What is the evidence that *)em(w7+kmz*fgxrr p( 6am 4sb f-dunsound travels as a wave?

What is the evidence that sound is4nbmwuk3 b*2 w j,pov( a form of energy?

Children sometimes play with a homemade “telephone” bdjcx7w 1du3-c y attaching a string to the bottoms of two paper cups. When the string is stretched dujx7w1dc- c3and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequenccm7j 75q .z(ilo yp03pp:w yfky or wavelength k i5 p fpypz0cmyo.3j:q 7(w7lto change?

What evidence can you give that the speed ) tl ..3tnmnx+(zu fgyof sound in air does not depend significantly on frx.t +tzu.l3nmyg(n )fequency?

The voice of a person who has inhaled helium(elg w)-jf3a c ry n.5+bzva(chq 9 h(lgix-,y sounds very high-pitched. Why?

How will the air temperature in a room affeei0vomfmcqjnn; a s. 5jl+i,6c1t* /dct the pitch of organ pipes?

Explain how a tube might 7fb :eb80 eiwilsc .4bbe used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is l0 wbi4s .bec8b7fi:e a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov;6f sk 4w+,kt8bmf:*tiz d hdee up the fingerboard toward the b s:8,d+tdz6 f wkm; btf4iekh*ridge?

A noisy truck approaches you from behind a building. Initially you h/x+ 4m3pc g4sec f-mwpear it but cannot see it. When it emerges and you do see it, its sound is su/wcgx-p3 me44f+scpm ddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spa v d(*zl)c9hy1 mlp2s,)sm bbrce,” whereas beats can be said 9b1)blrz(2y vssm ),m* dlhpc to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the8oqg.w xv7 +uh speakers were lowered, would the points D and C (where destructive and constructive.uv7q ogh w8+x interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in arq0 /agjnd(paf*+hp*p(sx(tbh3u me 4eas with very high noise levelsgqh 3p f+pjeb(d ( ma*uashp4/(*txn0 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 more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wacpxr wn8*rx99bx;g4-je* xk, wkr(swve can be thought of as a superposition of two sound waves with slightly different frequen*w*wk ng9x(,c s9 ekwr;rxjxp 4b8x -rcies, 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 k:wmz;,8z whz0ulkf;observer move in the same direction, with the same velocity? 8hkzz z0;w:w; umkl,fExplain.

If a wind is blowing, will 4p.s ef*: ;*ph(ea) nm))ioavyl pvlr this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavefl rl. *aoipn)am):ps v )y(4;ee p*hvlength or velocity changed?

Figure 12–32 shows various positions of a child in motion on zn xc- q:hymn9be,r- 0a swing. A monitor n zme9:qcn-ryh0 x-b, 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 reasoning.

  A hiker determines the lengo1r q9ob (,qnr0 c*ccjth 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 after shouting. Es,nqcj9r1 b ( or0ocq*ctimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echcwgoand:.yep5 +jp0x);9f lg v4fh x;o 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 significantly with de4 x5 ;ae0.jp9gy+dlcfwx f)g on hp:v;pth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airz;.1mgi fcx7-i zuuw *rm7- 9 wtb9axr; :fjbs 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 drif2csife o (8g*/d-f g-g-lshj lting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothe ig2f(h ed-ocss l/jglf8-- *gr 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 to0 isl)ex*,s.9vhq2fbr l. r y oel7l1ep of a cliff. The splash it makes when striking the 9qoe y.*10l lrlhv,r2)flbes s.i7e xwater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, vm4,fa3.eo;(t1i lhwpnw 5v gsees a huge stone strike the concrete pavement. A moment laterthan e v,; 5.fli4(13wvogwmp two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent m.i/yp is0wamqq07( e error made over one mile of distance by the “5-second rule” qw 0m0psyiqma7e(.i/ for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitd 6 mre9 7*38ypmhybbty 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 of a sound whose intensitd4zjs zokj+h rb -l08*y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyyh;60)lb9u+ok6dkgz+ x typ.yqi-ct at a certain place, what will be the sound level if only one is exploded? [Hint: xthlq0)-g 6+cyyi.k+ u zkt69o bpyd;Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpla(j nqihk0 cg)ug:yz7 j;uhbd*ud)9 7gne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience ifq*gyud(kguj)hhz0n)d7 ;bgicj: 9u7 the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signano+ly;2 q 8n 8n+kstgil-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intenoy n lnqigk;2s+8+ tn8sities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spealcyuy1*5ob* o h2a m6oking in normal conversation. Use Table 12–2. Assume the sound spreads roughly m1 yolbyou5c*6* 2oah 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 isi0gqf2e q-oglnpsx eg-r) u)5( 1hc8m $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest yr3*l6yu ce+ w2swv 5f)gem1 xamplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a pointwfs2cxv16 g3meu + y5)ery wl* 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front oflo a 8vy8ks vfqpv614* a loudspeaker on th4lvsakp ov68 1 f8q*vye 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 sounfoxz;o8 9shd;pvgq: mrm6rj( 1 8v 5zad level of 2.0 dB. What is the ratio of tx r9: 6magv885ds(mh;fzp;1o ozr vq jhe 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 factor will the inab1n6s)nh2tm ;j hr*mtensi mj b)ht;*nsh1man 6r2ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemeq1k(kt+zgto5 nt amplitudes, but one has twice the frequency of the other. What is the ratio of their inten(qo+tgztkk 51 sities?   

  What would be the sound level (in dB) of a sound wave in ad o 8x8g;/dqpu mprp aye1(u)4q6xpl6ir that corresponds to a displacement amplitude of vibrating air molecules of pxpd /d u(rq goax;)6 p1q6488mluey p0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10+w(31kn jrokg 0-Hz tone that has a 5kgj3on r( +k1w0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when m vgn t6pi0k8m(,vz d)the sound level is 30 dB? (See Fig. 1m6m t80g vink(),vp dz2–6.)

  Your auditory system can accommodate a huge 5p d4nq6)g qkwzdbi-mf 5x+m d3vd /u3range of sound levels. What is the ratio of highest5 gvx6dnm- 3) zw5udi4+kfdpq/md b3q 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 vw z p9cjk-c;6fundamental frequency of 440 Hz. The length of the vibrating portion i;kwp vjcc6 -9zs 32 cm, and 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,a7; / cwr)uq9 yxkenr and first three audible overtones if the pip)n9 rc;ue,q7y x /rakwe 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 blowiy8ejf -, xh m8zg0 ims1x,ip1 b38jpwing across the top of an empty soda bottle that is 18 cm18pii3i-jx8pxh,f,0es zg y 8m bmj w1 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 e+prd kdi;)oe2h*)j a a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of dkjoh 2; dapeie)* r)+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 h g.j9blx76 q swilqf23armonic. What will be its fundamental frequency if it is fingered at xjls69.qqb7gf l2i3wa length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7jyvze z95 )88n2gnjfy /yw o/b3 m long and is tuned to play E above middle C (330 Hz)ez)bj92f/5yny yj /8wz8vogn .
(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 C (262 ja,6q z;0 (.v0dqmaovhks)h0aoz 5ufHz) when the temperao,m(ks;50 f aqz zhajhu00avod6v .q) ture 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 at7 q .e -0t 7nmn0ishtxl)eqg,v3uyxe7s4o rf- 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpx/l y ,*-e41ued k(xfnpp(kx jiece of the flute in Example 12–10 should the hole be that must be uncovered tox 1 nxue, /j(fpxlpy (kke*d4- 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 resonamo i/j x*6agb-k aasv 0;6w:kate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwe66amoskj:;*a i/g- b0akva x wen. (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 1xr4s9q 8igjj82 b rw-k,d d2vh.80 m long is open at both ends. It resonates at two successive ha svjd2w,qrk rh8dx48 i2-g9bjrmonics of frequencies 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 h230mvhablaqm o, 2j +$^{\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 withinw) 4f3wz *sxf*bx5sf+miwhq i+ 2uoh6 the audible range for a 2.14-m-long organ pi mo*ub zh sxf3ih+*x+fw4sf)w5 wq26ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside a oz jlb)t7p1uxnze(7)d i.k f7nd bf 7dpj(7o l )tkz7ux1zie).nis closed at the other end by the 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 beat every ;r)iu(0l/2m 3veb/xzyzre-uy m i5p u 2.0 s when trying to adjust two strings, one of which is si)mpl 0r(mrx5 /3yez2u uibzv-ey;/ uounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middles hu,k9v e;q)r;/*okw chxqm- 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) ic v8ezyehi 74/e /rd;t5z2uxoperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine hci8i 5ve7ey /4zu2 ezr;/xt dof frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/cq(z/3 khhrn-t 2g; iss when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the i ( th/k3hcgz-rs2;qn vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one r- ,ecdkb0sq9 *sro;id;p5 frstring is then decreerq;crp0k d9s s,d;5 b of*i-rased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluauw0zx jk.,t hj2 ic54tes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 24ij5cwx.jk 20t,huaz 5.0 $^{\circ} $ C?    beats/sec

  You have three tuning 95tueo3b uiueuhky13: v 1r5uforks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the posuu eth3:3yku9ov5 buu1i 5 1resible 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 person stands 3.00 m from on.chgmo1eq u*w:./x e le speaker and 3.50 . /1x *ce:owlughm.qem 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 vibratin;hjdbn. zu l+tk4nw 66g at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, wk6l+zb6jnhuwd ;4 .tn hat 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. Hodzb l vz-u+2 zdr0/ hptavp8x0j7w 9h:w many beats per second will be+zjzr ahp 902 p-dub:0w/vxtvdhz8 l7 heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whemu6pho :iz *7nn at rest. What frequency do you detect if you move with a speed of 30 m/s h np:67uo*m iz
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency du8baga-::,dol -s oyur prp0/o you detect if a fire engine whose siren aluogby:dp0,p usrra8-:/- o emits at 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 toward yo4*aepj2,7 ak*f/:;atjozz mxbf xce;u at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are the;e x/b7p f m;e xf4zj2ckz* aata,jo*:y 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.nmpl7 innfbk/)5 m*i p z9p-c8 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. p m-m 7iinzbn npp*)95lc8f k/What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound,azn rjm,*o pl rpha()(5k -my waves at 50.0 kHz and receives them returned from an object moving directly awaya) zk,a, npoj 5(lh*mm-r( pry 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+ 3rx15 amc k8sxabw0dj/ja s8/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency doesxk dws8rac jb/3 81+mjs0aa5x the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tub:a32guu 48ej+cnc 9 zq 3jaa,bhga-yja was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of cn+ju-h:bq gj3c9,gy 23ae aa84z jau10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wftbc)z.h wywc ,jp 0t*20.rs kaves 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 1540ft t2cbrh0sp .c,) wyw.kz*j0 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 ult s4xp,/8wn yaerasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind9g/c(cliqm/ h u 1 ur:b4-kzgg velocity is 12 m/s from the north, what frequency will observers hear who are locatedm-i9b( g zgqlcc/r h41kgu u:/, 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 28.cxrri8)3 ahxv nuk 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 wh :nfn: g5zhe+dere the speed of sound is 310 m/s (a) What is the angle td:n5z:n f g+hehe shock wave makes with the 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 planz i41vp m;tv4wd.q1haet where the speed of sound is only. hv4dzw1pm1vaq;4it 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 the shock wave l;7tbbu:8pd sangle it produce7u:tb ;lpd 8bss
(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 (5o9m:w wm op/h:z uhn$/theta$ 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 exafl*;lt+u5 dhot r3j*g ctly 1.5 km above the ground flying faster than the speed of sound. By thgo *ul ltj*fth3rd5; +e time you hear the sonic boom, 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 5tfp (k 0z*batdt2a6 esends 20,000-Hz sound pulses downward from the bottom fd(0t abk*e256p zattof 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 range8oh 6v*acly8w ? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ozql lgj4 g 4wi2p/e do6yv61st9 a(9fef many plastic pipes of varifiy o1lqg ws24d4/ evagz 6pjl9te(96ous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes b3:5;p e2 oah8z subega sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoesb32:;e5sebuo8pzg a h?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dwz0m(o4 xajcei66i k3B sound are heard simultane ojwcik m034(zeia66xously?    dB

  The sound level 12.0 m from a loudspeaker, placed i2vq h7vgqvnq- i-z c1;pc+m),p bair.n the open, is 105 dB. What is the acousrg -q 1vqmqi;vp+i bp,c)2-ha cn7v.ztic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ratedk*c+s/r lq2w v at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powewk/2sl *c+vqr r output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tmm lp1z x*g- zdpwmr,rt/vmuz g0,+sp9:lb 6( heir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of(w,p/r:v-ulr b+p ,zs p9mg06mmdz1xm * gz lt 30 m from a jet airplane engine?    W

  In audio and communih,x2 zn7y;zh h i qr4/s0ffto4cations 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 tuned to a freque8ce6qgl:pt n28 tjlw/vsq: nr xp062p ncy 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 lo* e.dn 6c.fm1t l;u it4vj:nflg1mby1ng between fixed points with a fundamental frequency of 440 Hz and a mass per unit:*nndll1 b m;ef1 m1c.v f64t.yguij t 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 w7h vsqg/85j uuater (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air i58ujsu/q g 7hvn 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 and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is op xo8ajs 63 hh1sjpg99cen at one end and also 75 cm long. How much tension should be in the string if it is to produce os6xj8ga9hh 1c jsp93resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as ore9: gmz83gl 9s ium.) )hrqelne full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from t .y5u xcw+o;bku ,nt)awo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther f ot b5ncyu)w.x,u+ ak;rom one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H/k-w s j8* ygeb:z1)w3yz aldoz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency whl jg*)s/y-1w3 zabeozy kd w8:en the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam ta z 4y uhgj( 27wirw;og6o5yr9rain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (ji h9 g4a2( z yy5w7wrrog6u;oassume constant velocity)?    m/s

  At a race track, you can estimate the scyzw6lli4 /mox9 +/s epeed of cars just by listening to the difference/69swi xy/ oz4 lmc+le in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toge aj +33e(htrtsther, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othateh t(j+r33s er?    m

Two loudspeakers are at opposite eeq k fq *;jgcs33wu6u6xn1 9:bxbsn) 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 frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is6e1jq3g f3swbkxs; u n)6qnbx *9:u ec 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 o ttcwmbl smyr5r1;1z553-ui 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 wirow5m1m 5t5 -3t1i rlbusc;yz th a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m 4x0t cpi7zuc5ty 1f5c/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 detectefpct5yc t5 74c izx01ud by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it kf5 c yzbl8 7odn1s/k(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 dnykc57o f (lkbzs8 1/one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sigtevw y,m(*s.ui da q2(nals 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 opmqdti (v(w*a . es2,yuen tube.

  Room acoustics for stereo listening can be compromised by the presence69c3 +hkeo k/tp5srgz h4o)q w of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodeskpkhet3w5 +qh /)s zo469orgc. 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 ao/tn4m k/z ya9 5fd2fgluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, lo /zmy5afn4k d og/f9t2ud, 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 hear jpi( :do;l:rqing for the human ear at a frequency of abo(:jp ro iq:ld;ut 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 M:k5/lvuftzemzq. 5)i3h *oesach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passesf s5meq.tz hk/)ul z3* e5iov: directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbon6 nzwdmsvn6w ne2:67at 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