What is the evidence that sound travels as a wave?s::wsd4kyuq 9um o/w /

What is the evidence that ss-b )2do h-xd0 rfgmd,ound is a form of energy?

Children sometimes play with as6kip5 t cq3 w u)p2g05bgdud8 homemade “telephone” by attaching a string to the bottoms of two paper8s)pup q6wt 3guic2ddgbk05 5 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 wav-pza5dj ;p,opelzaojd;- pp,5pength to change?

What evidence can you give that the speed of sound in ak4d:k e 7learlh-c:) air does not depend significa- h7ke :r)lace4klda: ntly on frequency?

The voice of a person who has inhaled helium sounds ourl8 uu /f.wj5 -8ghsvery high-pitched. Why?

How will the air temp+f1pjiw wb jf /io 0o;gg 991u0pho6uwerature in a room affect the pitch of organ pipes?

Explain how a tube might be utx,,s 6f;cdg esed as a filter to reduce the amplitude of sounds in various frequencd,x est,f6 ;cgy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closenp au8nzzpr+b rk-(10(p dp c9r together as you move up the fingerpap0p8zz b(dn 9+ ruk(1r-cnpboard toward the bridge?

A noisy truck approaches you from behind a buihqwqs 1ij)is n5; e6y,lding. 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 noise. Explain. [Hint: See Section 11–jy s 5q,1i i;)e6hswnq15 on diffraction.]

Standing waves can be said to be due to “interference in space,”zlzot dh*h er *47 88/d1ubzbm whereas beats can be said to be due to “interference in time.” Explain.z t*ebuhz1r4/ *dm8o8h d zb7l

In Fig. 12–16, if the frequency of the speakers were lowered, woul14* q2 tf6q(vkvh2ihu ara*upd the points D and C (where destructive and constructive interference oa uv6 4vqa*t*1hq2r(pf uik2 hccur) move farther apart or closer together?

Traditional methods of p1,cciwl b3;hs ha97fnrotecting 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 noise, inverts it electronically, then feeds it to the headphones in addcnhbhc s,w 3i al19;f7ition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fia re l:xb, wg*+tdzrx4)wt /f:+-3m+joorjiag. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In t)ar irf:-rx*tbx/ jj 4odzw+e+ :wa+lo3mg,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 source8yx*, /gnh1 om gooau4 and observer move in the same direction, xa4nh ogm8o,yg*/1u owith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hea(l,c0oyhto z1(e: zvard by a person at rest with respect to the source? Is the wavelength,lzyz ( oo0: h1catve( or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A nf/d0;rlq-o// p x8) xmltmii monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for t )//df tnl iqlo8m0;xxp/mri-he sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeningmc(b 9eug+q;z9 s4;ud jo xqy9 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 o;qjx4(+99u9 u mdygbzqse;c the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the 84vshx-v esy*es5,gn waterline. He hears the echo of the sound reflected from the ocean*nv4gx 5,h v8eys s-es 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 wavelengths in air a3rst9 q) 6+d9lg ynoz f3qc;ust 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 foggyk)l*mc b qz+pt.5cw;y day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the5cwq kz)tm*yl p+c.;b backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cvp-yw0 nok4,rliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clifkn, v0rop 4-ywf?    m

  A person, with his ear to the ground, sees a huge stone strike the concr.yn 8 :hrcj nvjkp-d8(ete pavement. A moment later two so y(h.pvk:d nrn8-jj8cunds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b5r)l gz)lmkat zfk(7-t2s z-ky the “5-second rule” for estimating the distance from a lightning strike if the tempera2 ga-lf-lzk 7t5()z tszmkk) rture is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of*iz1s5 e /kqns a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose ni5iu(z gpr1hu,1i9zintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fibejce6rko -stg:p7vg/. b2ltl5)iv( l 3)lw ered simultaneously at a certain placercki7:lb 6et(v)pljt)sb2og /e wl3lv.e- g5, what will 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 with four equalp/ ne sdgip dj:5l4h09ly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitip dpd5ns9 h: il4ge/0jes, not dB’s.]    dB

  A cassette player is said to have a)2ai 6u q*v-hgflj4s o signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise q)a 6*lsf-v 42hgjoiu for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking 7emfq-)8) ) joh a: rucv+ewmjin normal conversation. Use Table 12–2. Assume the sound spreads :)u a ec7j))h m8rvm-fe w+ojqroughly 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 ann,acl 28y:pr57 l nrfl eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated att yl;rf+nr.wan* 6*telqc/wbi a57r, 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibely,t5/ +r*ac;lebiwqt.anlfrr 7 n w*6s 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 woc mp6bt(tn u.+; m7sm4zip0ybgld ,4hen placed 2.8 m in front of a loudspeakmzo0ttc gsn7p;p4i .+m(mb,l u4dyb 6er 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 sound lb*ec.iwklw0m nig 41f9,f3slevel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by t 4nbwl 3ffls *9w0ik1,.gcmeihis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte m:efh*, q9r;zrwu:ysnsity increas eh :msqr:9zuy ,*;wrfe? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal ebts ir :,*j/ndisplacement amplitudes, but one has twice the frequency of the other. What is the rats: r*bjn,i t/eio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that co7g m08ssobsja -3e.nwrresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H 8s sgs0nj3moa- .bw7ez?    dB

  A 6000-Hz tone must have whacq)/6lx5xy c 99pwb7rbfn. jlt sound level to seem as loud as a 100-Hz tone that hasbq. 96lfwr5 pn c)x7by9lxjc/ a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest folgawktnt-0j ; z2 r*-h4kt1jrequencies that an ear can detect when the sound level is 30 dB j--ko;zjnkgwlt1 tat4r2h0* ? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l ,qf27k rnkhj -wqz3x)evels. What is the ratio of highest to lowest intensit hzk-,) jwx7q3fqn2kry 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 ljvgnalci8s 8u p+ (66uength of the vibrating portion is 32 cm, and it has a mass c 86 8+agji6lpu(svunof 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental ando cj ie6-v-ilkf,9h4x7i iy w;.s+a by first three audible ove.+iavei 7i9jlb;xh-cs64iwy fk-y, o rtones 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 acrosw (w4)zq;v43 upli azws the top of an empty soqi zww;wv p z34)a(l4uda bottle 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 with open-tube pipes spanni:y nb +5qytoz7p9 xj/ zg93qb t:ilny0ng the range of human hea75y bqy99nttn jz/+ g3 ipqb:0xzyol:ring (20 Hz to 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 stringo:* wp m3l-t2m -ge9zrs3rbxmw qd/k4 has a frequency of 540 Hz as its third harmonic. What will be its fuw4t2qs *o rzb3- mkgpdxmewlm9-3: /r ndamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7.b e)5tpgexk4 mo;xk y,0sj h:3 m long and is tuned to play E above middle C m5 y ebepj kg o:,x0hk.4)xs;t(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that ,vzea9wewbbz4i h* eq85as,z1 u 8d a4emits middle C (262 Hz) when the temperature is 8 ab94isz4vede h8z,zqa*w,ae1 bwu5 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at,afu-, 3y) tgqrmf6ht 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 sh2aq:f*tw:b lc- tcg b1ould the hole be that must bewb2b c :g*l 1qf:-ctat 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 616 Hz, bu)l -raxc +:dqz 75 6b2izivrx7d-a ibat not at any other frequeixavarzcddab7qr+2 -b i 6:i)-57xlzncies 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 1.8i+nq-d be+(l4-vojf g 0 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Whae4 +-n-obivqf +gd (ljt 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 bn ,0hios3)kkf* 1j mv$^{\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 presup n ;uva1t1x 91xzii0ent within the audible range for a 2.14-m-long organ pipe at 2n;90axitiu z 111vpux 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apduha) 3am ;2iqproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph oa;) 2h3 quidmaf Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bta:weev0*0 *okz1fo reat every 2.0 s when trying to adjust two strings, one of which is sounding 440 H: z e*r*t0okvoaef1 0wz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C 91mbfrppazwt+ . -wz-(262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operat 7olaukhf 2:d1es at an unknown frequency. If neither whistle can beoh 12: ukdf7al heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fs bbsu:nba -fth0/p32 q/x2rqork and 9 beats/s when sounded with a 355-Hz tuning forkfb2x0s2 qh u/ -apsn/br3: qbt. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29cev :pye :j4l/4 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard whpjce:e4l/: yv en the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if i67gmm t4zzh: two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the otmmgi 6 zhz:4t7her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Cs )wpay(:fro-71 g gyf. Fork B has a frequency of 441 Hz; when A and B ayfw)poasg17g-y r( :f re sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A 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 standsh eo/t3)zyy) v 3.00 m from one speaker and 3.50 m from the other. o)eyt)v/ h3zy
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner heari37vx;3silb c s three beats every 2.0 s when they are played together. (a) If one is vibrating at 13ii ;33 xsb7lcv2 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 wavelengthf+h v (/np; :xdiwmib;utmi:;s 2.64 m and 2.76 m in air. How many beats per se muwn mxt;phd ;b(+vi;f:i:i /cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1bxwn1d qv7 k:o7jh* 4ur/weo /550 Hz when at rest. What frequency do you detect on* :/vho x7rkqw71ebj uw/4dif 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 de3ada+kd-b) u rbr: xn0tect if a fire engine whose siren emits at 1550 Hz 3a + x0d)-n:adkburrb moves at a speed 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 moving toward-lh4ecvbg 2h;a.gv x6m+kb uhd.3:ir you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cl4ga eh+x:lu -hcb.igh3d2br;m. vvk6 ose? $f'_{source\,movine}$    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 equu(9ioz:s6c3*ju p vtu ipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the hor:(6i zc9 3 uupjtsvuo*ns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and redvzjj ph8+v (p*d1;avceives them returned from an object movi d+vj*p;8v p1jahzvd(ng 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, the bajhd(8 ;*z; cnk4gwqc at emits an ultrasonic sound wave with frequency 30.0 kHz. What fre jgdwk4az;8c *q hcn(;quency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on hm 9q 7c)ryjqyf*ueql1i+s9. 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 heard if the train car approachedq.u9*ci+e q1l y97jsfq yhr m) the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spemg 7;5eaejbw 2f8t 5vzeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound sourcebgvfwe;5ea 285 tj m7z?   Hz

  The Doppler effect using ultrasonic wa d. c(ars;j:xfves 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 wind velg7.*culba-3 vrdmz k2m*so *vocity is 12 m/s from the north, whatr cb*sol7*-23 . zk*dumvvmag 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 morxb8j1r dx3p) ving 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 Machl.dig*2y1tm* 5ner 8ikv b zg2 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of t52em* tz* 2 kdnly8g.vg1i rbihe 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 of a planet where t9 lfb7ut/dh3kkz1e5f he speed of sound is only abouth/ke9ftu3fb7l k 5dz1 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 ocen p9mz kjpfdi7/, -kib.:rh n+an. Determine the shock wave angle it produc/,mn .9kpzink f:7p-j hbd +ires
(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 dd3nf/zt0, wr 0 rt4xo/sg6qb$/theta$ 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 g7 gqvf2npj*tg 63 r+gl48ihciround flying faster than the speed of soun2g*it3 +gi7 vl8 n4g6jhqpfcrd. 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 device that sends 20,000-Hz sknja v; 6baj8c*3oz2b ound pulses downward from the bottom of the boat, and then detects echoes. If the maximum de8*ak3 aj2z6;bnvo cjb pth 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 humanm)7 iok9k f1ww audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a d(r6o+z;t t fakisplay called a sewer pipe symphony. It consists of many plastic pipes 6(o;kzf +ratt 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 fq/qfbx h)z 2n8rom a person makes a sound close to the threshold of human hearing (0 dB). What will be t 8z/qh2f bnxq)he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sobhv-wqd /z 9n lw n( :4bzm)6pwcn*v9sund are heard simultaneoundc bv *:9 zmhzsw6(4q/ pw-lbv)nn w9sly?    dB

  The sound level 12.0 m from a loudsp/ pw+q e,aquxel62dz+msffoy6qtp/76qc 5, heaker, placed in the open, is 105 dB. What is the acoustic pow/ pq s6+566ual ,t 2,y womefq7feqczx/hqpd+er output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is ravwi .+8zea. 5ub7 2otl/fieqy1bpk: sted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the po5a8 +./e spbwt7 yifuiz21elokb.: qvwer output in watts at 15 kHz?    dB

  Workers around jet airxj. +9w*ikfen3nv fc,craft typically wear 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 aiw f,jfn 3.cxkv en9*+ distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th3 ,1mwvtx3 3yy ofo vvp*,9cnwe gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tokb61iel vvx:us6 0a d5 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 between fixed points with a +ocvf zl:p17y -on,kefundamental frequlp1z,eyk c:voo 7n f-+ency 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 filled wit.r,cbd/4dg0nb 2 k6vx-g hbsw h water (Fig. 12–35). Th2 nb-gcrdws0vhx.db4 g, b /k6e water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar st; o ub;a9cyw5yring of 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 hao9y ;c;wyb 5aurmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatr,i( n8 uzo2wze 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 f :-tj2o/ s5 nz0mdnvatone in the 500–1000-Hz range coming from two sources. The sound i0s- a/:tz5m2jfnv ndo s 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.lj 8dn2h 9prt *8ldn)m One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whad)rt28 m9l8*ndn pj lht is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachetepzpw,:7 6we*hpafos5x/g1 o *f;gy s you is 538 Hz. After it passes y/7;zh a6xo1tw5p gfopsy*,:fwee p*g ou, 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 listening to the dihc;3 2o ayf1pol(ky xg+j6hd;fference in pitch of the engine noiycyp f; (g+6d1j 2;hlhx3ok aose between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundingszvy v,r4 5+/v rb1n bfkxs9r* together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho +s 9 vb,vxnsbv5krfz */1y4rrw long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pas8ok 9rsokwr /)l h9i,jt 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 bet9os kilk/r8j)h r,9wo ween 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 bea7d :5utk wk.z44q7ehoryn(,) bcbw/ycu pk :gt frequency would you expect if 5.50-MHz ultrasound waves were directed along t :bwr4uogt k :5 bd/ypue4q,n(cc7hkyzw 7) k.he 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/sboqpoz) q by 5*h.god2*vc6ys n(ejo-zq. 8 q- while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wavy--v o68)q.pq (.*nbzq5 q2oc*ds zjegoybohe detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series h+wos/z j3,s cof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and ew zh+jso3/,cs ach is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals frod:)u.8ucr+vzo qc(ar m one Alpine village to another. S. d ruo+u8 v)cc(z:raqince lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pres xc0(1)ymavp5 0k qm ahawf3eiqqu03:ence of standinq: eqakqa(m 5whu3 )1ic3v xpfy0a0m0g 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 the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invnkfkz 2.j:y r0avsnbub5+4 kg ko227qolves 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 0skk2:+n.7ay onvrgk2 b5fz j uq k24bpractice, 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 7;vxnkzjsr.k d53e+t hearing for the human ear at a frequency of about 1000 Hz is 3jk 5.rdt+s7vez; xkn$I_0$ = $1 \times10^{12 } W / m^2$ 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*l, ,2 7mlg6lrzf:0 fpdxucxh.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What isz,g uprf7 *m6ldf: x20xch,ll the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 x6dq futeqs:n1x8.g4 $^{\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