What is the evidence that sound trav7 se0 mj;yy(nzels as a wave?

What is the evidence that sound is a form n1snktb1y46w7pc+ko of energy?

Children sometimes play with td, *.c0zwwk ha homemade “telephone” by attaching a string to the bottoms of two pawzwthk.0 d *,cper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wa5dj th3m v)ss2velength to cha)tmh jsvd5 3s2nge?

What evidence can you give that thepl,on8,dwf3)ln hm 7 bga j44r speed of sound in air does not depend significantly on frequ,j,4l34 bpfdmnor 7 ghwa n8)lency?

The voice of a person who has inhaled helium sounds very high-pit jzp (o-frp1 hl(o(9mwched. Why?

How will the air temperatureasci pb 5m:,6o87puwkq: v(pq in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ofx +i )l ep2bb9(oz9niv sounds in various frequency ranges. (An example is a car muffler.)i9b9 nv ox ip)+bz2(el

Why are the frets on a 97v;kc.e cizyq0ej rl0r.ul. guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge zqu cveykl j700r;e. lrc.9.i?

A noisy truck approache; zhgqsx6p c ud6z0df ici:-67s you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency nqux 0scg7hddc6 6;-: 6iip fzzoise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bemf m4*qnpqt9bv:pq-- due to “interference in space,” whereas beats can be said to be due to “interfe*-bn qptmvqm 9 4p:-fqrence in time.” Explain.

In Fig. 12–16, if the frequency of t2mz0d4ji/webw s 6f7hhe speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer tog7bzw s4dw6 me2/jifh0ether?

Traditional methods of protecpn xk 6+bqe1 d1hvc0orrrwl f54rc 66( d2ji:uting the hearing of people who 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 w 1e6 do+pbrklu6c:4ri0(jvr2n5 q 1rf 6cxhdnoise, 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. Eachrrr;g h 7ghin4p1:7uorwwxs1) g (y 3t wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wr x rih7 w:o3w7hr1sg()p ryggn1u4 ;thich of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift i..eo1 y(c d9b iz+zdudf the source and observer move in the same direction, wit 1ybiec z .d+d9u(d.zoh the same velocity? Explain.

If a wind is blowing, will this alter the frequency of tqg:g2 ecjw ,/ 5pybv4the sound heard by a person at rest w/ggc y2t,4v b:ewjq5pith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chii t-jlk8uwr17ld in motion 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 frequencktrw iu781j- ly for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by e)nis hj1 i/d-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. Estimate the length of the /)n-hi1disje lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears+n1cw hp5fkdz* .:zk n7( ntbq xbvk59 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*k 59hbkbcx(1 z.dvk:57zf+ ntnw qpn of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air u(-b4 tq js*pyat 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 mitl 55gyrxi:b94k :x drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 14:b 5xmr iy95ixk:ltg2–33). 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 spl5pdmbgr4m 5p2 ash it makes when striking the water below is heard 3.5 s later. How high is the cliff?5pdmmb45 r2p g    m

  A person, with his ear to the ground, t9 lkbk976viyo4ir3 yh 92yqnsees 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 concrey497kkbhtv9oq6y 39ni l2 iry te, 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 error made over one mile of distance by the “5-second yazd30 l5npg 7pn,f5das;3 hgrule” for estimating the distance from d7n5 a;zfp30,h5ysggandlp3a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levez..c cwjm:q n.l 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 into:5nk.1g c) sx 2oz0cqdt4gmuensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at (s1 5 lmtlelb6a certain place, what will be the sound level if only one is exploded? [Hint: Add 1sm65 lebl(ltintensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi m7 48 g:x8*bp4kc ;suahwuygvsy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut downhm *;8u47 ug 8b 4kpswacgyvx: all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh2oszmwt7:qf) ereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background2 mfqzw:os )t7 noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normf9p2o ) nuko6ial conversation. Ukpo)6o2f in 9use Table 12–2. Assume the sound spreads roughly 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 whosy b/k k8( gd;2ug*igbne 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 modest amplifier B is r-fr/-j( 4xok/ paasw9ggk+p fated at 40 W. (a) Es(k a9ogfwkpr4 ps- /f+ ajx/g-timate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed r 4-rpb *4dz( 0upiuit/fjo8 a2.8 m in front of a loudspeaker on the -tr/d0urijuopf4a(4 b8pz*i 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 d)ulaq ) a/xckav70k dm6m61qeetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds w akm0xqcma aqv)e 766 u)1kd/lhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a6 fx) /- nxsow:kh+w:0v hgicp sound wave is tripled, (a) by what factor will the intensity increase? Increase by a fac)k6: - wcx0xo/h ih+snwvpf:gtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement a ueq0oz mn:sy7k 3vw9-mplitudes, but one has twice the frequency of the other. What is the ratio of their inte9:- w0qzeusoy7vm3k nnsities?   

  What would be the sound level (in dB) of a sound wave in air that crz1bk o,-cof*orresponds to a displacement amplitude of vibrating air kzbo1cf r, o-*molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemeu t,t25 7q1toqxpw / ,uod+dt as loud as a 100-Hz tone that has a 50-t,2qq o1ttutp75+xded uo,w/dB sound level? (See Fig. 12–6.)    dB

What are the lowest and hicx q9tex+.;f3mz 7solghest frequencies that an ear can detect when the sound level is 30 dBcl m. s9oxz;efx t7+3q? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound level83h 01xfcyrgeat9 l x*7u3 tirs. What is the ratio f39aihc rtu e x r*0t7ylgx183of 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 violi ji n;pdp 3y uzs 6nd*lfd;t8d:mj*3*:r5vjv kn has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a s:83m ;rky uid*tpn l 5:d;pj*v nfzjj*d6dv3mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three attiu :0 t2;6z *p/ljy .o/f smnjd1spvudible overtones if the piptjvt*0 y/n m 61tsfu2odi.pz/;pl:s je 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 blowing across the tc8 k(qzdc. i0m um8)ebop of an empty soda bottb) mq8 z.i dceu(kmc08le that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ witho*fo .09e sppi open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz* 0ipep.of s9o), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmoni5mdym jd .9bhj1,wnd 1sj-+bo t tej.+c. What will be its fundam,b+d -t1d5b+m.s m dej1whj jyt.j9noental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar str82 3pd i6twyufqmra 0.ing is 0.73 m long and is tuned to play E above middle C (330 Hz). a0rywd3t2mq. fi8u p6
(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 orga5b 5mf tve+e ffq22t2rn pipe that emits middle C (262 Hz) when the tfvqr+tf5 f5meb22t2e emperature 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 * xix+0;t vxiu+zv2.f o/odyv at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exa9c17(/ka(n ld yh-kv t6hic q)k,ms/jgge:wdmple 12–10 should the hole be that must be uncovered to playg c /9kiawm hy:n 6ej k/1sqhg dc,(d7tv-kl)( 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 61dcns 7n+wbgo1wy:i5 26 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clos5 ybso2:c d1ni+7nww ged pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates q 9amo5(tlo:g(/,ar/:debhrj ,g t vm at two successive harmo ajo(g b/ grqlvmh to,9 mtr5:e:da/(,nics 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 ; 6eik.dol u f6pgsytb4;.m;p$^{\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.lu0b*; jmwt9t14-m-long organ pipe at 20ulj0t tm 9;bw* $^{\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 outsi:ufdz uk:abdz f7q;0:7ymx+yo 1c k1ude and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the 1f0af1kbdm;k :z:o u: y7udz y7+qcxuear 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 when trying to aqkiaw.la59qk9o k/bx; 0v yh 0djust two strings, one of which is sounding 440 Hz. How far off in frequency is thqv wyx9ih kl;a k/b0o59qa0.k e other string? ±    Hz

  What is the beat frequency if middle C (gc-.kx5u hdf)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 dpve, 8irg5/aoperates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimarvdga ei /p,85te the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wi *ffgqw8kt(i:q 5s +czth 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 yo+ wf(58: czsfqiqgk*tur reasoning.    Hz

  Two violin strings are tuned towltx t dv l2*ss92ced-8oxe4: the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be:td c2do xl4stsxw2elv e* 8-9 the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hear4l pdut58hz-*53f/8 z:vy ndyv gxq6bjw+awpd if two identical flutes each try to play middle C (26j-xfw4v8pzdy*vq :hyn 5+pg tw6a5ud lb8/ 3z2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forktaopr(+q60oqdjk) p ,nqnzj.f2ed07 s, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded tk0)r2atnjqe76fp0 d,+ dzqpn j oq( .oogether, 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 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 onmhg*q (zq) b3fe speaker and 3.50 m from thfq)hz b(* gm3qe 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 vlg);p8k vddm. ibrating 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 must be the frequency of the other ?p )8g.k; dlvdm   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.f: 5 lfeqav)6a 0:mlnh How many beats per second will be heard? (Assa:) :5lvfqhfm06 en alume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when:)c9zg(szl) l / 9x-/yky70va0ymqz nvby b xb at rest. What frequency do bn (lxzzqv -/v g:900y9 x/ayy)y)l c7 zbbkmsyou 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 frequennnjw*8 vh1/tycy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of yh1v 8/nn*wjt32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movinxq za+9xhsccds/vo+8:-ps r1psb + 6u g toward you at 15 m/s versus you mcv+b:/sd zqxcr1 paus9 - p+sxsh+8 6ooving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equippea.tpg: s unp,9d with the same single frequency horn. When one is at rest and the other is moving toward the ppat9 n.,u sg:first at 15 m/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 ultrasonicjg; q.y6ukvi5 sound waves at 50.0 kHz and receives them returney viqjg; 5u.k6d from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,xxp x;0dwb2f( 6q1 xnf the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bax(2xw 6;p10fxxnf qbdt hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler csfh8uc 569qyvjh8 uh9d4tq6snj r20experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same h0vjqsh s5 rthqnc29f89j6u 684 c yudtone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose u9ez) 6om,*l3 qdoj nmr1(ixf the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound soue m nmzlu16, of)*x rod9ij3(qrce?   Hz

  The Doppler effect using ultrasonic wavei-tq;n 2h xhc) qp25x wo8q:ujs 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 freque )7(xnh**bvh itwkss :ncy 570 Hz. When the wind velocity is 12 m/s from the north, whsxvk7 hswb)i:h *n (*tat 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 moving on land if its speed at 20 n;ph hp :sn, ,k-pn2:fdemnb 3$^{\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 obl)axv 36u.q*zjv9 9uwxf lq-f sound is 310 m/s (a) What is the angle the shock l fzju. vlb)93uxwax q*-9qv6wave 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 th+oken gd-a s:.xoi *v+in atmosphere of a planet where the speed of sound is:a++*ngkeo svix d.o- only 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 travelinfqz qat7ri)rp(u9.(+ eda tv deo-/4zg 8500 m/s strikes the ocean. Determine the shock wave angle it pr7 (de4+u/)der.9ov-itzq fztaaq(rpoduces
(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 ucgp i9vy- 55x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flyin9u zhe:3t n5weo/yd9s hadqtnzs6/ux 4l2d))g faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine oq3de6d sx9:)ntuz 2a s/h dezn5)uhl4 yw/t9
(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 so b,2a1;idilunnar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoesi1;iadu nb,l2. 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 range? :tj7 jq gc.ha:rm7b +p$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists z1 0k -i4ezx.a+hjdvz/u h h.dof many pl4ui1 kjv zh -xh a+0h.e/zd.zdastic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a soundi gr( d+tef.4m close to the threshold of human hearing (0 dB). What will be the sound level of 1000 s4fdt+e (gmi.ruch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-do*y9m:nkl,0rt ym ym6p . hls6B sound are heard simultarm6. 6hlyynl*, m kt:m9yp0 soneously?    dB

  The sound level 12.0 m from a loudspeaker, place* n)/f bgfx5wed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in allf b/e)f*w xng5 directions?    W

  A stereo amplifier is rated at 150 W j ai)xi+iv85 goutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kH)agv+8iii 5 xjz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. . /pi49j j:egr1jbvj5c)jnzwt 1n oc3 Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and wj/b1j4c315vge)j jjnor z9cin tp: .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 gaing1w qa zr*)h19l c5uf(k m5m,adm 9zum, $\beta$ 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 freoxzx0k xx7 +*yquency 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 lon/ude(sob ,ee /g between fixed points with a fundamental freque(esed u/ e,bo/ncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled9h4r :9y iz1 ctjub4zx 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 whej:r4 chi x4tu1zzby 99n 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 n 1f6n8i,l r, uxibhy3(ce5p hjear a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental ,p( jxehyrin3 i,l h65f8c1ubmode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a77f) fazfwa k m)yr0/yz8oan-s one 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 comixwy u9)*wb +mang from two sources. The so yb+9x)a umww*und 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 from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Th.tg e3nse ha9-e conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approntha. 3e9sg-e aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hzo +0s0 t5bujsj 5.tqyz. After it passes you, its frequency is measured as 486 H0su b0+z55t.qy jtsjo z. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by l2g+c/o ghy- - 8whewmoistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a fuo 2ghmy/wo-- 8wg he+cll 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 bucv4- n ,2-dcuu .wjwoeat frequency of 11 Hz. The shorter one is 2.40 m long. Hoouj-w c- 4,uu.dwc2 nvw long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it m, ,gz v 0eh**ducp6nlaoves 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 frode hz6n0c*p*a,ug l, vnt 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 what beankgzi/ e; 2 qus7+( *f6*lvmq-exwonbt frequency would you expect if 5.50-MHz ultrasound waves were d-z q+sx 2 /qfeubml*kgni;7 ( no6*vweirected 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 speed 6.5 m/s while the moth is flying toward the b ) 1ks0cbn:gcgat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequencncckgb gs)0: 1y of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series ofc7k k *fhvhyp8ph49vl0r pr :n:m6 y5t high frequency sound pulses as it approaches a moth. The pulses are appro rf8t :: k5n6ppy7v94ymp0hlkhhc*rvximately 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–3 d(ao4qeh:n s88) was once used to send signals from one Alpine village to another. Since lower frequency snd 48:e(hsa qoounds 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 open tube.

  Room acoustics for stereo listening can be compromised by the presed+s7l xl)vf* ence of standing waves, which can cause aco)*v l xdl+esf7ustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” 5onbkzp ; o-*7;ptrdkinvolves 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 rod can be made to “sing,” or zb- or okd7k p;*n;p5temit 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 abn1 z*zbpdlou7o) ,jx3e kdd; *out 1000 Hz;dzx*b d*o3 ,lkzd1 7uojpe)n 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 kzd- khj30sf 1:-qq2r 7seq xuground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitudzf -0kjks qqq3xr-: s12 h7edue?    $ \times10^{4 }$ m

  The wake of a speedboat(oc5ln( t0 nsc 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