What is the evidence that0g.7m eos8itb(r b9avdh o q(8i,wxv7 sound travels as a wave?

What is the evidence that sound is a form osbb i5ync;p6;e q0vr8p ( /dkc(nqk6 sf energy?

Children sometimes play with a homemade “teleph*ucx/ )qrrirp -zh0-done” 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 be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the othprdx -qz ruh* 0-ci/)rer.

When a sound wave passes from air into water, do yogaa3 01caffkj *gk. c,u expect the frequency or wavelength to changfcgkaa0 jf*.k3 g1,ca e?

What evidence can you +p( gje7tkw(kp(yrd,y lwk )(give that the speed of sound in air does not depend significantly on frequewy (jt+ ewgk)(rp 7l p,(kd(ykncy?

The voice of a person who has inhaled helium k3; fbxcnj002g7u rgmsounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p3(xk70nd u ouex/g du2,xj0c bipes?

Explain how a tube might be used as a filterp( gq4 8s e vu9:4cbbcpt;:mtw /jfm6l to reduce the amplitude of sounds in various frequency ranges. (An c: v;8b6 lqf4tebm4:mp 9pswcg(/ utj example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) /npz1ux4w d:xspaced closer together as you move up the fingerboard towar1 :/p xxwzndu4d the bridge?

A noisy truck approaches you from behind a building.yc3in8(r -qjnm q3k(3 j )onte 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. Expla3qo8rjky ne 3)ntqcni( m(j -3in. [Hint: See Section 11–15 on diffraction.]

Standing waves can be tpqp 9xdy.r6;-nuf) y,reo4lsaid to be due to “interference in space,” whereas beats can be said to be due to “interference iury. yn 6; tqop-4d re9,xpl)fn time.” Explain.

In Fig. 12–16, if the frequency o3o oo3e ;s;lawf the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart l w;s 33;aoeooor closer together?

Traditional methods of protecting the hearing of people who work in areas 0xj.lgiy+ 6bnk :r)aq5 ks ;vcwith 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, then feeds it to the headphones in addition to the ambient noise. How could adding morek n g s.+ir:l5bvj0;xacy)kq6 noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavdx:. dbjagqswi;r;: -e can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Inj x.;di qw:drsgb ;:a- 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 thewg1f gh/qx* y4dle6v- source and observer move in the same direction, with the same vel xgg fdyv1/4wq-6he*locity? Explain.

If a wind is blowing, will this alter thcvhy uqs6/0 joqu1p7gd4,v ;de frequency of the sound heard by a person at rest w6vyh1 7 q4vjuc,0d g;spdqou /ith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swiyg, qlux:g kzr078nnz4/s k. fng. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your re, /zq nrn0uy78skk.ggzl:f 4xasoning.

  A hiker determines the length of a lake by listening for the echo z 4kd:4xmv; dzof her shout reflected by a cliff at the far end of the lake. She heavk d 4dzzx;4m:rs the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship2 +jmedsdfod; 2u06t bve;ex; just 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 thfedo;2vd ; e;b 6j0t2sedmxu+ is point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavvq/ias f,p;.qelengths 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 drifting just above a school of tuna on a fo uopf2k*f8q,**mbqf hggy day. Without wa**,8oh2*b p uqmfffq krning, 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 splash it makes when sdu:oo p*bnh:2triking the water below is heard 3.5 s later. How b*: 2 ophnodu:high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conc+/fdp:rokg4b s9m )uf 6tmri) rete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, f/:u)ofsr+6gr m)t4ibdp k9mand they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-seconot3/e4pr+*:hc akktsdh -cbiw )/ iq2d rule” for estimating the distance from a lightning strike if the temperatuchswe-h biikt2d4 )+t3/cp* rq :o ka/re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitm7l1igq:ot g1b *sfoy2n4x 5p y of 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 ofkk )lx3*0.crgpwdh7uz h+ cq. a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prodj ye-fwbb yd5yu:u (qz:9- /3lhw t-cyuce a sound level of 95 dB when fired simultaneously at a certain place, whatlwb9(/w5fyyc -3u:t-jdze byh -: uyq will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy zm fu;(bka3y ;jet engines is experiencing a sound level bmzf(uk; 3ba;y ordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to /b 3gez6zb5ha-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rzbh5/ga3z e6batio 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 fa -qw7ra-/k*y ,7 r-s tdwcgdqrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o/tsgw--d-,aw 77r dakcqr*q y n 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 eardrummiwok q7b*15 d whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while theyc wja a8uaw/hg3. *y5 more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels youajyw.u8y5g h3a /wc* a would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m.ofblwi, t9yj/:u 3m z+ tl tnty4g3d2 in front of a loudspeaker on the djyy +wztgu,btl 94tf/o.ni 3 3:tl 2mstage.
(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 detecv hhe+( ;n iiy:a,jd;,/nviqekt x,6rt a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels difftqnv aynrvxkhed ii +;ji,,:/ e(,h;6 er by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of n f6cu -):lskqa sound wave is tripled, (a) by what factor will the intensitln6u:f sk )-qcy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, butu y sbaiftv a-ee/vg87h1 )c4+ one has twice the frequency of the otevacyfshubvat+ )ei4 /8 g-17her. What is the ratio of their intensities?   

  What would be the sound p q*tu8t 2 pj25vc5fmdlw(rr.ft( /svlevel (in dB) of a sound wave in air that corresponds to a displt2 5/ftr(p28u(tv s fjv mql5wp *crd.acement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lv c5l2xrgix2h46.x xloud as a 100-Hz tone that ha2xvxcixgx5 .h2lr4 6l s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wha;yd uo( w5m;evu 63fren the soun vea36u;;wy u m(5drofd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge r 3u; fkk5+ j ddizweiba4j5b54ange of sound levels. What is the ratio j uk53 4 je5ifb bkz;d+5ad4iwof 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 funda-wp.cttc3f4 su; r0q*uld2k0f ftqd :mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension fp 4*du.stq;fku t :q2fc-03cdlt0rw must the string be placed?    N

  An organ pipe is 112 cm long. W/*i amqef:rd *hat are the fundamental and first three audible overtones if the pipe ii :ad*rmqfe/ *s
(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 c d8 jnr,-m er(p7bo2zthe top of an empty soda bottle that is 18 cpr2-ndj c7oer8 z,(bm m 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-tc9ekk) zzd.kk ;p 00txube pipes spanning the range of human hearing (20 Hz to 20 k0k x9 .zck0tdkk;z)e pHz), 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 .5z f8n:nba2ag(wfpya frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered.b(wp5afz ang y: 28fn at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedo w +3b5gx/nn6yb3y;y pdw)nm) +glvz to play E above middle C (330 Hz). dzn ;o x635y/mlpyn)w3 bn+w) vb+ygg
(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 ,uoavm-j( :0b/lnntp of an open organ pipe that emits middle C (262 Hz) when the temperature is 2palju-nmn(o v 0b:t/, 1 $^{\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 2ybj *gcf-n(8t 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece 6zk,ann4 /kleof the flute in Example 12–10 should the hole be that musta64n,n /ze lkk be uncovered 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.nb:oor2 d1w elrx(e,f16eic e s.y6q resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any otxq sr .nr1:.eo,cy2f6(blo e6wde e 1iher 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 is open at both ends. It resonates at two ,nh 2 5xhqs/ fodr.32wibnz4psuccessive harmonics of frequencies 275 Hz and 330 Hz5z.qo/2wdi2pnx fhh3 b r,sn 4. 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 jbqp9 q88kkfb0e(-yt f3i6mdmz ew ,0$^{\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 akv0 7tf9ya; ujudible range for a 2.14-m-long organ pipe at 2uktj90 y v7af;0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximasi5fw z( 94apctely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What f wi5zpa(9cs4 is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,8p-: jdvb1iwu(3e xuvpdtov;z (f39a one of which is sounding 4ejb va-zpx3(;1 di:vvuf(odtp w9 3u 840 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency i o8;s9 otwycgss0 6i,uox zy..fg6x0kf 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 opera9 d;4k (ectvrptes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when dc4e;vk (9r tpplayed 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/sawo.(g e3 ;f v-j, vhc*6xzikc when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with awi,x ca;(hk3e -v * co.6fgjzv 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensipo yk:b(n68ryv(w h 2pon in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played tog(n2o8rpyy( :k6bpvw h ether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Ck3zf9zt:pf -a (262 Hz), but one aff z3p:kt9- zis at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, Av,i h:w +im+ 3zaznsx/, 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 fvazz:w,s hin + 3mix+/requencies 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 pedx/uif :t-1 kf cll :l9-vm)pmbm oq+)rson stands 3.00 m from one speaker and 3.50 m from the other +idm l :/ f91xv:mqo)tl-)l-ucfbpkm.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner h.oau: guq 0rpro; 7yq1ears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what7ugaq .q0:yo ur;r1op 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 acf7m r; uy2omn0,r t:cir. How many beats per second will72yfc:c 0um;, norrtm be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren issay/r*;ve jy 9 1550 Hz when at rest. What frequency do you detect if you move with avyy;*e /9sraj speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What q*vw e1vr8yjt 5 qd.4ii o0w6lfrequency do you detect if a fire engine whose siren emits do.y4 i lw85q tv rj6e*wi0q1vat 1550 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 moving;z cd.mlfygo.ev 4g+, toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly th+dyf ,4m. v.goel zgc;e 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 frequencqjm;;om8+ e9gp zli/m y horn. When one is at rest and the other is moving toward the first at 15 m/s the dp9mom;+ 8;il qj/zegmriver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves a8 nlwx,a eeye4ugs j1)h(v+-at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is tvy+uaae,esh-n()1gew 4l8 xjhe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the o* e;:hg,xg9fr glunn -x8(v 4*cgsaxbat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected ;*nh (ggcgoxg:9vfa,* l8x x-sn4reuwave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mopsgi)z0r0:2 sikcsf *ving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone0*r0igpi k z)ss: fcs2 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 ultrasoundfe7se pyg6cnd+g:*u +*nze ;j waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from thefc ypn*u*g7ene z de;j++g s:6 sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency iqn hp-g c8)jyj+ cjqj371(te$2.25 \times10^{ 6}$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 -vogxo emx6qd 19x 6u761lmsg m/s from the north, what frequencyxx6sg v16 oqegudx1o -m96ml7 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 lanyu- x6d:ov; dhd 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 Mach awyn08okgtp. l s7p/m qe+5m(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 mot y87+moe kw.mt0an5/ l(qg sppion?    $^{\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 sound i7u sh9gj56 qhr52i d*vcx,h l3lz.nkss d5k .h6 5 9vg,lz*r h2qchsnxuil7js3only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine ad:ih(lgbn -7the shock wave angle it prod d:gia(h7-lbn uces
(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 4a mktf )ypt40emu, x 57cp1 0+ql:(wwul noxr$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above 87*xk)c myfxjthe ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig.7*ym)xfx k 8jc 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 p fit(ek. d(x6sulses downward from the bottom of the boat, an6si e.ft((xdk d 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 tmu0 jtpp8xzqr5q : 70mhere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists 9cgsqkmqjb 27kj6,(fof many plastic6ck7b(mjfq kjsqg2 ,9 pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a penp.v sx 7 118ugfva9wyrson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such m. xf1197 nwsyv ap8guvosquitoes?    dB

  What is the resultant sound level when an n, dnoxarf2-,8ra+z2m s9s i z82-dB sound and an 87-dB sound are heard simultane - s,d2sirm ,fa zan8onrz+29xously?    dB

  The sound level 12.0 m from a loudspeaker, placed in dy dvjrh(.4 4noj76maq 6zj ,ot5m+otthe open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiatesdq5o4rto7dotj4zv,jn m6.j ma +(hy6 equally in all directions?    W

  A stereo amplifier is ra:r ysc qrwlyd3.thu)7.;4z xrted at 150 W output at 1000 Hz. The power output drops by .w4cy dr37z)ytr rhl u;xq:.s10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ea f9 1k6-kf-: ib z3pdfoe9c.wxlljp 6srs. 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 zk 9:pff ps.l6ojid6l w-93b kx1cf- ea jet airplane engine?    W

  In audio and communications systems, thyhw 9l:shghk ee39p; 7e 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 violi/2g8 e4vlj l ztxxv2bku0q(1pn is tuned 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 witsr1ht 5n v5syx. z*jh9h a fundamental frequency of 440 Hz and a mas tshr j1ysz595 vnx*.hs 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 wate0d2atos6r s:c -m bj7fr (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m oj6dsca2ftm 7b0 s:r- 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 e) z7*2z n(pcys5(wx r t /g,+inciddhnear a tube that is open at one end and also 75 cm long. How much tenxsz)p75c*g +2wi(t ,dd cryi( nh/n ezsion 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 one full loop (9d i+yie2tt0j kj)z.s2jg.nfbd) /e b$\frac{1}{2}\lambda$) 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 2:bfn d3dfjpom v0://w-blnnsources. 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 min 0/ 3wbp:n/om d-:nf2bdjfvl nimal 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 stationar37pf)sd z8lrlle15vnb h;e p5y. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whah ;7ed3z8 )15lpn fe5lslvb prt is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appbwvjv:e; g(m o8q 5-owroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz :;wv e(gbvo8q5mwo-j. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of;qxae ku1(0yi;zgud( cars just by listening to the difference in pitch of the eng kei yzx(1;uda u(qg;0ine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequencysy3 )c mr+9gf4o- waof of 11 Hz. The shorter one is 2.40 m lona-)4+gysf93ow or fcmg. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad jt;+oew, f-as 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 fret+fe;a,s -jowquency 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 flow in the aorta is normally ,*km/om*a 1f2n u o( e jo2z-*wnlsatxabout 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 *(oo* 2majnm-1o/wtl xk*n seza2f,u? 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 spe y*(o/0r;w-tpjl* pee c1cayb-v hja+ho/e(t ed 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 frequency of the wave detected by the bat after that wave reflects off the m/w;e prtp-c-( ejyha1 lhy *ob*0veco t/(aj+oth?    kHz

  A bat emits a series of high+ qjo:sp o22zq frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apar22sq pjo+qz:o t, 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 the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was2qml gkp m( km90opy2nzk1d 20 once used to 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 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 opeg2m0m0l m(1 2ozdq kkk2pp n9yn tube.

  Room acoustics for stereo listening can be compromised by the presence of h5x 1 2i a6lrwnv3h3e+g5hzsbstanding waves, which can cause acoustic “deaw3b ahxin625grz3e1lh+v5 h sd 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 this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”gskm8t u ou*dkc2(+rv z rhk675 t9rn: involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroke6urtvd7r(k m 2k+g5: ns 8ru*cothzk9d 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 thresh lqh:-5x4mv 6,bkan odold of hearing for the human ear at a frequency of aboutk,dqa4 m 6o-v:l 5xbhn 1000 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 obse 73i ei3k/gfq 7zhh(swpoth :e/p g.0mrver on the ground hears the sonic boom 1.5 min after the plan k/emzp:oiw(fqht. g/ 03 gp37ih 7hsee passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1nhj9 hj g9r*5s5 $^{\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