What is the evidence that sound trave8c.e96m 7z6ajhlxt3+qg b ibm- gmb+qls as a wave?

What is the evidence that sound is a form of e/r d1ek 0 rz6n+( bz;0gkodhvnnergy?

Children sometimes play with a hogktr(tjec,cx1p 00kf h;: v+gmemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can thvfcgk0+ kj1 0c xt:r ,(;gepbe 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 airuo:fl 8 6+fers into water, do you expect the frequency or wavel+fro 86 :esfluength to change?

What evidence can you giveb 7cu4e q-a9ow that the speed of sound in air does not depend signifq47 oae bw9-cuicantly on frequency?

The voice of a person who has inhalo57xyuz1a. zl ed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the p a92ur )9tb*zho*xybritch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of t3m 1s7 a3*o(t6ccxdme6z pxxsounds in various frequency ranges. (An example is a car muffleraxpx mm x 1 ec7ds63o*t3tc(z6.)

Why are the frets on a guitar (Fig. 12–30) spaced closer 6pi 6c3npi 8fp2k0 z9wykj:fktogether as you move up the fingerboard tn0zyp82wkf69 p i jckf:i3 6pkoward the bridge?

A noisy truck approaches you from behiixxw3zf vw-7q d/ 4ic,nd a building. Initially you hear it but cannot 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 x/4- ixw ,d v3ziqfcw7Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacem) 0a(r8p ,ij/;ejo1x vtj qve,” whereas beats can be said tte1jo;,)/jaiv r eqpx 80jv(m o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequ xw(.+cfuq- ygwn4ig* bl3km4ency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move u.4w*b n(i m+kfg- cwg3yq4 xlfarther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witvqpw ta )gu 6ewm-it,3**a7 slh 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 detasg tlweipuv qt*7 )6w m3,a*-ects 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. Each wave can be thought:3t.t)tt q +iljgm zfqn. sc-: of as a superposition of two sound waves with slightly different frequencies, ast.qt-gstlz3:)i . mnqfcj t :+ 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 k,ts lm89 *tnma jmu3m4/s5reu 8w2pfmove in the same direction, with the same velocity? Explain.fk net m98 u2mmpr4tjl5u saws, 3m*/8

If a wind is blowing, will this alter the frequency of the sound heard by a pev;nkpvgi02 4l:se 1jtrson at rest with respect to tti1n jv 02;gvks:4 lpehe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. zea* e j.r6 i8sr:8hx;sa-oqb A monitor is blowing a whistle in front of the child on the ground. At which p 8z*qas:x;es.e 8ob6j ah i-rrosition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines t gy /-m+eafzetc-5.xz he length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s a.a+-zfe g yctez/5xm-fter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the 8n;, po5bpyas9fw+ uuw4uvd+ 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 1560 m/s (Table 12–1) and does not vary significantl+b9+4up un8y5w p;avduwos, fy with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 28j3a s g qj:- a4 exyjpejmii2kk3d6110 $^{\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 jlw3;b0e( du pse;q;uof tuna on a foggy day. Without warningj;q;uwe u0lpd;sbe (3, an 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 splas42me5-z 13acsc pu lbkw n1qc+h it makes when striking the water below is heard 3.5 s later1cm1c+n3pw-b saul4e5 2zk cq. How high is the cliff?    m

  A person, with his ear to the6zy ewlz9nk wn/zxa4tc 2xf42zd. s( 4 ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far awayly2d s f/xz6.t(zc kzaw n92n4zwx4e4 did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over onet +fj9nvdjj08 mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature idjf j09ntj+v8 s (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1o.+ncuu i no;+r(cfn :20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose i6: 5ohv0za sva-dlb 4zntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simum2age lnho:9l 2 l 0-+mpw-d7my:ypvv2zn 6fnltaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Ap2yndeyl2w:0hm:o-v96l-pma7l m n+v gzf2n dd intensities, not dB’s.]    dB

  A person standing a certain distancekz+zijryylr lz;4wuv 7xw:k6bar; 0 ax3.39k from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound lev 9xl3z+r3wx; 4ybyw:k7k 6.azr0 k;vuzljariel 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-t9sr/l)bg1 iq2.sry6frx qc a5o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of qf9)/cqr sgl b15iyr s26xra.intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of ;o fi,l h2exnki0/ta/sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ove/kflh; /2toe ai n0,xir 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 eardrumddi;7nu k:on,q:o /ws f m7v2w 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 rat m9ttouljx(w) jb8vxz3ii i55 :/f px3ed at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimajtpm /jxb(ix:fziu)x3 l ot55i93 v8wte the 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 2tva ubk(yvatvao .l-8- /8ne 7e.drz *.8 m in front of a loudspeaker on *luvk-( n/o8t.-7ra tzbdey v. eava8the 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 typic89vsm*67z*fzpr;c 5 ,x)mgf vbz tzwqally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wqzzmxrcp f v*5v 6 fzbz,s)*wm78;tg9hose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripl 62u7b godt bh7zdt7)xed, (a) by what factor will the intensity increase? Increase by a faxdzt7du)o2g b t6bh77ctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but89 fu 0riek4a 85yov(sttu:og one has twice the frequency of the other. What is the rare( v kt i:o5go4fy98sua08 tutio of their intensities?   

  What would be the sound level (in dB) of a sound wave in 1p j5:x loj pc1h1j ldsiy9/+bair that corresponds to a displacement amplitude of vibrating air molecules ocy5 ij+pd1bj/1x h91 p:losljf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that,ggyl 2 hv8/dy1dsbopht4tin)-q9q 5 has a 50-dBoy/ g4 n82 tdhb qp9tsiy1)glh5d,-vq sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies ipv / l6a- fminn:pqi,t9qz8+ that an ear can detect when the sound level is 30 dB? (vi /p8,-i i nt alm96nq+zfq:pSee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levwkqv)dl 0m0+z els. What is the r 0dzw+lv)mk 0qatio 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. z5pr2/ myh,+- h m6stsl3/akxb( idqwThe length of the vibrating portion is 32 cm, d sxzms5(qhta/+ 3 bk/y-p, w m6lr2ihand 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 are the fundamental and first three audibleba6 vmu iw6uvu24dd *0 overtones if the pipe muwv *d 0au6di uv46b2is
(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 thev + domufkjq4*gg) -r6 top of an empty sod-j* mvq46+ukfg) odrg a bottle that 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 pipe organ with open-tube pipes spanning the range of hu/0 87q0dwzn8hxrt/zl )hscap 6teap :man hearing (20 Hz to 20 kHz), wapn/h ha8x0 6dz/twl0c :tz8s pq7e)rhat 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 third harmonic. What dk8nh( ko15 j-c6yt v9.mno kkwill be its fundamental frequency if it is fingered at a lenkc t o v.58 (-6km1dhonk9jykngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E a(cwf)o,nx 0l+9su0u;wyo r usbove middle C (330 Houulos(y c0n)ws rx+wf9;0, u z).
(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 px:h 7id2 tgh+jhmf 1g8ipe that emits middle C (262 Hz) when the tehd7ghf g8 1mx:2htji +mperature 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);y) 1b. azk pa7ltgrl $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be t7joqr )j1hcd, cr7 k.ihat must be uncovered to play D above mc7dk)jr1qh . i j,7orciddle 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 2is (n41 x:pl5v:nmu4c kacer464 Hz, 440 Hz, and 616 Hz, but not at any oth icn k(54 4cl:mu1nxr pvse4a:er frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long 8xofcqw+ iu s 70/;dri4poh w,is open at both ends. It resonates at two successive harmonics of frequencies; o i+0quswr8oc7p 4,fwd/hxi 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 67j e+ayw wg4kg6djv 0o 2tjsz)ulr48$^{\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 organ yo /xkgc g8w l(/(xldp-)hf7m pipe at 8hm/7wk g-p/f xlc y(dg)lx(o 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2. :5vuq*2k8 y xsg) moibjs+g)m5 cm long. It is open to the outside and is closed at the other end by theog *)8 ym gm5qs+:jiv2sxu)k b eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one be,fnc, r+9gv m-6bylkpat 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 string? ± ln prbf+v, -,c9ymkg6   Hz

  What is the beat frequency if middle C3l cq m(l3o 7osv8npn(an;s:l (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 u3ujzw 51i:a 1vgn f;3c s9 /z8ijvcpd(brand X) operates at an unknown frequency. 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/ udnui3wsja91f8z;ivzjp gc v3: 1 c5 X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 hz8mqgus2p02qp9tc+. wtxmpa/5kj ,(l-npl beats/s when sounded with a 355-Hz tuning fork. Wzupas t.(j 0h9q-,g5mpxnpl+qt 8 /m22pl wck hat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29l/ 8 .kc5clegah;vkm 74 Hz. The tension in one string is then decreased by 2.0%. Whatkvhle/g5c8l kac .m7; will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mi;c v upui:51sz-,njkpddle C (262 Hz), but one is at 5.0°C and psu5upk;c v-jn1, z:ithe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, an *5lfy;e q/l1rjk(cr6l szj) kd 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 possiblf ryllcl5r/) 6e j1jk*(zq; kse frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A w4qjp l ,lrf 6oh;3o*ryi4o( xperson stands 3.00 m from one speaker and 3.5prow 6( h;liy* r4ofxlj,3qo40 m 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 .; wi)uphcn* hvibrating at 132 Hz, but a piano tuner hears three beats evepcn; * h)h.wuiry 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. jsv hyd.4l * 84hn3gkbHow many beats per s v.y8kh3 b 4h4g*ljdsnecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a 96s ,kpdx cpo5certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speedx 5,6sc9dkpop 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 fxy3fu3.1 piu hire engine whose siren emits at 1550 Hz moves p h.ufyu i33x1at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequena:(ujacxgan 5z)07ov cy if a 2000-Hz source is moving toward you at 15 m):aac7 (v guxaojzn0 5/s versus 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 withb14:)8:innlyv7g br:dc59ptnaj kw l 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 frequency of 5.5 Hz. What i tb4n)8::1gcdy75bwp 9 rllv:na kinjs the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wa/m*tsxxqmv- .67n :rfbvb e*gves at 50.0 kHz and receives them returned from an object moving b. e* m/bfxnq:g7*6-vmrtvxs 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/s As it flies, the bat emits an ultr2dc4 a0y/ownqasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the 2cao/d0w n qy4reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dze)q2 :6ccuf soppler experiments, a tuba was played on a moving flat train car at a fr)q2ucs ez 6:cfequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supptwc+jra f)d9 tq;-77 nmrvwa2y0; ku cose 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 expec 97t rd7-qnr) auf2 +cjwckvawm; ty;0ted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency1,1n g5d721dcaqdvp hu;v okk $2.25 \times10^{ 6}$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 windq se malq igde5;nt3( w0;1t;t:j jf;d velocity is 12 m/s from the north, what f 1sjg;qndl;3: id(0 fet tqj5wm; tea;requency 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 speed at 2whj zm*6u8++v* yrb 6cj yyzv20 $^{\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 whereyaw.,bdje5bji6i)k 3,hf y 8u the speed of sound is 310 m/s (a) What is the angle the shock wave makes with thb3i ,fwd6i.jb, 5y8u he )jykae direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sod te* v04a34l uardkeg7m:;n lund is only ald;arnl ka7vt u4dm *:g 0e3e4bout 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 / 0non*t; n fj:nddikup/+,xdn -1nubstrikes the ocean. Determine the shock wave angle itjn+// *xb0nt 1npin - n;:kdond,fuud 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 r x/)hin bb..n$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see qkc 3hbo*pw:giy-;/w a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boy:c*b3 w;kph q/ g-wioom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dow9brs3sry w6 50w ygbd7nward from the bottom65 9wrb0 by7yr 3wsgds of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ranft f.w24yzbf*xf3 em4ge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cob47 91qcm5c mf(ilitug - q.vdnsists of many plastic pipes of various lengths, which are open on bothqc bc9.7 lvdi 1t-4u q5fimmg( 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 pe4xkjf5z*u;x7ez4j ;dfv y. n grson makes a sound close to the threshold of human hearing (0 dB). Wha54xz; j7;* ev yz4dk.gfjuf xnt will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound levw-vx0igu q 7+rel when an 82-dB sound and an 87-dB sound are heard sgxi wq-uv0r7+ imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in ttb-dr 8(gsbeayfj( .7 sb(t 4d e-g;okfr z9:ehe open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming if. erzdgbbfe;t(dsrgoye (k-bsa-4t :798j(t radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outd79d;wq onet i ml,p*i6)x rf7put at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power out9 nd7*l;x riti)e,q67wo d pmfput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective .z9 yr*x-w 1a9cicsao3x eoi8 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 powi8*9aw ro9. xc-1aceioyzs3x er intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g-741gga qsr sv w)7zcqain, $\beta$ 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 tli5 . mwib3(wufg j/9,who7kxo 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 wit birinc7 4;4rnh a fundamental f;r4nricb n 74irequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with + tyb9c .0gxt)reem:qr yxm- oc-/;bjwater (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork w mymbt q-ct +cgo:9jr)x;e . rb0/-yexhen 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 stri.vbo)a j-e9ljng 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 resonance (in its fundamental m.)lj9 ajveo-bode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f)6q ki 0pf:opuull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Thetim94 jme u3f7gd8yc (klh )-w sound is loudest at points equidistant from the two sources. To determine exactly what the fre fyldj7u94w -em 3)(8gtmchki quency 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 stationa- )mh: g8m 8zlp9v ibngf2v9dgry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movinpz98 m8)2li :vgfdmvbg 9 hgn-g train?   m/s

  The frequency of a steam tf1ndt ti* u.l0i6lgbd ff+kv7,s1j 9erain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured astefi6n f*ji l71+db.lk v0, t19usdgf 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listexb-d9r-bkw9/bgje3 q.fnug2 lm;cn; ning to the difference in pitch of the engine noise between approaching and receding cars. Suppo3brb-nw 9jxbq/dnlkug-. 92fm;g e;cse 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, produce a beat f onio/ xve 0fe2ps3. .o+n(wnbrequency of 11 Hz. The shorter one 3o.nv w/eoifnps n. (b 0+o2xeis 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as i7):wi fggu(z it moves past a stationary observer at 10 m/s as shownu:gi(wg z7)if in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood f 7 j4m pfyk9uv,-yjd8: :yfrnzlow 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 reflected from the red blood cells? Assume that the waves travel wpd: vfm9ujr8 kn,j:zyy4f- 7yith 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 t:md4i.0u 0 /nxdkk( qn,ttoiwhe moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the batn:nx4 io0kmt qwiku. /( 0,ddt after that wave reflects off the moth?    kHz

  A bat emits a series of high frequeam ysb9i;t ylf2mw3woq 91t(i *4e: eincy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns befor oma2yqi*94(w ftwt1:9be i 3ems ;liye the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used e dic+y 1:4(ol 5mofdbto send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is 5i e(mol4dc+dfo :yb1resonating. 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 pr6u8ms)*5 jh mka9.xvp mm z2pi0hw7qa esence of standing waves, which can cause acoustic “dead spots” at vz i8mxhpam mp. uhwm)95s 7q2ja0 6*kthe 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 this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aa/3u :5 nhi i7fo(zv t9plg-vfluminum 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 “singvtzgov9 -(i5a7n3/ilu: fp fh,” 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 qh 51( tqnxxgci9zj)g d 2x.o(hearing for the human ear at a frequency of about 1000 Hz j ht1xd9z. )(5q(x 2ingcogxqis $I_0$ = $1 \times10^{12 } W / m^2$ 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 grougju/c4cjuu/9d6ja:sit ib 4/nd hears the sonic boom 1.5 min after the plane passeuu9j uba/:d sc4 t/jg6 /4iijcs directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is tv/l/ms:oi1u 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