What is the evidence that sound travels as a wa*bqwrl e1j,t3ve?

What is the evidence that sound is a form of enerfk5g n uf3fd7,gy?

Children sometimes play with a homemade “telephone” by attaching a strie akeew13:od2anb 88nz o d31xng to the botto3 8eod3xzn:1do8ew1abka2enms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the f5t/kcih 7i dka6qp9/,g iky n2requency or wavelength to cyhk qigkpn72,a9/i/t5 kdi 6c hange?

What evidence can you give that the speed td8(hemma ck(6f g+b) of sound in air does not depend significantly on 8k(+ cm 6dmh)ftea(gbfrequency?

The voice of a person who has inhaled hmhjt nqmrf pr5a 15u1p211 1bpelium sounds very high-pitched. Why?

How will the air temperature in a room znq*c d7(m96 w* 5ydjj y8dpuiaffect the pitch of organ pipes?

Explain how a tube might bedw )mcz.on *f+.fh4qk used as a filter to reduce the amplitude of sounds in various frequency ranges. (An ex+ff doz)hcn.q* .k4m wample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer s2hdd b2rqdw8y5b 2 g-7gme*xtogether as you move upg rebsd2-gx 2d2ywd5 b 78q*hm the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it 0oqd6 1z1brohbut cannot see it. When it emerges and you do see ithoq 1 061zobdr, 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,” whereas beats 8f4 js 7p4qlzug,ssmrch5k,1can be said to be due to “interference i rg571sf ,u8shmz,j qlcs44 pkn time.” Explain.

In Fig. 12–16, if the frequeez3 p ,wkr 1b ub,f7gnbq9w1s8ncy of the speakers were lowered, would the points D and C (where destructive and constructive interference o1sz8nq,3g7 ,1wbbf9wr upk beccur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in/y.tl,x .pls e areas with very high noise levels have consisted mainly of efforts to b .,lx/lyptes .lock 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 can be thoughtl-fo :*,p*qu hw3ygtc of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component freque w-o:c, *pyu* gl3hqtfncies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the samc : ho:uy x*-.5univcme direction, with the same: *vx5uymo :-c.cunh i velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pmkm )x.vo8ewl j.*)wmerson at klx)*vm ejm. w.)wom8rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positiont)0u imn*f/l l;xa y*ys of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which po) y* l*lx i/myfan;0tusition, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the razcize/ t*7xnlz+ 57echo of her shout reflected by a cliff at the far end of the lake. Shezez7/r5l+ * zn tic7xa hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hfs vcf8(/2 ocois ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assum2covf8/fco (se the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in d7 6: hrztiq1,;9m z(j unb5eu.sqc(sa,vsr kair 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 dlogh 2)up-hf6 tfjc r,pe*k9(ay. Without warning, an engine backfire occurs on p cf9 lr g,*2-)pt(h6 okuejfhanother 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 mam;3l1r jjx:zskes when striking the water below is heard 3.5 s laters;:jrj3 lz1 xm. How high is the cliff?    m

  A person, with his earsruag a;a -1)h 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, and they are 1.1 s apart. How far away did the impacuas;)ah1- a grt occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rule6yximgpd8 z( 1*ka :pa” for estimating the dp 8gakdyxa z*pi6m(1 :istance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun3dhbv/e avr-8 d at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose ints:fv a*mf7ae bz(c 9(fensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously aut2tw, iiof: ,t a certain place, what w,t:, ufi2tiow ill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista*in6 tqju0t q* 2/ik-s1yc- qkkn b/mpnce from an airplane with four equally noisy jet engines is experiencing a sound level borderinpc b*m /jyikt k 1ntin02q6su-/qk-q* g on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratiou;c e+n-2ki lf of 58 dB, whereas for a CD plie f ;k-c2nul+ayer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output y+ gpy05up9 4yswj/ qwof sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a s5 g0sy/jw4pqw9y +pyuphere 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 em59n3ar0oh*yr 7o rbmardrum 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 th33 a ffmhpkb40e more modest 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 loudspeaker co0pa3hfkf3 m4b nnected 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 13jo3v vbz 46tfi:le6h 5p9cz2l0 dB when placed 2.8 m in front of a loudspeaketz 5pv3 h4 zi:fvo6ce29bll6jr on the 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 typicallyy9h.ju h7d 0 ex(tabs/0+ekbo detect a difference in sound level of 2.0 dB. What is the ratio h u jobas0ybtkxd e.7h+e9/0( of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bk +vv1zs wuneljj;1 14y what factor will the intensity increase? Increase by a factor ofu1s4+vw11j vej;lkzn    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal d7 pb3 *dtlh)7ovwvou if(2op;isplacement amplitudes, but one has twice the frequency of the other. What is the ratiofl7 wp*7ioh3t) o2v(ud;bpvo of their intensities?   

  What would be the sound levyfl ;).t-dvk x/;r-r phvj;*lb9a3rk/ruz qn el (in dB) of a sound wave in air that corresponds to a displacement amplitude of .)/9yubk rv-n/;r3ll ;arjpx*fdv rqt h-;kz vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lexi1s. 8zeeud-;2l jat a.x2h rvel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.). aaxit.2ze -e1l8 drh;ux js2    dB

What are the lowest and highestfmyv0 mjwn4x0)(k/zzub 4 ;n f frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6w4 /)v n;jk 4fuz0nm(bmz0xfy.)

  Your auditory system can accommodate a huge range of sound levels. W/+m)fr:peks yyy; usf -,e6n ehat is the ratio of highest to lowest pf rm6ey +)- euy:ksny,se;/fintensity 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 qrzxf*zlt.z3)xr 75a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what f .ratrz qzl )*xzx375tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first l3 uwy0od)tebi:cw. ,three audible overtones if the pipe itwce3dw bil0u.) : yo,s
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequenccc9-+mjfjd7qs okcso )1w)1 y tch: *cy would you expect from blowing across the top of an empty soda bottle that is 18 cm dees 9dmj*wc))c-fos1 qk7cj h1:o+c t cyp, 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 pipe 1rw, loa xj(jk18aso7s spanning the range of human hearing (20 Hz to(kar j11, o7wjloa s8x 20 kHz), 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 harmou4g+ao,bb:w enic. What will u,ob4+agweb : be its fundamental 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 tuned to13md;hw(rj9df ;r0 kw+a lfuij9w4ex play E above middle C (330 Hz)fwl;k(9 4 x3w9rwe;aid+ md1h j ruf0j.
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits ;v*xxvl6mz jd.lh)l0 middle C (262 Hz) when the temperatu6j;0vmd.x x*h)vz lllre 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 qq8qz64g j) :lv3di4sfcuqm; 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 Example 12–10 should the holeji:bvmb9bk17 o g:sy (gmdl0sz 5u1 z/ be thatms jb:9umg bz1lo gkdv1: (7ybiz5s/0 must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and v wwdo;cklccdaiedz: 8,:o/b(v) j 1 )616 Hz, but not at any other frequencies ze:c ;o)o)v/l cd(81:cv bki,w dajd win between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It2x x9ppzk.np. resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. 9..pp kxxn2pzWhat 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 k; 2(uzg(lkrgjj h6x i ,/9sou$^{\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 bo go1s2rqb;8for a 2.14-m-long organ pipe ato2;1qrs b 8ogb 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside pzab 8pmg4h.0 and is closed at the oz p40gbham p8.ther end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying kei6. vs+j6m ato adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other sk66ev. maj+i string? ±    Hz

  What is the beat frequency if middle C (2rk ls(y(o+ u/ j rxkq,g)xar6/62 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 op7o1o/f v9lg ha4i8a/j rzru,serates 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 sigz 7or f8our/ 9sl ,h1a4vai/jmultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork t y57hr1rxyu4 db8j(h.w, vbqand 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? b5hb81(tvr h,y jrq wx.u74dyExplain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The sq1h2onuxg.2b qi*jc7 l:ha b2 v 1bypse-8.ktension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two csq:a 12 * 2uv gb.nlohk j7ihe2x8qy1.spb-bstrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flqr(* eqis9 q;u25nm ryutes each try to play middle C (262 Hz), but one is at 5.0°C and the9 5q rqey un2m;s(rq*i other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; krra17;auu jyo 6 io52lf:a8r 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 8iry1r5: u2ar7kl;oa ofu6j a 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 apar 2 t: 7tqfandp;)e(dpn -wb.qtt. A person stands 3.00 m from one speaker and 3.50 m 2qqn;t dawtp 7d (e-:fb. pn)tfrom 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 supposej ql6x0)*er yfa*3bpo6 ugdt,d to be vibrating at 132 Hz, but a piano tuner hears three beats eqgl t60 6b3erxo* )y ,adp*jufvery 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what 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 soundi.0r tdw*g29ejj4x qzbk)d8 ;lk vq+z of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20*tdvxgq 0 l.rk2)e;q4 jzjkwb zd+8i 9 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when atib4yh1(jds f/ rest. Wha4ijbsdh/y(f 1t frequency 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 hz4 vtm1/up6o0rqt 7xengine whose siren emitzvtorp 70xq 4 /m1tuh6s at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq b.. 9ypv:-ww 8smo,e ombi+gvuency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at +-9p,v: w8 yvobo..mimegws b 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 equipped with the same single frequency hoihgs+j* cv b3 ;0w)6orplmj,nrn. When one is at rest and the other is moving toward the first at 15 m/h n+ j,jlmvb;rc0s3w *i 6pgo)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 and receives them 4q7st:o4 lg2:+eg; teyrvds aghn9q* returned from an object moving directly away from it at 25 m/s What is the received sound freq:g7stl 24:vr;qng t9*ys 4adqegeh+o uency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flzoxmb2g1/awx( 4 pi,iies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thxmp2gio 4xz w/bia,(1 e bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movbno5 t7) k7+- mjhok vuun4+(j1rntyling flat train car at a frequency of 75 Hz, and a second 4mt 1obu njj(+)n-+ lrk h7v7u5n koytidentical 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 measure bloov i) arw4 w;6aw fidrt1aa/.9ed-flow speeds. Suppose the r) iavetw6 9w.41fir/;aw a dadevice 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 source?   Hz

  The Doppler effect using ultrasonic wave( c sfy49 (pj ujhf a.19zrysctzn21o6s 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 9q 61ciyk qok(.d exb sg;pder7 i :)b5lst2/bof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observ7bel.:edq r)d s bp5k2qc(sk ybti1;x/o 69giers 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 objec9jumds*rp 3oaj ) 4j:j1ci;( d+xlwzct 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 (f fd/;rytgs :+a) What is the angle the shock wave makes with gf/fsrd +yt:;the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin a16wd/ykn3 z9--crkir *bdr ibtmosphere of a planet where the speed of sound is only about-nkz*rdkry i1bid/9-3 cwr 6b 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 9z fvy) a3cjv8ocean. Determine the shock wave angle it producesj9vyc8a3vz)f
(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 v/rqfquwm/c7,n 87 or$/theta$ 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 a g4-u*ylcpr52 q4q et iep3/dwbove the ground flying faster than thw*/52r 4q ti3 pedq-uepl4cgy e 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
(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 deviceg:91l wqeop 4n;r6c2dpy*wrl that sends 20,000-Hz sound pulses downward from the bottom of the bwl4o* l ey:2 pw6 ;g1qdcrnr9poat, 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 mank4*ivlkj .ej8l 7y 0esy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer *u;c5urg,+)aqefg nx pipe symphony. It consists of many plastic pipes of various lengths, which are open onc)a*xgqu ;fn+5rg,u e 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 so:,h5p f9q3akikhdiyq 15mx;zund close to the threshold of human hearing (0 i;9mpai55 z qqfhkhx,: 1d3ykdB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound levej s- ffc50nniyv0d51ml when an 82-dB sound and an 87-dB sound are heard simm ffvsnn0-5 01dyji5c ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,j44c9 6lzv 5 9-py6 mwsi;extqgcy,vi is 105 dB. What is the acoustic power output q-vi;6cjxsw94,em c 9yv 45zyit l6pg (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rap qh*uw 0y0qd7ted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What hwd pyq0q7 *0uis the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectvnk8 finom: pcw)s f:kk x*916ive devices over their ears. Assume that the soun v8ok6:nxpw)kkn*fs m ci19: fd 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 communications systems, the ga4tqmv*nzvyvzqj 39l :0+tl/ y hkj * epy7w3t5in, $\beta$ 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 vio)(lcvmm4,d v flin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betou72tlw sli0:+m g3k 3 4cvmbeween fixed points with a fundamental frequency of 440 Hz andec3o 34 bmgwlvu:m t2k 07ls+i 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 filled with wak51juv dkz0ywhm861c 3hrnd;lsn v+/ter (Fig. 12–35). The water level is allowed to drop slowly. As it does kdd 1 5chwh 36k+ juzyvnr81 v0nlm/;sso, 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 i wl )q a9q2eh0*nlr(ra 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 iwqar)(0l l hern9*2q (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed i kstx:vtt+0)3 wtth+um/4o w to resonate as 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 coming from t7pxipo m ta20*7iwq-lwo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the otixa72qmo0pl-piw *t 7her. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on thg5i+u0s: 5b:zni1 t( y;apavnp )w zcue stationar5w+ pvtgcinspa 0;:uia( ubz: 1)z5nyy train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appbxx 5,.vlean *:1y3lxar hcw1roaches you is 538 Hz. After it passes y1r:wyn51vbxa. a3 l cx*x,elhou, its frequency 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 lisd t,f-4fivr0ftening 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 f4-0, f rdiftvgoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding toget617ce fdhcpp6w ;3x3m 4n7 vokcnu6daher, produce a beat frequency of 11 Hz. The shorter on3 n7hdfc6pk17w cu6o e;v3macpd4n6x e is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroag qg*naqd a:cg6z0 d:1 cko2a+d car as it moves past a stationary observer at 10 m/s as shd:g+6:zc ng adqk 2ca01g*qa oown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he 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 y4dv)i)o 6pn .j 8ag8y5jdevkabout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the fl8 d.e5nj g) d8ypjy ao)4ivvk6ow 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 toq hx3(,fstw- xward the bat at speed( tqxx3shw-f, 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 pulsdt p;112su 1awr2*ytc hr;wbw5i u/wm sn. 0eres 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 dete;pc wrb1ey*iw.0m;w rs1n15t/t ur 2duahw2 scted 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 Alpine vilblysrm,w ;9cqi .j ,6j /d nl(b6krps3lage 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 instrmy6sclj / pn6; sjlqr,ik b3brw( d,.9ument, 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 m/uz;tmrm2l mi:,k 8x be compromised by the presence of standing waves, which can cause acoustic m:izmx ,m8/;mk2 trul“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,” involves a long, slenml7sn/wn)w p m57h +g0ow -xxqder aluminum rod held in t7gwoxh- m s7wml5xnn/)+ qw0 phe hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, 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 thr70 ubwf ,pmkr0eshold of hearing for the human ear at a frequency of about 1000 Hz ibmku 07f0r wp,s $I_0$ = $1 \times10^{12 } W / m^2$ 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 n cc8.1yfs4 6lc0 fwjaobserver on the ground hears the sonic boom 1.5 min after the plal0c 8c 4.nysj 61cffawne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1v 1j7t ,u2tof 3r0gohl5 $^{\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