What is the evidence that f azb g1;psq4vd p7/3rsound travels as a wave?

What is the evidence that sound is a form of energy?;0i:utfqxgoyqwpoi*t8y :aq 3 )o x* +

Children sometimes play with a home2h 0qsm28llou0+i sk4l;qshymade “telephone” by attaching a string to the bottoms of two paper cups.m4qk0 y+h2o0 s l8ls2hqis;lu 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 other.

When a sound wave passes from air into water, do you expect t1vau2l4hn.i fw/m cb4he frequency or wavelength to ch/4vwicn u2b4 1hm.alf ange?

What evidence can you gid sg,, q9xt8udve that the speed of sound in air does not depend significantly on frequeu9x,gd qst,d8 ncy?

The voice of a person who has inhaled helium sounds very hal+ )o-;.zqayu bl9 xeigh-pitched. Why?

How will the air temperature in a room affectv+p ( tg9y c)2 es/ux:kq0nnve the pitch of organ pipes?

Explain how a tube might be used as a filter to rf *u*i9dxc 5mjfrt2:ceduce the amplitude of sounds in varioufui9mjc5 ftx*d*c2r: s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethaq5k b4ys hi*w3x 3eww.,7flger as you move up the fingerbe,a3 b.h ilgq*54 yw7kw w3sfxoard toward the bridge?

A noisy truck approaches you from beh p(l3vo./wllr/bd x4k gm w;1oond5y- ind a building. Initially you hear it but cannot see it. When it emerges and you do see;xmyn oo/.3kdl-54vww 1rg o/ p(d bll it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in o0sscmhzpp2 /zy4 0. gspace,” whereas beats can be said to be due to “interference in time.” Explai. zcy04/zsh psom 20pgn.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points z 9.om2n98srpanv1w/hu5gmc D and C (where destructive and constructive interference occur) move far /v1mngc829u95pn m swoza .hrther apart or closer together?

Traditional methods of protecting the hearing of people whps2y,3l:qvagc*6s 8gngm5 fh o work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sovgna g28sc 6g *syq5lp, m3:fhund levels reaching the ears?

Consider the two waves shown in ehx 7+z8jme lsocr 5y:1h7wtz1i :vo6Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (aor7:87he l mzs czjw1x5:yvei1oht 6+ ) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t-seqd:a br- /s0q.5 n,mntgmvhe source and observer move in the same direction, wisangmv-.:t0mbq ,-q s5d /enrth the same velocity? Explain.

If a wind is blowing, will this alter the freqs9888vvrcexr2 / ee mrhyv,. uuency of the sound heard by a person at rest with respect to the source? Is the wav8h v,rr8 xsvr9mevc2e 8u/y.eelength or velocity changed?

Figure 12–32 shows various positions of a child in motiuuugj+- vk *8ion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain you+ujgk8-v* iu ur reasoning.

  A hiker determines the length of a lake by listening for the echo of her f*l e//m pod67ujq ol ,qw0 q4m1xlz/mshout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estim/lw0z do4/mlqo/1e ql*76jup x mf,qmate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterli4 jpz,yih9 /eu7prce* ne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depe*h4j, r/z7py9 pcieuth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ao2r2rk21 0 mxni89bxee vkj2o +p(stair 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 dxzp1(ru j:nrek /x7h6 rifting just above a school of tuna on a foggy day. Without hk71p6:rn zj(x/r xuewarning, 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 stx j+sxs+h9a 81b0wr1bxo dot3riking the water be81w a 0s+joxo+xrd9 3b1htxsblow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear4r*x*7o hnp af to the 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, anfha*o xr4*7npd 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 “5w;vg1nz iejq0g o*+(p-second rule” for estimatijz qvipe*w0+nog ;1g (ng the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityr29h ,6ccxz(8v6sld s( ncppag 4;kca 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 oo orx b:u-um 9l9v1jz3f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prod:-st c2 3atsequce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level itt2 e -ss3ac:qf only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain disy5+o v()++x 5i lhwanud 5scxctance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’ ulycwn+ (5+)x5 sid x+co5ahvs.]    dB

  A cassette player is sad;swfcgr vepn4))vb(w; k)m4 id to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =g4)m;bk; fwvs ncd4)(wr pe)v    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output ofzq y m-lrsbd :141dkqin8+7 .v 6gbahj sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centrn1 b7z4.:m6 hj d gaqvqd-sib yk8+1lered 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 w4gj2qq52ge x area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more n mope)/l9jp l/ys9ws:x7(rp pwxk-3 modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m 7pyp:en( -/9lrp3xsmk )ws9j lw/p xo 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 iu7 gtj8 bzoy5:n front of a loudspeaker on the stage. t 5gyj87ouzb:
(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 detpk0+g 7d6xghq ect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes x+dkhg 7q60gp 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,a h1an9le0kd the intensity increase? Incred,l 19n h0eakaase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacevo+yn*a*z t4p3wl : ,a.t mvjsment amplitudes, but one has twice the frequency of the other. What is the ratio of their intensitiep oy43nv*zvw:,.lt jamt+a* ss?   

  What would be the sound level (in dB) of a sound wave in air th d5sk ojbva4+ f*19gnuat corresponds to a1f vjsbg49*ound5a+k displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level t*)p :9 rdqq,2tk q kh6vly0jwoxzd(3 ko seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.h*0dk,qkxw j)r6:3lq( p dk v9tqzo y2 12–6.)    dB

What are the lowest and highest frequencies that .rfugv9ux zifd/ca52k2 hul 5mw460u an ear can detect when the sound level is 30 dB? (See Fig. a29ul/u h.cdg 2k5zmv6 5 u 40wixfufr12–6.)

  Your auditory system can accommodate a huge range of sounyr cd0l.l7n*y, q l*sfm4usi3 d levels. What is the ratio of highest to lowe4sscln*iyr*q m3lldf0 ,.u7yst 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-ju0hu3k xmqi5r;mdc g7+uf * 440 Hz. The length of the vibrating portion is 32 cm, anux7 hgud;iqmu-3rf 5k+ j0*mc d it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 tc/beqh ob i ta1*z.,z6o;sz9cm long. What are the fundamental and first three audible overtones if the pipe is 1c* bzzq6 h;9toz/be si,oa t.
(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 dwcd*m(rvu95a*fd(pacross the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tu*cd5wdva um *9((prdfbe?    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 pipem jo) :c 9sl( pyd4lvu+tr7aru*e;+ffs spanning the range of human hearing (20 Hz to 20 kHz), what would bufrfr7l9o:t cl y );*a+ vmd+(4sjpue e 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 i1wav- o4-7:k+ lscdphwew5z g ts third harmonic. What will be its fundament14scwzp+v h 5o7awe: gkwld--al frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is dg1km. ;lxtv 1tuned to play E above middle C (330 Hz). lvgk11x; t.dm
(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 orgfqo, p 4wphtpwbd2z (-6;60nmyx 4j jsan pipe that emits middle C (262 Hz) when the temph6m sx0p2p6,-bw 4pt;qnj4(f wjz oy derature 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 2r+mjmk )5 dqvj;l-u,d0 $^{\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 7 tiqa/8c:qkh c1tk;x;cs -w tbe that must be uncovered to play D above mikc i7w ;cxtha1;:c t/kq-t 8sqddle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 ttevutb8z / *5Hz, but not at any other frequencies in between. (a) z 85tvtueb/t* 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 ek 1dz e1(p an0im9lm-nyizbzw;+ p:)long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What iy+9 zln zbpe mek(:0w;-dnpii z)1m1as
(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 u:m8r2y svebc 6u *b)d$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long or 5eblt+i 03c9f+njf etgan pipe lf+ f09itcebe 53tn+jat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is d en-h4 1/0.rurut niu9i0yj+cfj5jc approximately 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 is the relationship of your answer to the information in the fn 01uj. 90e ur hrin-y+cu5tj4 jcd/igraph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 *t,n*4j +hdjlwv/puvs+.zmog o eq 94*9rd vss when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequeq*dhje.nv orlovz 4dt*j+gwus4 99p v +ms,/*ncy is the other string? ±    Hz

  What is the beat frequency if middledq6i z;8gn xd-5wol2l 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 (bra igz/rt dbx8 wa-wql ,7;l(-pqnd X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a /( itq7-;w al p8-bdrzxgwq,lshrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundexk) s85q9/as(38fxn3e dvj jnki rq9a d with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain83s 5qf d ix3n9x()qaej av89krj nsk/ your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension inkxc y -v adfa6e17g58n one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hintvf a n yc5d8a16g7-kex: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each,)z(xklci r-kzl;) sy try to play middle C (262 Hz), but one is at 5.0°C and the otk r(l,zysk - ;)czxil)her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 ssoh huqyrnu7:9*9: zHz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A os 9 h7u:9*s :yhnrzuqand 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,xx 5aule 2:vi m from one speaker and 3.50 m fromu,2 vai: exlx5 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 vibrating vuuss4(1v a o0at 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, what mustosa(0 vu1suv 4 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 ob)vdidxaa ,t,t1p g.+f wavelengths 2.64 m and 2.76 m in air. How many beats per second will be ,d 1bxtgaai+) .vt,dp heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certai9x6iaj)r ,hj fq0gn 6o;f1jnx n fire engine’s siren is 1550 Hz when at rest. What frequency do you detect ifj ,g)6 ;aq9jxnnoi6rf0hfj 1x you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What wtd51 a-so8yia 5ebvw-5qb-8m +qd wffrequency do you detect if a fire engine whose siren emits at 1550 Hz moves atq-1d5fevowb idws- 58 8 w+taqyab- 5m a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequeny 0 6*clyl (acku+ q9 he9z7,ppiwkwsy.+t:oocy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? +u a76t0zlw9oo q e( yl y ,k9cp:wsyk+.c*ihpAre 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 siq(0a i6m5ncbqusq gy42mx(/p ngle frequency horn. When one is at rest and the other is moving toward the first at 15 u/yspiq g5 c2 x(4b(0qm mqan6m/s the driver 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 at 50.0 kHz diy)7z6rf d8p+ dqx(1 i h9xarand receives them returned from an object moving directly away from it at 25 m/s What is the received sound f7x+(6 f9dr1yad dri)q8hpxizrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bqa s+uw8/gw -gat emits an ultrasonic soundwq+ ug8-s/wga wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat bnht,369ei k)mnk(i dtrain car at a frequency of 75 Hz, andii ke6k,tnd3mhb9 ( )n 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 measurdmh9bm /em0y 5e blood-flow speeds. Suppose the device emits sound ay0mm /e hm5bd9t 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 the sound source?   Hz

  The Doppler effect using ultrasonicw 2*hje,0w6zg j:spkchcft;2 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. csl(;u9u/ -lli(hj5e1ki2-obsfpr u When the wind velocity is 12 m/s from the north, w2s1(l blujlp-u ;-o/i9h5f( sekui crhat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object+lmhc) u;e- nm moving on land 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 2.3 where the speed of sound is 310 m/s (a) Whj l.nfvg 1: 0 qtgqob3+u+7yetat is the angle the shock wave makes with the direction of the airplane’s mt+y 7. gb0+guj:o3 le f1tvnqqotion?    $^{\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 atmosphe:*2j,h3 unz ibqruai1re of a planet where the speed of sound is onl1* z j ahi,2bqu:n3ruiy 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 sejqn8 a:i5 ikg +8.jjmtrikes the ocean. Determine the shock wave angle it produ :jq+8ngmk ei8j5ai .jces
(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 d+pmw:va 6ii8$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plansjce30ikhn(4x-0zc rf;zd z1e exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic bx0 d4z3kjfzzh e( ;sicn1c-0 room, 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 0 tm-qnzis13)ia/ mjkthat sends 20,000-Hz sound pulses downward from the bottom of the boat, /jqi i s mmtk1)0az3n-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 audibleb qs)ca20 i(gs2v eer c 5v;lk5urmp1( range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sg 1k - ;b6qayqoi4;ca+8weyzk ymphony. It consists of many plastic pipes of 8;a-4ia1 6zkygoc b q+eqk; wyvarious 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 a sound close to the threshold of 2v xs5dl3pc1 hf:eab )human hearing l fc 5)ep2b3vx: h1ads(0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sourhcxdm zljt0xnk188 ; t(g )5(-endoznd are heard sx8z0;8rjnl( n mo5c(dkd-g xz tt )h1eimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plvfnxj/4h1 c5 haced in the open, is 105 dB. What is t1 jchxfhnv/45he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powt(s: ;vux;h2 ahi+gdr a0j+nkhmg u-0er output drops by 10 dB at 15 kHz. What is the power output in watts at 15k+sx+(gut 2 v- r;mh: a0u0;jdahg nhi kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eh ; nr5sqdep)k3zg37qjld - 4iars. Assue3s-d)kqlpjrzq57n h ;gi 4d3me that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationt lo3 q(y7+jyos 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 freq)z3: gpi:bdiz kvj,3 euency 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 violinlb:8,q cd,v 3yski o;c is 32 cm long between fixed points with a fundamental frequency of 440 H,visc8c;b,o k3 dl q:yz 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 wnn1b .:9zmckojacz;) ub+6))npdup vertical open tube filled with water (Fig. 12–35). The w+:pkbnc 9p ncab1)zu); du. )jo6nmzwater 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 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 tu)edb/e1naya(,oe p sh 0o5:sp be that is open at one end and also 75 cm long. How my:)ebhda1n,e(ps pe sa 0o o5/uch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop 0jr20azx nkm1paa:a6 w (q8wz($\frac{1}{2}\lambda$) 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.eu0 vr to8 .ti91zuyn0oj6 i0,4u kulm The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds uyt 04mle9,uoi8 n vuk0. 1z0jtu6oirthat 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-Hu+(67oflf:j i uh ssm,z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat,fs (o6 l 7fu+uij:shm frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trmr)o8,0c1 bghhf fo6 dain whistle as it approaches you is 538 Hz. After it passes you, its f cho 18ho,mdf0)f gr6brequency is measured as 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 listening: u isr.ut95woxiu a06 to the difference in pitch of the engine noise between approaching and receding cars. a95u iso.tuu:6x 0ir wSuppose 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 frequency of 1iw dosu**e9 r9* t3ff447lmba3jetp5e-ioil 1 Hz. The shorter one is 2.40 m long. How long is iiood9 495ej-btie*r 3l sl43fatw uem 7fp**the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s qq6:(p 7hnkca5x iz7ftationary observer at 10 m/s as shown in Fig. 12–37. (nfh5z 6k axp 7ciqq7: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 flow in the aorta is normally about 0.32 m/s wha,(2nd j2bh lw:dm7lhbt beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red hhl w,:nlbbd227( dmj blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mp y3p,a.0 byrioth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 5i,ypy b.3arp0 1.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency2dvx5z3pot 8y sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eac 5yo2tz3 v8dxph is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one /ak(v12s +wv8/yrmo,m8mr m 5ekcnkh 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 op,/mmo (sav82ymkw/ hk k1rcrv 8 +5nmeen tube.

  Room acoustics for stereo listening can be comproho v:41 ep,ilj fx,hf.mised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. ,phf v.hli1 o x:,jf4eConsider 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,2ptim sdf5 pgn64x)oyzu /j -)” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rozis px2yfg)pjtdo ) -45mn 6/ud can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of,l2yj0/psq e d abs0 j,qped y/2lout 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 obset h5z6o ni+;tg7/ahmf0c5,y6jt u 9gr yztpv 5rver on the ground hears the sonic boom 1.5 min after the plane passes dirtjt gn 5 6uhchi7 0z5;p,ot/z5vat9y6mrgf+yectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1bls1rtku7 +pc m n-5aash ,)f65 $^{\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