What is the evidencexvw )d8o* zx.a that sound travels as a wave?

What is the evidence that sound is a form of energy3* w+ ) vq7qnkkc5htdl?

Children sometimes play with a homemade “telephone” by att7 7 ;hykqx(ewkaching a string to the bottoms of two paper cups. When the string is stretched xkq(7ey ;7khw 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 th q4v-q,e ltzp- 1ps:t6mtmpg3e frequency or wavelength -,1q:p 4qv etmt3ps6zp tmgl-to change?

What evidence can you give that the speed of sound in air does not depend 5fdh+hjj (n2d significantly on frequen5ddj j(+h fh2ncy?

The voice of a person who has inhaled helium sounds very high-pit fjlv.6qzk2 *g491iohkgtcn/ched. Why?

How will the air temperature in a room affect the vz5i ri t+:trx/k ji1:r,:sovpitch of organ pipes?

Explain how a tube m;v ,me;i6(vbx char a4ight be used as a filter to reduce the amplitude of sounds in various frequency ran;cm(, avxar6 e vih4b;ges. (An example is a car muffler.)

Why are the frets on a guitar (Fi c): w)-q;rs *qmbjouwg. 12–30) spaced closer together as you move up the fingerboard towarq ;wbr sq*) mj:)-cuowd the bridge?

A noisy truck approaches you from behind a building. Initially you he6 +ps6 jqyf/teneo.t* ar it but cannot see it. When it emergesjy. o6tp teq6f *+/nes 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 “kgqj/ 6ztwa61 interference in space,” whereas beats can be said to be due to “interference in tim 6tj/w6a kgqz1e.” Explain.

In Fig. 12–16, if the frequency of the speakej1yevld1zy q+ e th t479vw)+o:nma1irs were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer :ti9wde1 4q v v hyjtl)7em1n 1a+y+zotogether?

Traditional methods of protecting the hearing of people who work in areao rb1w5m ;a y(lf .c+h-prvmu hha*)6ws 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 block5wfhwy1 a vorlpm;( +6 )brh-*ahmc. u the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eacn ets;ib(r7v vie).,gl :nia1h wave can be thought of as a superposition of tv. lbg7irnn)i(s1i:ae v;e, two sound waves with slightly 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 t /wkbe m/ fsmw ) .;rj,jt/f*-mfby9ekhe same direction, with the same velocity? Eb-)f/fy jbf me;j/9m.w ,emkkrt ws /*xplain.

If a wind is blowing,jzk67 ) ifsk)non) o3) sytiz) will this alter the frequency of the sound heard by a person at rest with respect to the zf y7) )n iijos)k3k o)z)stn6source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mol*nz) ltxsc(zj(r3/w nitor is blowing a whistle in front o ) rws/zxj(lc(*3ltnzf 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 reasoning.

  A hiker determines the length of a lake by listening for the *8yr h,dg* ttpecho of her shout reflected by a cliff at the far end of the lake. She hears the echodh*g8tp*y ,tr 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship ju,s.2br hhftw :st 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 is 156h.2:rfstw, b h0 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ,hyz1 7ls vmwkde;bj/** p6l kin 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 boay0vaw xeg+( gay832v0mjvhrx y */*r at is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 0 3 w yega80/var2vxg* y(raym*hjx v+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 thhy0do-hw,is 6w:5lgr(y7z bee top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff? ez6lsbygi ,wo 0-5h 7yw rh:d(   m

  A person, with his ear to the ground, s uc2q,uyhcc2 4k u,mh1innrmf.a2)gs:, d ry.ees 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 concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12,ra4n,kgmrqum2h21ccund.f s: ,hy .yc)i u2–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent ;i jv gp8iv52 ,n:.l fa.agoqw w*jid-error made over one mile of distance by the “5-second rule” for ;,a..v wlwn-ipd j o*2gaigi5q:jv8f estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound i gb31; vh wiwkb(s9d rt7h:/*p*n eqqat 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 whosrin4ka(allh-4x: r)q; 5 xblez7hh x+e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at d;;frdg zi.c3p,p7 firyk45u a certain place, what will be the sound level if only one is exploded? [Hint: Ayr5gi d3 4.ir;fpp7 ;ckduf,z dd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eqh3c( uw0(9g2acultg qually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shu h9tcl(ugw3g0acq 2(u t down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh:2n emp -o4+x 7fsqmpqereas for a CD player it is 95 dB. What is the ratio of intensipxeq2m+ps7-foqn: 4mties 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 peruc1k5. . pppfzson speaking in normal conversation. Use Table 12–2. Assume the sound spreadp kp5.pf cu.z1s 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 strikes an eardrum whose area iiyn,kh :y-5qgf 5hcmyj4bdb* 7x; vh;s $5 \times10^{ -5} m^2$ (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 m 3 7+kfzokvi(gwjv5x8(f2x cy odest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point8+ivz3kw ((o5cjy kv7 f 2xfgx 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 whl; tg5vc x- ve496uiehy8a7jz2eus x8en placed 2.8 m in front of a loudszyev 8 x9 hvcl5i8;tsu4jae2gu6 x7e-peaker 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 of hj/4u fwkti1w)xp, nkp2rrxb, n u*7+2.0 dB. What is the ratio of w w rpxhxj+47 21k)/ unitnrp, kbf,*uthe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what faccu ),5 aa/gtmu b21loxtor will the intensity increase? Increase by a factorga,bl axcu)2uot/ 51m of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemolj:sz f )5 w36wih7oxent amplitudes, but one has twice the frequency of the other. What is the ratio 7) f i6wosx3wjo:z 5hlof their intensities?   

  What would be the sound level (in dB) of a sound wave in air that42kd or re sgn8e.dynfwm3.9; corresponds to a displacement amplitude of vibrating air molecules of 0. 2n.wo9rne.8gd3 f4m;ry kdse13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1lu0 qbdtxxll( z4ba7,7o1z: o00-Hz tone that has a 50tzd lxbo,(l47bx 0z lqo1u: a7-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear caxe6e ph wx853un detect when the sound level 5e86x xpu we3his 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge gv 7rnsil kh*b++2dr 2 p*il-prange of sound levels. What is the ratio p+k 7rlnhi r-+vl* gs2pdi2b*of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengthee6 bep+jzh9mxrn0+9 of the vibrating portion is 32 cm, ae 9e0+m+ 6pnbxjrzhe9nd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What de wha349z7r/m58rzl q+i p evf35rkf are the fundamental and first three audible overtones if the p+3ikmf r/75 vpw5r 9qeaf4z3hd rz8elipe 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 blowiixdff; /l b(q *moi4h(ng across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clhdxo(4i ib/fq ;m(lf* osed 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 rang 9w pcaq9*qb8n0w h,dqe of human hearing (20 Hz to 20 kwqpc aq9 *,8hbn 0qd9wHz), 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 540 Hz as its thpgd shk 7 66fvt857uizx5 8tpcird harmonic. What will be its fundamental frequency if it is fingered at a le576 p8sfuzk6xpdgit 58c7h v tngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E gi1 : i/3s3xd 7p: ndjx7ivfsyabove middle C (330 Hz)xpgf :i/d33 dsn:xv7yis71 j i.
(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 Cb r9*e 0,ctdao (262 Hz) when the t9ct0oda* b,e remperature 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 atmcw5zp/ f,v x0 vm/hl5 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute pndx;zbki5j,e73gl i :v+tt/o p2iq . in Example 12–10 should the hole be that must be uncovevg j;piqx. t7netp:lk5io,3i db+/z 2red 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 9 a2 dupz9 jr1np7/arg616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a rg12p9ar/duazpj n7 9closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates atke+gdga)g,v71s7+h gwmjpg 1 two successive harmonics of frequencies 275 Hz and 330 Hz.kp+g7, )mgjgg+e1ds17 awgvh 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 o5 r 78bkhxbshnfw 21*$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long or o-)hntu*g ba4sd18b fm89dzz gan pipe at8z 9g -z8b1a)fn*4mutdbhosd 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 outsidee6qp kosb152m and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the earbm 1soqp 5k6e2 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 bela1 .0k*/kmjfmm xc5dat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other sx5mk1a .dm*fmj/ ckl 0tring? ±    Hz

  What is the beat frequencyxsd jjs,f4w4 3ft7u3 i if middle 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 at 96u2uvyoq :t4k/plaqc .i evm j9 p,.ban unknown frequency. If neither whistle can be heard by humans when cvv, ql.e q64:iuy9.tuoj 9p a/p bm2kplayed 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 produce/()s:a h jroses 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency s rjs)e:oa/ h(of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenck+9fxl xevn. ,e9 +ccxy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be tex nfcxv 9xl.+ce+,k9he 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 playflx 2aw 7 lqm-.hl)m8g middle C (262 Hz), but one is at 2l m)fg7m8alhxql -w.5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has*1y8h(t hygypym6yl i e vh7;; a frequency of 441 Hz; when A and B are sounded togyil7;het6y h1*p; vy h ygm8y(ether, 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 apart0z+ esbxl9d)db ou6*c4pecm/. A person stands 3.00 m from one speaker and 3.50 m from the + psm/)c6e cobde*bz9d4u0 lx 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 pianog8oq7dw*( q1w9q(s +sxu fopy 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 the w(ouqqxfso7 w8 (y ps9*g+d1 qother ?   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 ys o0i u/;.xylgk*z6 8 nua.ig2.64 m and 2.76 m in air. How many beats per second will be heard? (Assuoys/g.;z6*ig 8 ukx yua0.linme 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 ref *40ob1bjfjfst. What frequency do j1 fbf0b*4jfoyou detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng01:jj2rdsla mzi sg5: ine whose siren emits at 15l2r:gzasm:j ji1sd0 5 50 Hz moves 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 source is movingwyg+q0rxc/a . toward you at 15 m/s rqx/yw0 gc+ .aversus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When2 7f ,5ytt/ojatk 0tte one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is thtjot,t0yk 2fe7/tt a 5e frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receivevi9a -tujv/ap5ejep .o6ef .u6h ;9ihs them returned from an object moving directly away from it at 25 m/s What is t . aiuh;6veei-j95/puea 6ov tj.9hfphe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wxtml((v yx7.,rju:u klpk1; nall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frer:k7umjvxlt u .1yl kn,px;((quency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplpc 40(p*njval sxf,ovn z:,/d*k.sqjiak,7u er 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 whili jv.qnv0xup ,kajn*c7afs,/k*d, o4pl:z s (e 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 ultrasou jrc9 d)dy;(.- buu1o/wnztl7z5 oid qnd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz,n1;9j yduz obt/o-uic ld5w(qd7z) .r 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 away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofmnm6a o4pb49a frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12 x e8i s gk+rboh849a+am/s from the north, what frequency will obs4+axgre9ik+ ab8 h8 soervers 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 lao 9wmd7 -gl,kknd if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Macv2vbgu jr/,j * ur*t/(h 8fuobh 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo,orv* f hbru/t( vju*gu8j/b2 tion?    $^{\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 atmosphc)iln5d.cu:yc l0 h2plu7 :btere of a planet where the speed of sound is 72l d:c.) tplc 0 bciy:n5uhluonly 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/svea pepzm0(.g 7,o lplv;6kp;jv-b5v strikes the ocean. Determine the shock wave angle it produceppek(m l;b5o j;p0v az. v,v-pvle7g6 s
(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 q.dqc-0r+w xr$/theta$ 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 a0 zwulv9 sl0fs*l(kvlfz23 67 dls+m pbove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance udv sl*lz+70f6 92z fv wpl(sl 0lmk3sof 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 puli +etjbvak1o 0sqah ,5bxp2v884z4 jpses downward from the bottom of the boat, and then detects echoes. Ivs45,4 b e xkhj01pv b+p82a i8ajtqozf 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 there3bfawtq 8-h+ y in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consisx.nu, p rn4p3sx , tpwkq -qaskbz8,;;ts of many plastic pipes of various lengsakbq ,n8 p3w4, krz nxuxt.q ;spp-;,ths, 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 perso3o4h-h(4k9k- xgkd xdz. qi ann makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such 9xxq. okd-z-k h44h (g3aid knmosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87gf8gt iwwgbe ; f0d-q u4b02; wl)zj6x-dB sound are heard 0e 8l6 ftwzgw;uwdfq)bgi0x-; jg b24simultaneously?    dB

  The sound level 12.0 m from7j2iqkm)7 sk l8vuj7 m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alkj u7kmq77iv8jm 2sl)l directions?    W

  A stereo amplifier is rated at 150 W output at 8jjpr04 zhjzf u;2,b7dq+h tr 1000 Hz. The power output drops by 10 dB at 15 kHz. W 74j+ dq z,j2;80bzruprthjfhhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their:n9*4c /+fccyxrj iie 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 intercept :ijnf 49ci+ y*xcrc/eed by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communica 6dj1z0sp-tm asuep )9tions 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 tuug qt,a2k(. avned 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 f+yxfzm ,hkn hh,g7h;v ;6wh+n ixed points with a fundamental frequency of 440 Hz and a mass w,h6 hhg+n+;vk;,fh7m n z hxyper unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with(erd2 9n diy6m water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above 96ie(d dmnry2the 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 mo4 cbsww5d 1 w:f8k9h8ur(gakcwe4r *ass 2.10 g is near a tube that is open at one end and also b(gcer dh5uwk1848 *fws a4rkwc w:9o75 cm long. How 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 observedt 6 79drax+kdggq 9qh: 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 z,meev2 -ju l/u +l6xrthe 500–1000-Hz range coming from two sources. The sound is loudest at points equidis+ r2m,lljuvuz-x6/ eetant 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?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor ont545x stb0onzxbrgu*a w)9 uk6p4wi9 the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving trt5xbru64gw4u5 waz0ob9kspx n)i t9* ain?   m/s

  The frequency of a steam train whistle asz pgp2f zswo+u (.u eivl4,x38 it approaches you is 538 Hz. After it passes yopou(px.,3glz8wu fvs 42zie+ u, 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 spee mh-vocn2hrw u ;9t+y i hhs;:hojp/y((r4cp4d of cars just by listening to the difference in pitch of the engine noise between approaching and re4iu hpr+hn yrh/w9 s(c-hyjo 4hp ( v;co;:m2tceding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prod.fbb8 ct qz+ 1d2a zsr*gg-7hquce a beat frequency of 11 Hz. The shorter one d8 +hzfqg7a2s-c zg1b*. brtqis 2.40 m long. How long is the other?    m

Two loudspeakers are atqx vnt xi5tgw h7b.tomjp+2o(b670z3 opposite ends of a railroad 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 fren pwhttqigv+ .zb7mb5t3 j72x(0oo6xquency 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 blo acqr1c; y4ue7d8royp1zl29olo 7 sn ,qavm) ,od flow in the aorta is normally about 0.32 m/s what beat l7, e , c r 71)q94d2oanvs1apm8yry; ouqzlocfrequency would you expect if 5.50-MHz ultrasound waves were directed 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 s6)o je0f7az6zwr(f 3aekug g3peed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequen6eo az7e 3gw0gzrf a(k3jf6)ucy of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hb;8 b)w52b1tezgu cuio3 vd s21fn1kjigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eacc;2oek1i1 t)b uzf8b2djgs1u 5 w3bnvh is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi 8yujwjmtpz72 zj.*4+6ge qew llage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a g2z6 j8p7 wwjtzu 4qje.e* y+mmusical 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 ste 9ltmj 9/a ncqb7a6ef-reo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider t-la9 qen/a7 bf6cj9ma living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvp.dqq)-k,prmik/uwz kn*b (,5 u 2szpes a long, slender aluminum rod)2k bd5pip sw /q(p,* zkq.k-munr, zu 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. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequencye7 u (l;vjv3e:zu,m17tkqvg i of about 1000 Hz is(juv:vee1 qzvkt mi73u7l,g; $I_0$ = $1 \times10^{12 } W / m^2$ 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 az7z cc/o3q wei8;bs9Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the z 7 3bccwaesz8iq9 ;/oplane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb wle 7k9)wz*4md9ux)tt ukaz,qn;: p joat 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