What is the evidence that sound travels as a wa+ ,:kmoawym2oyt: 2nb ve?

What is the evidence that sound is a fab3adtz7 v.ew+a hn.; nr 2sd/orm of energy?

Children sometimes play with a homemade “te *awaq7.vpz a0l.r l:clephone” by attaching a string to the bottoms of two paper cups. When the string isa 0pawra lz*7v.:qc.l 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 hb(u 7dg 6eus+you expect the frequency or wavelength to chagsu(h ud67eb +nge?

What evidence can you give that da3*lmoni l zysg uc.0h0v 5/*the speed of sound in air does not depend significmiuylhsa3z d 5v /*nc0gl .o*0antly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Wa0ox,f. p5(b 1lx svdahy?

How will the air temperat))sqvsbq nofi o+.6 s0ure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filte:g2a sf46 npv dancxxo76t+/dr to reduce the amplitude of sounds i n6xa4ds :fpo7tgan/vd + xc62n various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitarubn*.; )kx2p4t 9ln1t)rlq y iabpwo: (Fig. 12–30) spaced closer together as you move up the fip 1 :al y;tr*nw)kubb9ti2nxo .pq4l )ngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initisswr1j8 / 1aqyu3kk5wally you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighrk1uj/15ysks3aw w q8ter” — 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 beatt9:t7i pp5q bapuqbbr 9g83 ,r2rc7 jns can be said to be due 3:9 iapj9q tb 7r7 2brb,g qtcr5ppn8uto “interference in time.” Explain.

In Fig. 12–16, if the frequency o y/; da+ne2i fjbkmxed 3a9;3of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move ed9+3kfm x2oy;/3aidaj b ; nefarther apart or closer together?

Traditional methods of protecting the hearing of peo l:cb91 ss05n lpqn*hsple 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 noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding n5nb* q slss1p9l: 0chmore noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be though 9p3;bn1+gb) kjylwz2y-pbozt of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12-bbwg kyy n)3plo;1+92j zbpz –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 sourcete b)ied38/k4 rm3 m3xhe-wfm and observer move in the same direction, with the same velocity? Explai wmme te 8 3fkh-4m/exdrb3)3in.

If a wind is blowing, will this alter the frequency of the sound herr)j2wt-qxjn-lb 6l 5 ard by a person at rest with respect to the source? Is the wav jn-jt)65r2lrq-x lwbelength or velocity changed?

Figure 12–32 shows various positions of thu3.-fq sbp5a child 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 hefsu- 5.3q hbtpar the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sz4k4m )+p ruxbhout reflected by a cliff at the far end of the lake. Sm kpub4+ )4xzrhe 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 sh hs; 3(b.zbciyip just below the waterline. He hears the echo of the sound reflected from the occ3hi. ;(ysbzbean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtht) sdev64w qfdzb g137s 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.k o2: wkk3:al+ om1fdp Without warning,k2f+do3o wml::kp ak1 an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. f757b ojcodrit1; b/(esd01qu - (sbhp a-oytThe splash it makes when striking the water below is heard 0o5 ot d-q ;oty((ab/1r7b idbc-1 7sh ejfsup3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground,:vmk u41fsp //wukdux rg5*t 4 sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and:m/4trdkx wp5 g/*ukuv1fs4 u the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over onebd/ w-r2ch 7o cc .(nls,/kw 6gtior)x mile of distance by the “5-second rule” for esrcnw6xbgritwo ocd7k c .s -2,/lh/()timating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soutfmu7u,r ( x2xnd 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 intza:0bz,uvm+ f ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim+ey r.jy 2 gdkxw2g9yg6-vo9 cultaneously at a certain place, what wil+ c.r6jk9 2xoeygvg- 9w2yygdl be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wim;5xx l/r 7ls 7o9nonr *aofd*th four equally noisy jet engines is experiencing a sound level bordering on pain,9 l**7o o/rdn moxr anl;s5fx7 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 is6*hg4 u da8jzf said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB846agd zfuh j*. 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 of sound from 6b3n dvwa7b/fm9/3v s 8peyht a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cefw98n /y bv3d te6/3shpbvma7ntered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is 6:m/r,7re.ksi hnwu su/t,hs $5 \times10^{ -5} m^2$ (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 rate2*mmcliwj)wd i)6m, jd at 250 W, while the more modest amplifier B is ra * j)2,wil6dcmwjmi)mted at 40 W. (a) Estimate 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 go+q ttwc77/pregistered 130 dB when placed 2.8 m in front of a lcw +7ot/tg7p qoudspeaker 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 typically detect a difference in mcl6f)vf0hie ((5,kl5bjmehsound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose le0l(mef me)i ,j ch5(lfkv hb65vels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wh(h1 lli 1f k w568nh (+5dg2ew3 dbzvjog.adqwat factor will the intensity increase? Increnw2wf3iaohjgq v( bl .d 8d16 hlkde(z51g5w+ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementgc 96 s+-kwzwv;k3hel amplitudes, but one has twice the frequency of the otcz h +k s;egww9vk-3l6her. What is the ratio of their intensities?   

  What would be the sound le u) pvnv;g,rp,hhsi8 5vel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibratr,8 hh5gn)iupv,v sp;ing air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soqf,m 6ri)7v mh;,imzc und level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–7) ,imr ;6vf qmcizm,h6.)    dB

What are the lowest and hi6w+uir1ks) m--fr cdsghest frequencies that an ear can detect when the sound level f)r6r-i1+-mdwu skc sis 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a ),ry1aj)is.+o vr5uzaq2se p huge range of sound levels. What is the ratio of hi,a isys1jr)2 .ar+ quopze v5)ghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The len-.f: ffvf2x l/rgtul.gth of the vibrating portion is 32 cm, and it has a mass of 0.35..vf/tlflg xffr-:u2 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and wl im0d*8mx ippaf5-:8tu-nf first three audible over5*-f- lmu8xa:i0n ft8p mwdi ptones 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 frequency would you expect from blowing across the top of an a kp /0n)tf).zqcu f1iempty soda bottle that is 18 cm deep, if you assumednk0 q))ta1zcpf. /ui f 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 rangey 2si*td5)l ci of human hearing (20 Hz tcd*l5y2i ) itso 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 ol- uof5btdmxs zrof1g 86te-cc- q( /,q,k9xgf 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originalmzqs fbq , (1 8gk,--rucxd9tcotxe5 6-f/lgo length?   Hz

  An unfingered guitar string is 0.73 m loym4)x;3 y2p m gm9-kv hh+dayvi 4xk5jng and is tuned to play E above middle C (330 H 4 ;jmx+4iymgvm5 ap2ky3hv)k 9dy-hxz).
(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 middweey+,l*;qxb s7 ft3gle C (262 Hz) when the temperature+y;g*3s,e7 q eb fxlwt 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 atzptu p ;cbcc05oqe6*k3. f4vo 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 hole b0)erz lees*6ye that must be uncovered to play D above mi le)6*eer0s yzddle 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 pier)0xd sge+wf5uazvu) -- 7 yipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at anyvs-a5 zyd7x+g-e ))0iuerwf u other frequencies 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 both ends. It vse74/oor7( dbec2w( b odgo ;resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whco4/ b vese77(ro do(owb g;d2at 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 sybx92 j 3zis0$^{\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 - 4xnjlwmmg6 a he k(;tfva+9(within the audible range for a 2.14-m-long organ pipejhmlgvf a9 m(e6;4ak-n +x wt( at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsidpu4o ftn/k5s(r w. 7ebagux*8e and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is bt5. x8w4u7e frnag*p uo/ks(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 adjust two strinnxhqn4 ppv :.;gs, one of which is sounding 440 Hz. How far off in frequenc :vn4p;x. hpqny is the other string? ±    Hz

  What is the beat frequency if middle C (262 aip29:zlf 22k j gde5tHz) 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 opwnd)p+:nwca .z(pfbj. b 8)y gerates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, ) .d cj(:b.abzg fw+wnnp )py8but 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 with a 37 qaq+t8apueh 62nh m250-Hz tuning fork and 9 beats/s when sound7hq2+e2p 6qmt haan8ued with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings avk h 8 kni;zuf,z7r)9yre tuned to the same frequency, 294 Hz. The tension in one string is then decreasedi;9h8k7)yzukvn ,zf r by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try;g0 sqvhsnj- ghc3 3v6 to play middle C (262 v;cv33n jg-sh 6 0qgshHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C2gxvap -l7xb b z9(ip/y*.wjs. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequenc.2x szb 7x9*iw/jalpvpy b-( gies 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 pe ;j *+k)d uruqwg0+qegrson stands 3.00 m from one speaker and 3.50 rg ug*q)w u dk;+jeq0+m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed coo tea7qol. 7t.(8od to be vibrating at 132 Hz, but a piano tuner hears three bta.qt d(e8oo.o7 co7leats 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 ?   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 l98*j(fkpghbf , kia4m in air. How many beats per ffgpkjh9il84* a kb (,second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency 772gw4r d svv 5;nwiuyof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wi2u v7yis5w4g rdnw;7vth 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 o8i4:p vuor9 mfgxe9i :o8 bf3fire engine whose siren emits at 1550 Hz moves at a srfe:49iu8xo :3mpo fo vi 9gb8peed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movin mj7fn**1w c-5twsdyrg toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they-syj r5mwf7 *c *dn1tw 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 freygdq2g 63xd .jquency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at res2ydxj6 3.qdggt 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 wavegj4b(qmhdb ai:5,)- cf :zu gcs at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency:adg -h(fg,5ib) c:mucq b4zj?    $ \times10^{ 4}$ Hz

  A bat flies toward a 5fmhdmb..j 7gw tcg wf(s-lox* 3+x3zwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? h3*73g wfxm(f.g- otm d 5+bc.wsljzx    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was phb98zx+ tr 1+mh,opiylayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was h 9,+zth pi1+orxm8b hyeard 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-flys,o4tfo8; z9g3 fk nuow 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 Wntfs kyogf4u398;z, o hat 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 us.19 xupt d7or giablf*9.)k njing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the o olwxxs: cha+ nq59+bf0o9 +3e c;powwind velocity is 12 m/s from the north, what frequency will oob qc9+psnw+ oxo 0cfl 9ox;h3:ew+a5bservers 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 s ob5if(e p6h s(th:wsdg -8t9land 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 g wpi9 5sijk+k jz+ii lc5k,3lb c;j,,m/s (a) What is the an+ kij9;cc+ilj, bs5gp,5wk jl, ik3izgle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere al/0 ugivqpd 4 2,3ldat0b0: p1 vutldof a planet where the speed of sound is oni 0al/tq d,d0bvt4gp3l l2d1pvu0 :a uly 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 th+ptprw,s4xy: 2x 1ojz hb mh,;e shock wave angle it producesxho,4p, trbzyxwmj 2 hps;:1 +
(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 0 cy46obblj*zw4b7nri l; k, y$/theta$ 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 exactl4hmozu,fmbf u 4)o /w (igxs;ug 04wc)(oxbr4y 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 horizox)u cx0hu/obsm)uwm,(o (4i4f; f zogw4 4bgrntal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000rc.b dqt x/vf7w2.0su -Hz sound pulses downward from the botxw2c0 db us7/rv f.tq.tom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many 93wcexe4tj srfl8rr0t 2z;h 9 octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a*(jpn c uiqce8 p.y*m8 display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, wy8e u*cj c*i8p.pn( mqhich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closel/vf,aw ;7sxq to the threshold of human hearing (0 dB). What will be the sound lla w ,7fq/vsx;evel of 1000 such mosquitoes?    dB

  What is the resultant soundj2pmp n/)s h-q level when an 82-dB sound and an 87-dB sound are heard spsnh)- p/q2 jmimultaneously?    dB

  The sound level 12.0 m from a7wg wrhs+ 2uo2 loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates grwh2ou7+ 2s wequally in all directions?    W

  A stereo amplifier is rated at 150 W output at 8suzj:p y20mob3ctb - 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watj b o8upszc:2m30bty-ts at 15 kHz?    dB

  Workers around jet aircraft typically w)qop99hj4 u jdh:8qq eear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from 9 h89:e4jo q pqjdqh)ua jet airplane engine?    W

  In audio and communications systems, the gainqz*nsk o8x8 7da8/tdt, $\beta$ 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 frequedz-s r w+h6n8,n*1wyzv+hg29n k kwnincy 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 be,uk)cc7 hd :obtween fixed points with a fundamental frequency of c7dck)b ,u:o h440 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 abbg /bs8y,w d2y1xf9kvove a vertical open 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 tuni,ksd91ygy 2xf 8bwbv /ng 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 o8c6mrgc, ) .y igd(hp9.k fhqkf mass 2.10 g is near 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 mode) with the third h h.gcgyk8qpm kh, (cid9)r6 .farmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on:)3z)1 vzswflv-v uq x6azs,ne 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 two source 4uv2frnbe57 ;)5s rjo.lumgo s. 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 other. What is the fre ; ovb7lr5u2g)o.sm4u5 nfe jrquency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationar+qa) /krv :te6;rfieuy. The conductor on the stationary train hearva;6re+ fiq et:/r)uks 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:wke9-mfkxx u( .,crk train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measuredx: (k,-cw mu9kekrf x. as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spee8a 6pcq,v mbjh/6-qp s5g xi+rd of cars just by listening 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 goes by ppc6q/v58jbxi ,+-ga6qrmsh on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding t0o kfe3b,.9*rpas j qqd --r dnp0ln9vogether, produce a beat frequency of 11 Hz. The shorter one iqd-3l r,0qfovp 9snb0. 9dk ea*nj-prs 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movolc t n.(n8b;fes past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the n oc;b.tnl8f(speakers after they have passed him, at C?

  If the velocity of blood zv8aj(e mu+ z e6(1fjzx9 mme+flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bz ef( umezx+az(9j+vj8 emm 61lood 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 .l5*wjy z-wdmbat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave d.-wmwyl5* jzdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap ou* xse7w2/+l6av rinxplxci- 5jg/.proaches 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 de ai-5 v.jc+7x gn//wrloslxi*2pxeu6tected 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 onj(mp2fwzqz0) e Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? q)wm(z2j 0p zf(See Table 12–3.) Model as an open tube.

  Room acoustics for s n)p. 4h:k8mgzp v (kwxsbj7e5tereo listening can be compromised by the presence of standing waves, which can cause acoustic “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 t. 4:n)w (p 7xzkgs8ehvb5pkmjhe standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender al yth2dmmlcwst*6k52 r7 do1* suminum rod held in the hand near thecdl*26*1 kom hs rtw27y 5mtds 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 threshold of hearing for the human ear at a frequency oquyr6jy8 ;bj *f about 16yqjbr;8ujy *000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground herqvb04gvc-s snsc/ b+ q1 1iy/ars the sonic boom 1.5 min after the plane p-qssnyv sgci/1b+ r0 v/q1b 4casses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1ni ut.oq5 u)h65 $^{\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