What is the evidence thata :0tl+ y)totf sound travels as a wave?

What is the evidence that soundh n jyk,m1r co:ajxtbz.)/m *. is a form of energy?

Children sometimes play with a homemade “telephone” by attachinf; cc0.0l/tk7f:z itvzh sg)vg a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explailg vctsf/0k.z;v: t h)fic z70n 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 c.cq5+d .w tk/ay/lprfrequency or wavelength to changp y.q5 /tcrwc .+adl/ke?

What evidence can you give that the speed of onfk1z;z27xaj f7 4i5q*o34ylbzyfysound in air does not depend significantly on frka4 b3nzj zlfi25 1x4oyfqo*yf;7z7y equency?

The voice of a person who ha ntyip+whzx2 ; d,j,-fs inhaled helium sounds very high-pitched. Why?

How will the air temperaturzlph s: h):*an +l;ysce in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds ra +m64(mh zfxin various frequency ranges. (An exampl64fa(m +rxzmh e is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spa *vks9fpfi 7g)ced closer together as you move up the fingerboardfsgk)7f*ipv 9 toward the bridge?

A noisy truck approaches you from behind a buildingenca u7,1f3+wu8 ayy l. Initially you hear it but cann1uanl y8,c wfey7+au3 ot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wherea +rppt2wyt )g7mv/z6x s beats can be said to be due to “interference i)w p7r6pmgt ztx/v+y2 n time.” Explain.

In Fig. 12–16, if the frequency of the4z6 (l*rq tgpbcaeq w3l):p 7l speakers were lowered, would the points D and C (where destructive and constructive interference occuwz:pp6ba4*)c(tq l7e 3glr qlr) move farther apart or closer together?

Traditional methods of protecting the hearing of pe)w0 eu flqmz44ople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically,uflze)04wmq4 then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thoubmfm4 kfs zvq;n;fe+)j)/z e4ght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of4 ff qvzmj4;zn;kb)ese m )/f+ the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the so vaut,o p7k2yj85ppm ,urce and observer move in the same direction, with the same veloci7m8 52ty a,jo,kv upppty? Explain.

If a wind is blowing, will this alter the fre6+mmth9be+- wxvmj( 3gsdlo 7 quency of the sound heard by a personheojm l s3m w(7dm+9gxb6v-t+ at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various position)ux .:qyx2 skbs of a child in motion 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 h2b ux:.ks q)xyighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for th.9 n64dqvcwto tpkw3zcg. e5-c: js w9e echo of her shout reflected by a cliff at th3c jvnzc w4sww te.po.gc k t6-:959dqe 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 jusf tf57 ukl0*s25q elgjt 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 sound in seawater ig5*7 l k2ufl 05sfjqets 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt0g )ehb.kh+eipw, r5ghs 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 driftings4in; 1vhiy 1t just above a school of tuna on a foggy day. Without warning, ah11vyi4is ;nt n engine backfire 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 makes whw*,7a d* fy9n9gpvh feen striking the water below is heard 3.5 s later. How h *e9yf , adw7*vfgp9nhigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the v1.jfb04m:ugtjo,u3tr qr4fconcrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See mg jj roq:3frt ut0ub., 14f4vTable 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erz+9 yus+ zasc*0e wcsy-m vi48ror made over one mile of distance by the “5-second rule” for estimating the distance from w+8a - y4yc cemuvi9z0+ zss*sa lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of8 d1ecgu8 ctomf-6ti) a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound who c2t px4t3 gi8ju0z9gdse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prbv9f s w dsku(x3awg*)wt93d0oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the souns9) gbvkx3ww s (3f*d a9d0wutd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance xqdop lc +0m.k,)up+kfrom an airplane with four equally noisy jet engines is experiencing 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 intensitdkp mcou,0l+) q+k x.pies, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh)gze,h ehcb8 5ereas for a CD player it z5b eche,g8)his 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal con;wqx-8r,w 8vena(6bk) q (au btseo1bversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered ob8 -)e tq xs1; (wnbk,a6bqurwov(8aen the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whri ul4zml4:8 cose 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 amplifier B is r* a5:s qkpf;fqated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in tuqfa:5 f sq*;kprn 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 2.8rf;. k b g.e8n1dis,4 fczcoh8hd:n5m m in front of a loudspeakczn,5f.1 en. cobmikhghs 88r d:4fd;er 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 difference in sound level oubhsd*nd(m .xj4xt0z*.l igm7 i :v5k f 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: l x 4.uvni*(.*bgjm x 7tksh5d: 0mdziSee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will8 hpj)md 1;fmq the intensity increase? Increase ; h 8pdqf1m)jmby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampcc4bm;:, egelpmbm (6 litudes, but one has twice the frequency of the other. What is the ratio of their intensities?e g (4m,eccb:m;p6m bl   

  What would be the sound level (in dB) of a sound wave in air that correspondv3(m5 )5mjkfy7a26kfm8an3x ddv qfds to a displacement amp mvd37d(ka35j md2mf fq)68nfkvxa5ylitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wu3ws 8fa2 hhj, +xgr9xhat sound level to seem as loud as a 100-Hz tone that has a 50-dB so8r2xswj f uh39a,+hgxund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that ao ( w/ ge;kn1dhzgabo8+,hgx0e,)v ri n ear can detect when the sound level is 30 dB? d0k 1obgx+)/;i 8hn g,zvreg ,aewoh((See Fig. 12–6.)

  Your auditory system can accommodate a huge vi3qi9 -inj +py1dvl uc9yd9/range of sound levels. What is the ratio of highest to lowest intiip1 jci 9q lvy-unvyd9/ +d39ensity 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 440 Hz. The length of thwt4n,;(ktp u,tvvi .ge vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wh;i.,p t,4(wtvu ktvngat tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thre6vwn8d)w q iv:b51k loe audible overtones ifvbk5wv1lnw idq)8o 6: 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 the top of an,y7 hhp);ilxcg 0j-6o h: vpbf empty soda bottle that is 18 cm deep, if you assumed itbcix7l ,hh)0jof:-g pp v y6;h 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 r:hu fp0jybgp w-z4)4e ange of human hearing (20 Hz to 20 kHz)fz)-yjb u0w44pe: h pg, what would be 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 545s ju.0)x wwkq2a5n 2skfsnu+0 Hz as its third harmonic. What will be its fundamkwk0sa2nq+un w.fx 2js )u55sental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunejl6;nk llfz rs*4,* qud to play E above middle C (330 j,u kl* l 46q*szflnr;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 vxiw5;bi-n 9m C (262 Hz) when the temperativ5 ;mn-ibx9w ure 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 w3emn* -j hp-c20 $^{\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 should4ze+k + zcnjv: the hole be that must be uncoveredzzjn:4+k v ec+ to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at a:cty s5tngx m :3u*rn.ny other frequencies in between. (a) Show why this is an open or a closed piprncuttx gy.n : m*5:s3e. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at boej*yvq*485etw jlzj8th ends. It resonates at two successive harmonics of frequencies 275 Hz and 330w ej5l488jqveyz t* j* 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 dzc+ +loi u /*f(7uso yu-k6pt$^{\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-ifl+/1xin6 f qm-long organ pipe atql x/i61i nf+f 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside and 9t9ef z+4upxx g /q(okis closed at the other end by the eardrum. Estimate the frequencies k exot+( 9qpg 9zfx/u4(in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 sihwb 06q m0+1 fj3ih ncjb:fi, when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency i03qih06i w f:b1+,jf j mcnibhs the other string? ±    Hz

  What is the beat frequency if middle C (262 x (8iconevni1ty017 df +wn0 dHz) 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, whik9gm0 w3)voahcpl t89f;f m*ple another (brand X) operates at an unknown frequency. If neither whistle cv 3m;)t a 8f9lckhgf9owpp0m*an 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 soundedafr3/ d6ixk m7 with a 350-Hz tuning fork and 9 beats/s when sounded with ad/6m xa73kf ir 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned t)guyplh4+x, uts **b do,jwz 8o the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.p u*dj8 o)yl* b4,tzs+hx,ugw 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 o v(oo*d)icx ;p4l xm(heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othecx4()o d(oo pxmi*l ;vr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin.p hqtv7yn t.5p(7h:9ckk srkg 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.r 775k:khpv.tsp(yqkc t9 nh 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 3.00 m from otr/4t-slfd .*, ezxu xne speaker and 3.50 m from the ot4 rf*/t. t,sluxzdx- eher.
(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 f)7 air)q3drcv99 2mr(fkjnd132 Hz, but a piano tuner hears three beats evea dmcr)r9r9i dfvk327qjf )(nry 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many be3mn6g hh.sz. n rjvt30ats per second will b.s 336nr ghv0.tjm hzne 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 whenelnm k**or mf h*t*0p: at rest. What frequency do you detem0 np *tlf* :o**mkerhct 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 fire engine whose sipk,5sc ajs- 4fren emits at 1550 Hz movcf4pja5- s,ks es at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz soum a:0 djk) lo:ycppi82rce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are th8c:aj:d kiy)p m lp02oey 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 bv0ffad+dem9ru8 -) qwith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat +b-d e9frmv8)u0adqf 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 ;f fen3g4j : 2p*grclomf/xu- 50.0 kHz and receives them returned fro*ep4f; jr xl2:foucmg g-3f/nm an object moving 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 speed of 5 m/s6(dyz -zo,8z*n eyfi y24,woa t4 uvmm As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflece z,-m 4ity862vmzu(* ,o4 foazydn ywted wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played ongj s5t. f5hp3w a moving flat train car at a frequency of 75 Hz, and a second identical tuba played thet wjhgfp .355s 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 measurd6wsl0 nb- c- nhb/a 38rimtz5e 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 is flowing in large leg arteries at 2 cm/s directly awayn-wch 53 sl0b8ad/m-bizntr 6 from the sound source?   Hz

  The Doppler effect usiciv8ecb3 jyvg+s8du/6z1a +58m fjaung ultrasonic 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 of6t3ue gzuzkpw87 xm*x q)v )5b frequency 570 Hz. When the wind velocity is 12 m/s from the north, whatk6 bue) ztv m5p)83quxzxgw *7 frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its sl)i-; 9a g7 kigr.5guv 4uoqoc af3vg5peed 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) 8:x1eulxc(rfu, 8p bvWhat is the angle the shock wave makes with the direction of the airplane’s motioncx fueubp 8l8r:( ,x1v?    $^{\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 th ;u9g+;; bkk6ombetihs) d+6obx+z aj in atmosphere of a planet where the speed of sound is only about 3ed;g9b6smhu+otz ;k6i ob+ ;bx aj)+k5 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 s ,pq,7ids*b rycahs9:bproy3(:- kiy trikes the ocean. Determine the shock wave angle it pro:pii-y(ksa 9pdy b 3, rybo:cs7r,h*qduces
(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 l7ild(6j* uddhc f8s:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over5+gzpqyz 0 0ao/giz4)dcf n5qhead and see 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 distance /gqy 0pog +a qcz)5z4fn z50idof 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 seke4 gzex8 o0kfi*)4s ynds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for wh48 4e)igkks*yf0 ozx eich 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 range?t: mh pb qn 49c:kv/0l)t/lmtj $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon) u uopa1 irj6hgtp44+y. It consists of many plastic pipes of various lengths, which are oiu+po)6jatgr4 up 41h pen 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 frokb oslq9u3uvtr:+.:8)m cys am a person makes a sound close to the threshold of human hearing (0 dB). Whatubk: ) lo+3y8 tsqr9vuasc:m. will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound)dt hu(b fpl,/f,s3 gb and an 87-dB sound are heard simultaneousl, pblf,)hbf 3 (gdust/y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op bxr0j pq.82coen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directio jor2pqc b0x.8ns?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Th/ge6 zyfn2/fde power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHzdne /fy 2fz6g/?    dB

  Workers around jet aircraft typically wear protective devices overm/9f-w . -ttpf5gmlw3a od; it 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 from a jet airplane e5fw - p9-omtdla ;wg3/t.m ftingine?    W

  In audio and communicatipw1 h(tqs h6d3ons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuny8z. v. aitwh,ed 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 violin is 32 cm long between fixed points wit3h3dv7k/hu mo1 mumv4 h a fundamental frequency of 440 Hz and a mass per un 4u7/ v31mhkmvoumh 3dit 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 opeg* u ;cvsw1t1tn tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube abo*w1cu1tgsv; tve the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at 0 6frxawsq9is1z 1u o t2(h+lpone end and also 75 cm long. Hotoa6+szr1 0h qiwflx(21u 9spw much tension should 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 observed to resonate as on 3tao ;+ovfyay twtj.p3,)t- be 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 500–1000e0gw6.ppqyt h 862oxv -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 0.6t2v e p0o. hqwpyx86g34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz w+ow p/.mdz0yi px+l;q histles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz +qzmi.x; lp/d+yo 0wp beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftedgy)9joae p .6r it passes you, its frequency is measured as 486 Hz. How fast pa. jdy )oe6g9was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate kpi6gbc6:zz. u;z , obthe 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 po .bbzg;zu:k ,ic6z6goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produwim 2cd9va3 5i:rez;a ce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long;ie3rd avaw25 z9cm:i is the other?    m

Two loudspeakers are at opposite ends of a railroad: oq syrd)/ l8:okq)l+ap 5cng 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 frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speaq gon8 :qs:l))r /c o+klpa5ydkers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in fv7xwas* z ,0jthe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed 0 ,7za*fxsw jvalong 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 th 09hsa4s)(sphex- m j1ueyom1 ezk-8xe bat at speed 5 m/s The bat emits a sound wave of 51.35 kh -mu0sye)9ox1xps- e( esa8khj4 mz1Hz. 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 motw,jk c rh.3l)m2 i,zdwh. 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 t3ld, wjkzh r2m,w.)iche next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Ampd4uy ,neq flvwo9-fme (efm8;b 93:lpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds.f-fvpm o3 ufmq(n;l8: weeb9ym4 9, ed 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 presenc-e7q8s 08q*2+ dl jjhjf 95depdfihxue 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 standing waves in thisx8jpsqjjd i8-dueh 2*5d7f l0+9fhqe room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”-) m3stxe; urv 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 sound ;rumtv) e3sx-. 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 hear )i)ogzjkibnl/e;g l.68nz +a ing for the human ear at a frequency of about 100 8nn i)b/z.j a+kglo g;l6)ize0 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 th 3a ont; dr vfy),8:yit7c(qzoe ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? of7 iyqt3),tc nrv; za8y:do(   $ \times10^{4 }$ m

  The wake of a speedboat iguq qw+0e(v (es 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