What is the evidence that sound travels apq7)s ;gazhd* .i po)hs a wave?

What is the evidence that souwsi6 qe/5:omkn+lwyqs p;9 rxgv n8q 7j5y,q4nd is a form of energy?

Children sometimes play with a homemade “telephb w(ac/yv8j38/ kj2sao+gh i jone” 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 83g2sj bw8 /h+o/ a(ivajcjkycup to the other.

When a sound wave passes from air into water, do you expect the frelr(a7d i, srgh dl*)q7quency or wavelength to chang),g*h( l7rqi sa7d drle?

What evidence can you give that the spef98f g+-iul6ntn br, ued of sound in air does not depend significantly on frequen9u ,uf+6-rl f gtnbn8icy?

The voice of a person who has inhaled helium s q04,nk khit1k)e.cc9yo ,x kmounds very high-pitched. Why?

How will the air temperature in a room afb kkw ,kj( 9m)vvl.+gnfo/a8s/t w w(bfect the pitch of organ pipes?

Explain how a tube might be used as a filter/3u,:k85b iu whqyiy - qfw81vvhea- o to reduce the amplitude of sounds in various frequency ranges. (An example is a car muf/8vwqa-:5 by3,-uhvhf ik oqu1e8wi yfler.)

Why are the frets on a guitar (Fig. 12–30) spadnysc(+uz q,5 e8ol;n mxc2v :ced closer together as you move up the fingerboard toward the bridge? ys5xnol ve uc28q( ,:+dmn;zc

A noisy truck approaches youwfj-; 26 rndk6phdr/w from behind a building. Initially you hear it but c d w/rw6-hpjf26 rkn;dannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” 7/,eff 6klfsj4o1o4: 6su6q6cd vmws p w8lhrwhereas beats can be said to be due to “interference in time.” Explain.euo6l:okq6s44 /d76p fwcvsf8j,6flw h sr1m

In Fig. 12–16, if the frequency of the speakers were lowerezg wr +zw)p0;kd, would the points D and C (where destructive and constructive interfer w+r) wg;k0zzpence occur) move farther apart or closer together?

Traditional methods of protecting the heari 8 ua:3vn3 2trt7dzum9 5qqseing of people who work in areas with very high noise levels have conqund3:ar mv95ti82t7zqes3 usisted 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 wave ca87 :qay0gt jfrn be thought of as a superposition of two sound waves with slightly different fre: 87 ajryg0ftqquencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction,0x rd4v/)tra87naqx(4c +gbzq (o ls n with the same veloax74+)s8cq(4ln/t xgran(q rvodb 0 zcity? Explain.

If a wind is blowing, will this alter the frequency o 7;a s94zbrab83y fvuff the sound heard by a personb84uy7f3rbs vfa ;a9z at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows va )t2f s5w nz4zb0sr:vzrious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the5zf4)w0zb: n2trszs v ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length o cve c+6-.zafuf a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. Scc .-fv6a zu+ehe hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinp6wt tlko;7m w ih+)+ye. 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 signifpy;+l+w )t67kwith omicantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength088 okk -:nh.+vwj w3w5g alc (catfyvs 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 foggy day. Wq/tk-q 1j(e: 8cyefi(zsf , jpithout warning, an engine backfire,1(czq /yj (f -qeksji8t:pfe 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 wt5;k 7( ny,jovxjpk,g hen striking thv5tjk g(7jn oyxp,,k; e water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sx+oz;4z wb,o , dhy;kmees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table,4kz x wybhod;;o, m+z 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secoa /pt9 w;l8ip eot.go:nd rule” for estimataw 9o:;t e/tl.p8gpoiing the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofw2 e-htd xt75 y;nlpp+ 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 haoa ..,x8tvq,vg9n pof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundkpuvpf d. gufg-di0 //23thi8 level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB3 8hift0./i kdupg-2/dvgpuf ’s.]    dB

  A person standing a certain distan zhhab1l5f.a 0ce 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 engin0 hafhl.1b5 zae? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas:ayn3u + phnm/d-.oa 6ck 1pss for a CD player it is 95 dB. What is the ratio of intensities of the signalsk 6a:o. nuymc nsap p/3d1h+- and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perpi35fk3 n2w9urd z gc1son speaking in normal conversation. Use Table 12–2. Assume the sound spreads ro2kz dp rc3fw gi315un9ughly 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 striked)xcrb35iahd7 oj- ql7 rzw,9s an eardrum 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 the more modestwg3 q o90ekhbgj-3 +nd amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a louds-9w nq3o0+g khbed3gjpeaker 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 wvt7h986uwitv9n ,pain front of a loudspeaker on wtiu h89 n p7t9vv,wa6the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dx-;i yj-;i:xb 1 nuqmqB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11u-j q :xim-;1ny ibqx;–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi2:e+vb (k govh; 63o:zzg yjlmty inv log gko(y6mh;b: j2 :z+z3vecrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampli uoo8jc -zt*xjrvj1*.tudes, but one has twice the frequency of the other. What is the ratio j*x*j tjc1vzoru.-8o of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thjr3a(c be g9eg./riz/:rujz 5at corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 .zbe/jr rg:a iuz (5j3gec/9rHz?    dB

  A 6000-Hz tone must have what sound smkar wt,4:xe1j4 wo 3level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See 4wt 3 jwmeo krax1:s,4Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when tuk 8b/ 8a5vmzuhe sound level is 30 dB? (Seeauk/z5 b8 uv8m Fig. 12–6.)

  Your auditory system can accommoda hgj /ptd(i1 wg,6/jqmte a huge range of sound levels. What is the ratio/ 1gj(mhi q6jp/d,gtw of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has anja:1*plujd p42nk t2 fundamental frequency of 440 Hz. The length of the vibrating portion is 322nkupa2tj4*1 pd j :ln 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 and fir k(mj)3jwhfnpfx2s;h8h4 po 9st three audible overtonenjf) jp9 hh( k4;8sfhp mwo32xs if the pipe 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 freqbz(s (m, h/z;jqt5yx ouency would you expect from blowing across the top of an empty soda bottle that is 18 cm de z((,q5jxyzmh;to/s b ep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the r ly+usb - ,pvyo+9)8sk;hhacv ange of human hearing (20 Hz to 20 kHz), what would be t vhbyyuva s,cos+)k8+9h lp;-he range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has pw0gfs3tlleo ;riwy2b 3 ln525s02zxa frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originy;ntl0i5lz 3 2e sbxf2p0wlgw32ro s5al length?   Hz

  An unfingered guitar string is 0.73 m *kc d4vq9a p2fwi;lo +long and is tuned to play E above middle C 4i w2cl;pkav+ q*dof9(330 Hz).
(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 a i-zdb1 d8knq;94jt-iqm3hqf ;kil h5 n open organ pipe that emits middle C (262 Hz) when the temi m;d31-4 9 t8dq 5i-hkq nlbfjzqikh;perature 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 atidv7. r a)aqg:v3tvl4oemt /, 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flo n +f.xsljko,gc06 b.ute in Example 12–10 should the hole be that must be uncovered toks o+.6 x0.flnc,g ojb play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, butx:vfyyh-iv+ y:t)itm v 2+t +v*srvd* not at any other freq*2 tim :)vvh+:tsy vrfdvxvt- y+ *y+iuencies 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 bothc46u lp m-e*rx ends. It resonates at two successive harmonics of frequenci -ml6u er4px*ces 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 j 9dwu 89 .o*zsyuetlk 5as/0y$^{\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 v 30tfpzsm69othe audible range for a 2.14-m-long organ pipe at 20v6 tf m90zp3so $^{\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 an.h;ax.:pzh( qul0y in d is closed at the other end by the eardrum. Estimate the frequencies (in thh l(: .qx0in z;ah.upye 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 2.0 s whfdbw* +1)b mnsggv q,2+: zlo y:ceseew/t,. een trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequencytz ng el/eb+b 2c+:,f*.w1sqmse weo,yg :)dv is the other string? ±    Hz

  What is the beat frequencyjtux93qklx0j m/gkhn3 c-l*5 if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X)on+70:qhfpl f smj l f:sjc/39 operates at an unknown frequency. If neither whistle can be heacjlfofsfnm p/l +97q30: :hsjrd by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wilpn6kb59x-wx(.gl o*5q7jdb6 a es)wxl c8tjth 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? Explain yoa98llqwpbo7sxjwjk d t- clb x56n(g)*x.e6 5 ur reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 ebrky7,v-y,. . ftb xxy)m3by Hz. The tension in one stringx b,-7)byyv3. x,ymryekt. bf is then decreased 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 tu.ayhlw,+b8 nbe: e7pwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.08l. e :wh+n7pb,ayueb $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forko rkv ).le/(xv*.jgi y 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 frequencies of A. yogx/ jir*v.ek )(lv 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 one speakesj:o;gx(9dtw kmw 6 7fr and 3.50 m from thwo(mx7:;jw gkd s 6f9te 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 arep lddsis*wsyn; s082t3p 2/b-igdqq9 supposed to be vibrating 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, what b 8t9sgdsdp- i0wyq*p32qln;s2 isd/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. How many beats per j7z/+4g skgwa sw 4az s+jg/gk7econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirero:6 pr5kef lsa3-(zn n is 1550 Hz when at rest. What frequepoz(r snera3-kl5:6f ncy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine a6zxyu )sh3;gwhose siren emits at 1550 Hz m63s ;x )zaguhyoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fad/qc,jp/b 2k requency 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 exakc jd ,/p/2bqactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wyn ozgx 8 (+d9t:fyw8rith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assumy f :(8n+xo8tygw9z rde T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recyra7 mj- k3 nwx 8ybedsf65d blxjmik/*g) 3*4eives them returned from an object moving directly away from it at 25 m/s What is the received sound frequensyjkw3* dmm7 )j4xg fbiy3e bd x8ka-*65/lrncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wn dqm *3t2vwz w)g0pztho7j;sf 6n( 6sall at a speed of 5 m/s As it flies, the bat emits an ultrasonic s(w0f 2;o7 mw)n3npdjzshtv* sg6q6tzound 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 flat0cl;jx(g )bhe train car at a frequency of 75 Hz, and a second identical tuba played the same tone whilegxejb 0h;l) c( at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flo*qlmuo hc81q.p .xyp- w 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 frequc x- *h m..q1puqlpyo8ency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waveslpq3 4*v(rs dk 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 w :+x :ityt6th570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers:6y w:t+ xthit hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed athtwp uqp 1.n;9 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) What i2zen94uh 8/ fr wnge0ls the angle the shock wave makes with the direction of the gl8n0r 4ew/ uhe 2fnz9airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whexk ln) y-)u-wy-gms35odlv w 6re the speed of sound is onlyl)lv go)yn6uwd- 53kywsm--x 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 shobdecwz)t;93+ uj zs+x4d nnt2e999rd fmjz2zck wave angle ib 9c9reuftdjz ) n z2m9e4dw9+zj;xdn +2sz3tt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ezy41a)c+o7jm:m v qx$/theta$ 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 ex 05l7kvld(uyir +)ao lactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizo(lui7oly0)r5 kav+d l ntal 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 v j6qeq o 9 2 unyxp.(h6: j-(80kpl.accaedkbsonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the xj6l (.e(q:dvcpk0o bj.an y-chq2e ukpa86 9 minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there ids39bnhis)v.kq2 nlp ;o-fo7cs9o k 3t +-kuxn the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a s5auu,jm )5 u9xz e.nvuewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. a.vun u55u, 9u xzejm)
(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 ct.5rn;*64tr8hsn 8(;f1qpcihh zbmy 0q mx lvlose to the threshold of human hearing (0 dB).ihtfh*hlpmqx 51qr0 v8 .rycst8(n4b;; 6zn m 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 sound are hepgq,(wk 3n ):8wgclqy aqpgg()w, ykqln :wc 83rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in th(cf- kli),et/ur u2rye open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates e iut ) /f-el(rk2cr,yuqually in all directions?    W

  A stereo amplifier is rated at 150 cvyo4 q s6:nf)is3gb6 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outputvsc6 y:q)6boigf3n s 4 in watts at 15 kHz?    dB

  Workers around jet aircraft typicax4 ff3c3t2+xyzxcijm4d **felly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is42y mx* xjdz*f4+3c3ecixt ff 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 communications systems, the gaiykp6 up48d 0t0ujhvm .n, $\beta$ 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 frequenb.d(0quh0 n;v q5sgyzcy 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 with a fundamentza1i 0quis04xal frequency of 440 Hz 0i0uaxzsi14 q and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical opewdvoriv4u++/hnv4 5 en tube filled with water (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 and again at 0.395 m. Wha ew/+vn4r ouv54d+i vht 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 open;e jt,nsz, ,hq at one end and alsqsn;,ejt z,h,o 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onegqa6 c -3s; 5rxm6yanj 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 to;-em gbb:g6k hlsk9- xne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and findbmb lgshe:x6k;9- gk-s that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Onerz; w/pllwtmg 0h;7 09u 5nozb train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving ; t0lnb0g59wz lhrom;wzu/ p7 train?   m/s

  The frequency of a steam train whistle ask-upy*n-w cy+kvte2;0lb1rh pce92 x it approaches you is 538 Hz. After it passes you, its frequencn k*2v 21c-pewc-t9 ybhkl+p;0ey ruxy 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 listencudc* tlm-w my-*1lg -ing to the difference 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 guclcd-gw*mml*ty-- 1 oes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequen2i5pt;l +co mwaksb*/m7j(gl3 wzv+ tcy of 11 Hz. The shorter one is 2.4k/g i5zv (o m;t+7clbm3 ptwa 2lwj*s+0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves psr:u-b(*r 2a8qxwcmm1 dbf w:ast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical soundmd(qc :r-b8x s:wu1bmw*2 afr 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 flowzvobsjq.9ya2 id- j 2 m+:9dni in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dion92.2- 9b+ z:iyavdj idsm qjrected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at :.x(hfgnm20oekmu e+ speed 6.5 m/s while the moth is flying toward the bat a0 2hk+e n(mfu:.g exmot 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 moth?    kHz

  A bat emits a series of high frequency sound 7op gyf4yu :j2(ubc;ppulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns bey4:cj (;f7g2uoypp ubfore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals frivv+39uis *g08 ivhc-vn2x n dom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When p*2-u 9g 8vvsci0xvvihn3 d n+ilayed 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 open tube.

  Room acoustics for stereo listening can be compr:vsjzkhob r6z0+z-j 9omised by the presence of standing waves, which can cause acoustic “dead spots” jr:-o k6 9zz shjz0v+bat 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,” involves a long, slendxtbhp)en8rzatx(9 m p ,hs5 -3er aluminum rod held in the hand near the rod’s hsb8xp, m5aerzt(t9n3x)p h- midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thres)+hivta)bb8won/ n 1vhold of hearing for the human ear at a frequency of about 1000 Hb8v+vb) )nwt/ ih1na oz 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 observer on the ground hears thekl.nf:,/wa.tg dzw 1p sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?fzkw1,g/ tn pl.a: d.w    $ \times10^{4 }$ m

  The wake of a speedboat is 1v* 1d*rvrj c80 pddme;5 $^{\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