; ge;usrection, with the same velrt vu;eg+s; 1iocity? Explain.

If a wind is blowing, w3*6pvoscoz6x r+3f igp1vcq4ill this alter the frequency of the sound heard by a person at rest with respe* 4voqg+p 3 for 1s6cic3x6zvpct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moti8 neyz1hwh( ivl6-:vrfjax9: on 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 the whistle? Explain your reasoninilvz-:9wx6jnvrhye8ha:f1 ( g.

  A hiker determines the length of a lake by listening for the echo of her s4:ksfng wjy2jy(76hyhout reflected by a cliff at the far end of the lake. She hears the ecyn sygw2fj:6khjy( 47ho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jusy6jlovfl+vvo),8 sx2q gs 3x0 t below the waterline. 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 souno0qlyxvs38v sv+f)j , gxo 2l6d 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 20l j 5fysa3f3.b $^{\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 ofv u g23ztxcz88 tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before 8tcugx v 38zz2the 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 makes when strikd4xagg6o+-+k-u5wn pm , rwkw ing the waterw wapo ,uk6xw+rng+m-5 -4dgk below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sev zic-gb tu0l/ 3 +lo4,ssmgy,es a huge stone strike the concrete pavement. A moment late - 3i ,0,uobg/lmylzvg4cst+ sr 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance bymnx*y4 xm/wj.9 rey.gy -d 9by the “5-second rule” for estimating the distance from a li 4 e9wjm.r /.y-b9yxngm*xdyyghtning 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 level of 120 d+je 3*,)rvhyloo/wx tB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leve4u 1ahw1-v :s rqg9xlsl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9yydoz-)ef a8 dur+ucf:s/+0 h5 dB when fired simultaneously at a certain place, what wilh)+z+0u/a- roe8cyy f sdd: ufl be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equasttiummu5 ip/;v( p hh)z;s )*lly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whaps5hmu;; sz (ip* i/thvu))tmt 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 raz;4 qm+sjf uxk-ya*/:g a )pcytio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroufms/a gcjk xpq; )y+z-uy:a4*nd noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a :zor-r /+ u9hb do3g/ gily2dr2url(hperson speaking in normal conversation.hr ugb: (2odr9 +g3-/lurdozl ry i2/h Use Table 12–2. 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 strike al5cwz9kyun3;l-q md6 v 9/x l.nj;xk fwl:6ts 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 d lglvyvs 3+;8pj 3)vk250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate 3l v+kglv;ps8y j )3dvthe 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 fr bd1l()d1b6k 3xzlhwu ont of a loudspeaker on 1(l3dbdk)wzl xh b u16the 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 typicall ehnx w4nx13w sn1- nz5/ehdu5y detect a difference in sound level of 2.0 dB. What is thehxne534eu1 wz/hd1 nx- nwsn 5 ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tr7s jyq)9mov5y ipled, (a) by what factor will the intensity increase? Increase by a factor osyqjm o5y)79vf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement0cus)*.rf di43)iwl* kwf*hxzc k p (x amplitudes, but one has twice the frequefs*xkwr*0i)kcf( 3 )hp.z liduc *4wxncy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to5u4 7wu:y vbsq a displacement amplitude of 5wyvbs q u:7u4vibrating 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-k0pf rmmqtod:0-d6 g7r85e zdHz tone that has a 50-dB sound level? (See Fig. 125f:r dd60pgt q80medr-o7mkz–6.)    dB

What are the lowest and highest frequencies that an ear canv (ggbue7w:j8 detect when the sound level is 3:(7egbwv8u gj0 dB? (See Fig. 12–6.)

  Your auditory system can accomm8( u mm1ul ,vxlgc;kr:odate a huge range of sound levels. What is the ratio of highest to lowest intensigk l:mcl8u(r u1,vm;xty 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 f y*5 k4fevghc:d5pkb2undamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has d*pf bv25 5c k:ekghy4a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fun ljv2/8v pdv) z)1oy7u,qzgqy damental and first three audible overtoneqpv2/) dyy7vz)g8,vl u zq o1js 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 expect from blowing across sp1zz/+agg ddhtq,m g8(zjn.y8 b(1athe top of an empty soda bottle thajta/hzpnq8d,byzs d gaz81( + g 1m.g(t is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pip2uq fa,rz b)0avl mf:rqy d/o-,5kxv5e organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths oo0r:lba yk/uqzm ,2fx a)5 dvfr-5,vqf pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of c w/ z.x(z9;sfl.rasjhf+ 9ka 540 Hz as its third harmonic. What will be its fundamental frequency if it is f/fjksws.l ;a(z +ra9chx zf9.ingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle5u)*e2sqlns6i me, y vm )i9po C25 eoy q9i*)spils mnm ,vue)6 (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 of an open orw v5gy ,a 7apgwmr :4tft3d-j:gan pipe that emits middle C (262 Hz) when the -vg4a : 3wt:,7 wr5dayfjgmpttemperature 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 7t jl7fp)uvc1 $^{\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 lzbx7x*e4o m iopn)ta/50 k)(d:sruz12–10 should the hole be that must be uncovered to play D abovp4)()ois ma: xoz /7nudkr0 l* zx5tebe 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 db15+2p(1m ;mji typhcfnlm) at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a close)lh;mc+ym1fpn j 2 pdtb15(imd pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m loleqd+ +3e lh8qng is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz qql8+eed+ 3hland 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 : 2o-7z:qh91avdzlely pddc1$^{\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 psl i:gs 3+ngo-6n emrk95 ,aerresent within the audible range for a 2.14-m-long organ pipe at 20 :nemln 5skg36 rg-o9,sr+ei a$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Itmj756/ipr*,d *pxci wu npb0c 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 id,u/7bc 5i6jp0mcxp *iwr n* pn 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 trying to adjust two strinjxpw5q6 9x( jmgs, one of which is sounding 440 Hz. Hoqpj x659(mxw jw far off in frequency is the other string? ±    Hz

  What is the beat frequency if mid :terml*)8sgmdle 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) operates atv -kddg21p *nk9rwp, y an unknown frequencypvdy-wngk9,k1 pr 2d*. 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 dg/ er1i*b( i : )374 nnfuuxygok8poma 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning forkeumyi 7n1do3/)k 4gg f ouib:n(8 rp*x. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arht 092fgion733 y v h:bwb8-zraj4 zyde tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What willot bzi7v g4d 3 h3:h- 09ynywa2jb8fzr 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 identical8d2b7e /mf/:k qzn bii*rh3 :1xnsj gm flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othnrndhqb : eiib:/m1j gs8/z 2mxk3 f*7er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning c- 6zauducfgwc9 p.y:8 h(i;xp8o(wa forks, 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 C are sc6a cwawfp8-(dh9ugpu8yi(ozx ; c :.ounded 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 8maqlc g g.97f2 u-ijvone speaker and 3.50 m-ai.gljq8g 9fv2 c7um 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 piano tu1rahsvk 7c9.aamn /i/1s2wcqner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 1cv7qw 1 sca2/1rakn . mh9s/ia32 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 beats e*7ef4 j 7+ ofkq4pk4kkmnh b+per second qk+nek7om4* k4 4h+e bp7ffjkwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at uno:3 ez;*omz rest. What frequency do you detect if you move with a spe;3*ez:nm uoo zed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stil4 v9r grn. 3r-iyig0zql. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spe3y g 4nz-rg vi0r.9irqed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifot.7)rmk z q,it in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s q,oi) .kzrm t7Are 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 evwe2m)p i/c/mquipped with 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 cpiew m/2/)v mrest 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 th. 4.dkfws*wpxk5b fx .,aryd /em returned from an object moving directly away from it at 25 m/s What is the receivew*krdw.ff sx4xby.5 k,.pda /d sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ats+;q23 ysohe,cadb)x-cdh /v a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thqchax)cysh-vs,d/;+ o2 3 debe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler+ivb j 4gc2*k- vlxwbax1+9i f experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station-4j1v+9cxa iwvl +fbbx gi*k2 at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsg2vqq5 7 .fg) pxphcu;. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/spgchu qfx2 gv).5 q7p; What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasoni m.s;h/ np5thmc 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 velocit67ds avea9o d ighb72/y is 12 m/s from the north, what frequency will obea/hs 92g77 idd6obav servers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speeg bvz0hlm5n/: te/tt5d 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 speebjn5d;*l7gg - pzu;ked of sound is 310 m/s (a) What is the angle the shock wave makes with the direcj;d- n5pggk b7u*zl; etion 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 ftl5a (4i f awekb:d,zi +hx--ei-oy3planet where the speed of sound is onl b -d35-ie4o xf,alikhew-it(+a:yzf y 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. Determmi;2l ;hz-pb 2v/twqoine the shock wave angle itp z-qm;;toiw2v /2hlb 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 vl4:rs g; i*pl$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see*o0ypt hl d,6 fj 06us-xre3oi a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal d0hyrloitx*3 06-p , j6ouesfdistance 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 sound pulwl32tl7+a wmt ses downward from the bottom of the w3t l7 tl2wm+aboat, 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 humbb-1ns7 b;s eawxe3 :tan audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manh(g w6q i:7k 2lpvn,xry plastic pipes ofxn r k,vlpw(g726:iqh various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes rkb 2;/xy (y 9xw5 csu(g0ea2;wmstypa sound close to the threshold of human hearing (0 dB). What will be the sound level ofy wgy2xtb((a s e0/ 2u;y95xckws ;mpr 1000 such mosquitoes?    dB

  What is the resultant sound level whenu28y9rpuuc/mo1 og . d: w1ktz an 82-dB sound and an 87-dB sound are heard sipw1 8ogkduo.:u12/rmu t9yz cmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is b2 h-u:najcj4v8 7-lg jd,blu105 dB. What is the acoustic power output (W) of the speaker, assumi27ua-dgjlv:j,b b4j- h8 n lcung it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output +k0)-u:w p,w f rio v -xme;y9aaqqsq8drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHa,ui)ef v - sqyw0o m:wp89+- xaqq;krz?    dB

  Workers around jet ai95t-f v0lavkbnrz :cb0 q 6r+grcraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m fromcz 5atfln : vb0vrg0-+b6rk9q a jet airplane engine?    W

  In audio and communications systems, the s0 p/bl)+oggw2t t cf1lin0b(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 freq )gm-4i3gmc gjuency 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 fixtv1zt( (hl1u tyazl/mq q +5b1e yn,q)ed points with a fundamental frequency of 440 Hz and a mass per uni1qy unz(q,ttq y5l b1zhl vm/ +t)a1(et 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 g suknml8+;d;nf e;m5 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 tunigdnm ; +;ne lf5;sku8mng 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 strilszd, txqud qj3 d83o;6b/xl1ng 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 produce ruo 81 d3;d63sx dzl lbq,xjq/tesonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed 8 rbv1:plsea7v5grub:k9k e 3wa/o q-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 pur6a, go.t d/h ufkz o,lg2,fe0oe tone 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 level is minimal at a point 0.34 m farther from one source than the other. What is the frequency ofo02 gg uda/, olo,zte6fh ,k.f the sound?   Hz

  Two trains emit 424-Hz whistlesistcneh /uvgds3 z9u (f h/u9*5ytnn g7;b/)e. One train is stationary. The conductor on the stationary train s7hgt;i /9*bu/hnuu 3v(t9/s)e n zycefg5dnhears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appro+7 )z i98 gh*/sr0ilzki r55 zgdnpkweaches you is 538 Hz. After it passes )ziki*g gz5lz/hps85 dre +ni 9k0r7w you, its frequency is 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 jun9 pso.j;b 3gh3i ys+sst 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 +s gn.ipso933 ;jshby halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundino )-p:hxn py*ksb .bk8 )-) pudijvfr,g together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Hoi)p8-jbbv kdp y xrps),:.*h-n) fukow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stati03jfho zap1mg; s5)olnm6 l 8(d+3 *fqbssvfqonary 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 speakersdalp135f* 0q(o ;qnfs 8ojghmbzf+3ssl 6mv), at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood fl:6.vuc crk j-hheb:( iow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refle c:hb-. iuve(:hc6 kjrcted 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.h *6dnf3 6yuzh,mg+kvseu * d the bat at speed 5 63dy*u6 s . h*n, muhzvedg+kfm/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 approaches a moe f:txq4 n+wj1gj:5+c )jkuerth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. H1x:kwq+5tj:)c 4eregjnju +f ow far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send t/uon,k /4o dhq1 jlg,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 instrumlk/ uohnd4jo,1/gq ,t ent, 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 compo1oa7ie.)exag9*t e y romised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the stan.xoeti oae9)1*ye 7gading waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calledartm 67vrq45/yj(j (qnpa0 hj “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sonj4t07 5rh( ja(pr vjq 6aqmy/und. 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 hearialao(ekztaw,ct vg. 0:up8-wq8,8obng for the human ear at a frequency of about 18ubp8eka zal,wov :,0 8qttgao.w-c( 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 sony5z0i vc8ove /ic boom 1.5 min after the plane passes directly overhead. What is t ive 0/z85oyvche plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15w:ku+f5yrooy t 6 ;*syjk.sy2q e)v5p $^{\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