What is the evidence that sound travelsbt 9v rg04vd)c as a wave?

What is the evidence that sound p zt1ct.5 :5ybdeq wd1,2 vlrris a form of energy?

Children sometimes play with a homemade “t)v,+fr (gaxmrelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks int, +)gmvxfr (aro 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 wazx1q 4jw n,-eenj22asvelength to chan nq1s4a22 ,wjeexz-j nge?

What evidence can you give9uo8 y,r dcpb: that the speed of sound in air does not depend significantly on frequer,8u:yodc9p b ncy?

The voice of a person who has inhaled helium soun7krwb yr(gl)) q*c1uyds very high-pitched. Why?

How will the air temperature 9g o,abuko04l )sr4*/yroyumin a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducelrv,r,s u)t );o-pola the amplitude of sounds in various frequenltal ovrsr- o)p),, ;ucy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. q ;6msz6qvn0h1dno;:1 qszjh12–30) spaced closer together as you move up tns;jvs6qhh oqzd6; 1:qn0 z1 mhe fingerboard toward the bridge?

A noisy truck approaches you from behind u mmb587 fna8na building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on di7bunf5am n88mffraction.]

Standing waves can be said to be due to “interference in space,” whereas beat;: ;uf6cddabjs can be said to be due to “interference in time.” Expl;; dd6bu: ajcfain.

In Fig. 12–16, if the frequency of the speakers wer gg*hr*w 3su:re lowered, would the points D and C (where destructive and constructive interference occu wr3r*:h*sg gur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with- k ,dov n *gxmxk2i8/pl/4eok 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 t/kg*l,n 2xmp-xv/o8 iko 4kedo 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 berl:frlcgo xa0t v07/ ( thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (al00 7/ol:g(r fx trvac) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the rt;, xc o 8f9ete7w.gysource and observer move in the same direction, with the same velocity7 wt,tr8e;. gf9xoy ec? Explain.

If a wind is blowing, will this alter the frequency of the sound hea 1o0 //*,ih3qs chrsu-vh 2s boni4vjrrd by a person at rest witr4cuosh3 s i/i,* -o hqvh10/2 sjbrnvh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various position(x,uv f etm51is of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which positiofv(1mt,u 5ixen, 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 th29pfmsmm d 69ks1)otq e echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afters 9)m 6sd29mpfoqmk1 t shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the1v;6a 0ru.z2wi6 ecvp-ki n lk side of his 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? Assume the speed of sound in seawater is 1560 m/wz l.iv6kpn6c 2u1erkv-ai0; s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveltq vocts92sjtf a ,023engths 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 tup9ng;. kk/t-mk66a aj f :xphona on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (F pm/.;6k-6 oa9:pfg hktanxkjig. 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 clif njlaswaa7 m,r*-ohp)j;;p 5mf. The splash it makes when striking the water below is heard 3.5 s later. How highn,a m7*ja5 lwmjr psa oph-;;) is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thea y a;rv4sx38jnz,y/ fw7zhz8ri8v p: 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 f8: ayrazf/svrz 8 ,47zpwi3yj8 hv ;nxar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the it;j8zf xo b+h2: ./w czw5nvu“5-second rule” for estimating the distance from a lightning strike if th8vjf;w./ c zx:oz+b2 tn wui5he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1pqlr/ ttuo m.j1 j5/+ncdf5z .20 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 inten*,gtscel6po)0- cq9arfzhn *sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of l*l r6lb xti;;z-/ bswegj 3/x95 dB when fired simultaneously at a certain place, what will be the sound level if only on6r e-j/ ;xli*tbx3 bswl; g/zle is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four ek6fz-e8t/ nh equally noisy jet engines is experiencing a sound h/6 t8fnz-eke level bordering 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 snu06 e4v mv g:nu3y-pkaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities ou0 vu4k engny vp-3m:6f the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norma) *- *sr+ahbt7zk ga zw5bsjg5l conversation. Use Table 12–2. Assume the sound spreads rou+g zbaw s r5k5sag*bt *hz-)7jghly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an ear 6 cjw*ky p(n-su:9i1kvx( yccdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B c/ 17jros)wufis rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeakerjs7 u1/fwc )or 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 regiss7 m*de. 9ssextered 130 dB when placed 2.8 m in front of a loudspea. 97sedme sxs*ker 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 levelb+j1v 7t/o,db0 hje wj of 2.0 dB. What is the ratio of the amplbobj71 ,dje tj0 h/v+witudes 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) by what factor wiva(vi3+xhghl/ o f.w:ll the intensity increase? Increase byol3 /vg :x(fhh.v+iwa a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa:-fu ( +tfzx jrtgw 0ogk9-d3bcement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?3b0zrt(djtu +k-: o-w fxgg9f   

  What would be the sound level (in dB) of a sound wave-h/vqtm/8 mtgd0:mm1fguj - m1btf x ( in air that corresponds to a displf1-0( mx8jv g /tbtf /guthqmm m:dm-1acement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seekox;-lik)k,(qq z qvza.x)pbz3 - 8b. dva1ynm as loud as a 100-Hz tone that has a 50-dB sound level? (See za.ny8iap )zq-xokz (bklkv bq31-x vd,)q;. Fig. 12–6.)    dB

What are the lowest and highest frequencies l/pvaequ e 6**i a3di lt7g f1;-id+djthat an ear can detect when the sound level is 30 dB? vale i76a*/eiu g f p+jd1;d3*iq-dtl(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whvczfn,p -q,(o/1s o zb(0ihmiat is the ratio of b v0/fom,z,cnsh(i p oz(qi -1highest 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 viol8 fxiag2906ib6 b6wjmg tcq-o in has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a g6cgtwbi680xa 6-9ib m q 2jfomass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh:w;hrxhi5 9z frsfnp0/; 3nztat are the fundamental and first three audible overtones if thhr;f0rz h;nwti f5sx93:np /ze 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 expi5 *r54 x xbvyqq8qe)br+o7 2)kcplgvect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wak 5cv+q 8xqr)oevrb 425g )ip7q* blxys 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 5i2s:2rbm6wx xmq7 csspanning the range of human hearing (20 Hz to 20 kHz), what would be the rangxs7b2cx2 s5q6wi:m rm e of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string h.a 7s. 0colzwycvwa ).da o4j8as a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if idj0o.4wz) .so7c.a ay lvwac8t 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 to pt8iw3j1wk3 s klay E above middle C (330 s3ij8twk13kwHz).
(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 middle Cs9i4(/qpc6ag+v6v wgqv lnmefr 7 .9,7lclf b (262 Hz) when the temperature+ea,lgnqg v 7 69/l(i4bf6s .lwv7qc mprcvf 9 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 at 20 8iwqc)pa*iv. $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl ca-lm- y6s,mwute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 2m- 6-mw lay,sc94 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, andp8f (cg y,h)nb 616 Hz, but not at any othe gf,c)(p8 ybhnr 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 e d;kst5o3p )pm long is open at both ends. It resonates at two successive harmonic5s to )3pdp;eks of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 d.):mnzt9e et$^{\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 withinbw z7dw4vy a -dd 4kkt-7wv-2h the audible range for a 2.14-m-long organ pip--4v-d7dkba wdw kvw4yz h 72te 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 outsidef 3i)b m+no awum10ah6 and is closed at the other end by the eardrum. Estimate the frequencies (in the audible ran+3mnu6awfm)0 i1ah b oge) 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 be7u zo4sx8i 2od4mb6wg r16iqc(f9i vjat every 2.0 s when trying to adjust two strings, one of which is sounding 440 1 9vqco(ibw gj u46 2rio6z s7if4x8mdHz. How far off in frequency is the other string? ±    Hz

  What is the beat freqsvm f7ky08-gs h1fec2uency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (branpo *i,7gs3z dgd 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 occu gz,ogds*i7p3rs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded w7 4tnv,vp6 f*6vvcyz qith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuzqv,p y4vv7f cvt*66nning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the/5kwmo i*b:ah -:zur c same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard whe5birzawc h*:u /m o-:kn the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each /0qa3pnq hv3(lawsx-try to play middle C (262 Hz), but one is at 5.0°C and the otl0- w( aphaxqv 3/n3qsher at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequqn;+ (wd/sg5f pddwaxxj 0r95ency 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 f0; ds dwdrnjw+5 9f(/qx ga5pxrequency 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 apasi 2644 +tgholhcb/p3hg).fbbm s:6j,vxw qn rt. A person stands 3.00 m from one speaker and 3.50 m fromh 46bivq xsg,.sfhc:)w t mp43g +n/ h2jolb6b 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 supposedbdi(7-g sdm4mxkjt+,qbe-.u to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must iqd,7 ukm+.gbx-j estm(4- bdbe the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in a fhpvtbp 6s;v4.: ukr)ir. How many beats per second will be heard? (6.vk rt4ubp ;hp:s)f vAssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certad9kaunxe0(g mz 8;pt4 jx1)cy in fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/a40m e( xk 9gntpy; c1dzux)j8s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine who,.ia0 s7xl 0d8enyaauq7+a wise siren emits at .uxa7yn i,0aa eidas0w+l 8q71550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency o9tt 5 .;8tskltpwp7s if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward s l9tw;85otps t7 t.pkit at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singgbspu5 3 ni6;jle 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 freq;isu653pbg jn uency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras;jhjl*/t xp f3onic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the tj/jfl *h;3x preceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the qwte ij+n3kc2+ mi qbu,e1y*: bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the c 12i3*m qbuy,ee+:itk j+nqwreflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba hnmiq,. .d+ biwas played 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 heard if the train car approached the station . ndqi b,+h.miat a speed of 10 m/s ?   Hz

  A Doppler flow meter uses u osmli)fyva:(e:1kj ) ltrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and j1l) (y:k fas:eim)vo 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 ui rkl3e6d id+6 h1bq0lltrasonic 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 wind velp x;w97e;pghh9 2pbcfgk4ef+ ocity is 12 m/s from the north, what frequency will observers hear who are locatx+bkwffp9 gc p p294 ehh7;;geed, 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 movxmd m(2 vpu+o*ing 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 whc6*-.pporwo z ere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplanec wp6z-o por*.’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 pla51- vefpdo:c:nxuk: onet where the speed of sound is onlyo xuc:-f5odn: p1e: kv about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the sho(x l;rd/spi ,u-0 slxb5un:i ick wave angle it p :/bp5iusll r,(- uxx;nisd0i roduces
(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 2e5i viovj)t-vv.-g i$/theta$ 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 exa*,idn+vna i7,t em-:s*wgr ed9t d:ctctly 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 horizontal distanc r*t7ed,vw+mc9n-ddgti:*t , i:ea nse 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 sound pulsdc(jd+ cyq79f0e yg ii- bv+.zes downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the. 7i dez9c0b-iycyfd++ v(jgq minimum time between pulses (in fresh water)?    s

  Approximately how many octmveb ,qp dc,r47pq 7z0aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pip+hzcnv5.11sdg1 re.o/hvnr p e symphony. It consists of many plastic pipes of various lengths, z1prd5cor/e.gn h hn+s1v1. v which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person maprifc0e1,v u wop;2 8okes a sound close to the threshold of human hearing (0 dB). What 1;upwic2 ov8 rpf0,oewill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB +.qrqcu3e6(z l qj4jbsound and an 87-dB sound are heardq3j6qbq (+.c ju4l rez simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,of r.nrxq3/8 0xugw 6hc.ay6x placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dig3 /a0x fnxuhy.6cwx q6ro8r .rections?    W

  A stereo amplifier is rated at 150 W output at 1000 fm 9(:xv;;htaid6gsk Hz. The power output drops b:svmh6ax;f di;tg(9 k y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devig hi3y 5ep7.czl1dgz-ces 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 eg5yz- 3d eg.lhiz1c p7ar at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the 7ycexrx/ d+ g :*ytv5tgain, $\beta$ 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 s);m te1 0 c0urrlq/r xw4rbz3q 3.sjgto 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 cwoqge9d7eh: h3. iut. m long between fixed points with a fundamental frequency of 440 Hz and a mass per uni7g. eo.t:h e3iqdh 9uwt 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 opehwu v4s/2t) rqn tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water s 4t2v)rh/quwlevel 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 nedoe,630 mcfaqar 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 hao3aqf,c6d0m ermonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wasbk(3*f2mkkk k observed 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 i,k( 03 .2ucj5xblnvhwzls+f2 ep yfo +n the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one sourc sj3yk5+lc(nvu ew,p xfbh20 .ofl2z+ e than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hsqa7 88wd hqwu7n9 :/.zclt jbz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat freus78t.7q 9ahdcb:q lnwzj 8/wquency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Af ,v5s5s 9cqwfb 5j)igxter it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assu) s w,i5bs5x95cqfgjv me constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the rd ohu(/ q4d5ko6l4jzz 8:blxdifference in pitch of the engine noise between approaching and receding cars. Supz: o (j xud/5lkzbrod684qlh4pose 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, ss 8rl34u()na)i,0wtliedi l sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thel i 4)lssualei3tn80)r, w(di other?    m

Two loudspeakers are at opposite ends of a railroad car as itkzti/u 0jm87y;9uqia.o+1.d bkoue f 40l eog moves past a stationary observerob dkqj iuul074ze+/e.ogmo y09i1 k.8 f tau; 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 speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s w4/k0;bv u/ou ,1zvt ejq 1yeufhat beat frequency would you expect if 5.5jko yv/vu/4,ef utbuq0z1e;1 0-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6., ee 2vx-hlb;x a-og4,i )jdwc5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a so) x,e ,hdwv-liba4x2;ecg-ojund 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 syq+y q;) r 5n-y4*6lsvlzg uk0j. zocof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms r-l qny4q*; 5lss) cyoygzj.z+v u6k0 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 uswp7jti gi/fnfp ;6 1ssuov 9).d9 may.ed to send signals from one 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 mosjpn6g s t;v9muip. f7sw )a9y/foi.1dt 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 d7,1xn*ehdi 3.3ka+j shmsl e the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure is73hxkhe.lm*3sd da e1 j+,n 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,” inv;1wrs:ix5 ec jolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked wiir5 ;jscew:1 xth 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 humanu-. fw.w4 jlem:w,hhq4r omy . ear at a frequency of about 10.m. hw4rl- e, jomqfuw h.4:yw00 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 hears the sojk v98/3 :1 opqsmclv4zm1kqanic boom 1.5 min after the plane passes direqckom9am1v /v l8:j 4k zs3q1pctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboctuni+3a6 )yg :e: f wpqbd:e 8zf58riat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h