What is the evidence that sound twaq76d q 6-nm nu;y+hiylu7b 4ravels as a wave?

What is the evidence that 14z7 qlbfcaf6 sound is a form of energy?

Children sometimes play with au(fg 7fav 0y4u:vm9olb.z)yo6)ka am homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29vkm:oay yaz0 f4uvg fl7 6 9ao)()mub.). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do b3hlk)w+e*4mcor i/ uyou expect the frequency or wave*uk4o mch)le w+b3ir/length to change?

What evidence can you give that the speed of sound in air does not depend ss51 bzxmh.ku0ignificantlx0 z.sk1 u5hbmy on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. yot0* 8xaoa)p Why?

How will the air temperature in a room afems6d4*b961oih)5f wf tizs xfect the pitch of organ pipes?

Explain how a tube might be used as a fil+ lf*l6 r /tqe5k :hv6qy+oqjlter to reduce the amplitude of sounds in various frequency ranges. (An examploq 6r+etyhl/q q v ll:65kf+j*e is a car muffler.)

Why are the frets on. r 5ps9m zu0c)g3k*vxeuav 4a a guitar (Fig. 12–30) spaced closer together as you move up the fingerb v4x9a.euvmz)sc5*0p r 3kg uaoard toward the bridge?

A noisy truck approaches you fromjdc*2 l zcahrsato8c(v6y37 5 behind a building. Initially you hear it but cannot see it. When it emerges and you do s vadc 3hysc 2(z7alt65 r8jo*cee it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be duek4 (d6lh;k k)k -jsryb to “interference in space,” whereas beats can be saidl ykb(k r djk4-6)sh;k to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequeuvyf8l:de;vtj /n6u1mto z+7s /zbsnz8i(v+ ncy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farth(+s6+fbmy/ou 8 ev zzi7d:8 vtsn;ujtlnz1v /er apart or closer together?

Traditional methods of protecting the hearing of people who work in areas448m2ba*s0 i r s hdsfa.pps/p 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 ambis2dss 4rb0hifa. * 4p/ps8pma ent noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of aqmsu3nw ;b- *xfn3,6g4f c)d:w.lik hpo1ldd s a superposition of two sound waved 3 d;3ums6nb-)fdxo.cn*f4pq hlwl 1:w gki,s with slightly different frequencies, as in Fig. 12–18. 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 source and observer move in the same direction,6wf- +x typxyp0awv+7 with the same velxxp awy +0pf6+tvw7- yocity? Explain.

If a wind is blowing, will this alter the frequely8a gh vbsatp231q0 5ncy of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chanyt3a8vb1h0la 5q psg2ged?

Figure 12–32 shows various positions of a child in motion on a swinvz fbde/b 9i4.pzv s(4g. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your fv4s .b ( vz/p4d9zibereasoning.

  A hiker determines the length of a lake by listen;k8o d :7lwdpring for the echo of her shout reflected by a cliff at the far end of:ok l;7rwd d8p the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of k(zq0qe0is 7s6 isk2j 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/s (Table 12–1) an06 7qiks (0zssjkq 2ied does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ayx6g7p 9w2x h*o 1oui imgd98pt 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 lk6erid r3ye vxot*/7bw1 4;va school of tuna on a foggy day. Without warning, an engine backfire occurs on another 6eodb7t3l;vev wi x /*1yrkr 4boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it magcfaqoeo6 /eu *syh3fy 01(/z kes when striking the(yf/1 su feqeg3hoc*0y6/ za o water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees1 pdryk:)0v hi a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1d1rv h:ky)ip0.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by tjzilneei y// )g8ru 62he “5-second rule” for estimating the distance from a gein/6izer/ lj2 8)yulightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ( d-0zke2sho5 0fv0 )(xbg+os clqmg na 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 oarq .i. y,l7.(z3khpfpqx1xkf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when,leigsua jly7du7f6h04k5 9 f fired simultaneously at a dj47 ufslk0a 97 i5ey,l6ughfcertain place, 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 airplan4wa dk gqdds;7/8 4dj-4khwo8p cel8me with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person expe kp8kd ;d wl8 -4da844/smecwqhg7odjrience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rat*khaiu w sf(14olp35 bio of 58 dB, whereas for a CD player it is 95p 1 3kf(5hb*oiw 4ausl dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converks(r(im 9m sceyq54;kv ,i 0prjrp81nsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on thv rjk9 k;p4se c(8 y(irrmn5isp10,qme 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 strik+4:svpk d. mayes an 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 at 250 W, while the more modest ampg b pu5zs35kg. k8;giblifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conk 5gpszb8b. uk3g;i5gnected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placebs* n6uoh/6jz d 2.8 m in front of a loudspeao6z6sh/ *jub nker 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 typical0o-bcakm 6ft :( rzd86d pm/nhly detect a difference in sound level of 2.0 dB. What is the/8nb-6tm6rd d okf:cmz0hp(a ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, w3ncf, /ezu/z (a) by what factor will the intensity increase? Increase by a factor oznufe w/3 z/,cf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice th.mh4 utpjyj0 3e frequency of the other. What is the ratio of their inymt juj30.p4h tensities?   

  What would be the sound level (in dB) of a sound wave in ai 5f-c7 6evopzft2qkb)kg; l+wr that corresponds to a displacemczflvbkgwp7k2f);+o-e 6 q5 tent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev rwey/dqnu)kk;xd)9+ * 9f amtel to seem as loud as a 100-Hz tone that has a 50-dB rd me*fk kx)ndu/9+ty qw9 ;a)sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wg8le3 qwt6+plhen the sound level e+l3twl6q pg8 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huu+d lzaxwuxl-+2q 50 yge range of sound levels. What is the ratx d q2lwl++ 5-uu0axyzio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz(nv 3p/uueht *. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what ntvhupe 3/(u* tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental anobqktgi azkr 7rl2(i17 cu4e(w :-a m(d first three audible overtones if the( r7412a (wb keickgio-q7rz(aml u:t 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 e90.v6npwlddh0 ip w4blowing across the top of an empty soda bottle that is 18 cm deeplih 0 vewp0.6d9n4dw p, 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 spanning th18pin -c8kho9htcr; fe range of human hearing (20 Hz to 20 kHz), what would be the range of the lengt no8 kch;rhci-p8f 19ths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmon: rw6mxoo aa-)ic. What will bem 6ox :aw-)ora its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar s;cbyk dupcprpcg;xq+t7 7** ( pz9 tn3tring is 0.73 m long and is tuned to play E above middle C (330 Hz). b;3t g7y*zp*pr( xccnc;d9 tpu p7+qk
(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 tup0n15mow;n ghat emits middle C (262 Hz) when the temperature is ;umn5ow ng p0121 $^{\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 am8p2eit5w8lr 5qq6 xt t 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 be juirzjs.r cl0:d(w+l: p .1eothat must be unrj. d0oz1jw ls.ir :e+c p(l:ucovered 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 resoa9c5t 7ca x.1/ dgpamfnate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed x7a/d9cm fta g ap5c1.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 res f3-, l5 zi dvp:obv(2r1cnxqvonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What isd3vnlvcbpq ,5:1(ro f i-2 xzv
(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 00hjup: o 2 vclth3t:v$^{\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 presen8:qyv(p6+ar d lh2jt it within the audible range for a 2.14-m-long organ pipe at 20 q+y:2lapdi (r6 tj vh8$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5ho. j3,n e(tkw 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 relati,nj .h3okte (wonship 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 ea. j/i8*du9q.jmjnfo - uti9+ m7cdvi very 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency ijdt 7o.f99jd+ j /qan8u-*mumvi ic.is the other string? ±    Hz

  What is the beat frequencygt4 e- +sq r1(go-f1)rkeci td 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 anotherwxdgpueh6wp6-3 j 7t r:*p-hp (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shril6: g pt-x- 73dp*pheuw6jpwr hl 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 tunijtju* (4adgs y - sxbd:rob*:7e.8 opmng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationax*s8ebmory: apto4-sgjd j:u7 *.(d bl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiy r;mskbr*6:v on in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. sr r:v*k;6ybm 11–13.]    Hz

  How many beats will be heard if two identical flutes eachrw-mm2eqtks/lp kz14-a s h3 h4dk,/h try to play middle C (2-4ks khsm/4 1h daklw3p/q,2tr -ehmz 62 Hz), 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 C. Fork B has a frequen7(,sspufw:rj e.q x(n cy 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 fre7snx er(q f,us .jw:p(quency 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 t m37 ai04q,umals kp;9 bowl:m apart. A person stands 3.00 m from one speaker and 3.50 m 4 o ,lwq0;bp7kamt 3:isum9lafrom 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 to be vibrating at 132 Hz, but a piano tune,y*gma5 ay4n jr hears three beats every 5gajymn* ,y 4a2.0 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 m in air.rl-ri;ty8j3 .px y ,ec How many beats per second will be heard? (Assume y8 i try; lp3jrce,-.xT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire e:k hid5t8nzep(c5 4 dungine’s siren is 1550 Hz when at rest. What hi8(kp t:c4u5dn de5z frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fir *a(krhn p7,zve engine whose siren rk, av7nz*hp(emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20 cao/wz: x i id5e33-yxhv5i- -g 3gnw6ifir,l00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exa f 6xriz33-5ngi3lix5h:ge w,icy-o- idav/w ctly 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 sdt0a6dae 5hs3ingle frequency horn. When one is at rest and the other ahdat3s e5 0d6is 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 horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasxyn8yl/n/hyt l)x6,ieu3nu -onic sound waves at 50.0 kHz and receives them returned from an object moving directly a-yin3 elnu8, nty /)u xyhx/6lway 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 bms()rz0hkfo7s, ied )at emits an ultrasonic sound wave with frequency 30.0 kHz. )0,7ifhm( sdse o)rzkWhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimh0 0yf 85xd8q etyh0uzents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played 05d0eq8 8th xz uy0fhythe same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measurewcvvts j 3w7;l zj-s)c: itcintp,8 69 blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human:sl8i ,vctj p67t3ij cwvtz); w n9sc- 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 ultrasoniciqkbpfvas3c*b3/ )-34 siaxu 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 velocity is 4gbcuq w p-45a12 m/s from the north, what frequency will observers hear u 5-cpa 4g4wbqwho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if i4)8k7 sq oi. t itgcc(,eh:bujts 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 30- *(svskpg y-lkh:u.m: s ctvf p)-j+ 9dvdhf10 m/s (a) What is the angle the shock wave makes with the d9fgh+vk -:lssd *th:k )d mjcvfsp.(vp-y0-uirection 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 ieqqpkp0x /+6 fznp*4 the thin atmosphere of a planet where the speed of sound is on0 kp6 4fep*xqzi nq+p/ly 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 mrh1o,zit bc /*/s strikes the ocean. Determine the shock wave angle it produce /hzrb*1tco i,s
(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 sd4s5 u;*qkgxynhzx 61 r t)a/$/theta$ 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 grouniw7 ulc)-t5 fd s7cmc8f 3)upvd flying faster than the speed of sound. By the time y c uwf)sc5vm7)cut3id7lf- p8 ou 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,(i0a prfem6q k+om(h-000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is 6-m(r p+ihm akoqf e(0designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how mat*5nfx) bw j 7w ,5gr2vkya:mpny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum haslyk4 0fz0p 2pxrn *fm8 a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on botlrf82pfp 4nyx0 k*mz 0h 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 close to the threshom;0 pb0jbvfg) a6 7qeurcv+ ja0hwu38ld of human hearing (0 dB). What will be the sound level gv uw)u 37a8ap0hj ;m6e0r qjcfv+b0b of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dBxojt( 2,) yxvy sound are heard simultanxvx ,2)oy(jtyeously?    dB

  The sound level 12.0 m from a loudspeakerwr.3fwy a5 szr3l wl2t 4m;f5a, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiate; wwf3srrt24ml a.f zyw535als equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The poweaewnn qj*u w ))fp+ kaju:/c9c-jztnwq5, .h.r output drops by 10 dB at 15 kHz. Whatu. wf jjqaw*pwa/t j)h n) zu,e.cc:9-qn+n 5k is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically w;8 2lv+ij g+/dmeo kduear 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 d;gj+kmu / deov8d+ 2liistance of 30 m from a jet airplane engine?    W

  In audio and communications systey hvx 1.gc3n/ams, the 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 to a freqzjqk0a ibit8)r-f(j,be8 4 iruency 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 fixedq)s.:pbksuif0n, 2b x w7dp(f points with a fundamental frequency of 4pwfxubb2, ik7ns()dfp0 .:qs 40 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 filled5ljf4 l q-i(co 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 level is 0.125 m and again at 0.395 m. What is the frequency of the tunin-o l(lqcji f45g fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at on ysgz6mmd2 szoip(k y7by- 179e 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 harmonic in the tube7-y7obs62s d91 gkzm izypym(?    $ \times10^{ 2}$ N

A highway overpass was observed to rtq) /n*r mgkvkl35w 9fesonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 52n45vcas ywwnp2 7v, t00–1000-Hz range coming from two sources. The sound is loudest at p4a2 w,t7nvvypn5s c2w oints equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s bj*h5m3 (pwuwtationary train*jw(um 35p hbw hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it veg1gox*9m7j approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocie91om7 *v xgjgty)?    m/s

  At a race track, you can estimate the speed of cars jusmw hotd ktk 97:73(wbp4 *1vk9gtfpylt by listening to the difference in pitch of the engine noise between approaching and receding cars. S197w(kvg ofpl:dbkttwkph* 49 3m7yt uppose 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, soundiyg*py/t;ol v el *,w5jo a5kaxme99l /ng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long i;x5tk lj9* 5lylmo// 9 ,yepowaag*ve s the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mmthi8j 8z u;h5oves past a stationary observer at 10 m/s as mi5 jt8u8h;h zshown 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 theead fqa(a )(d8.r0b t-hy ddx79l2ume aorta is normally about 0.32 m/s what beat frequency wt2rad9db(d-)laex fuy0m.e 7h (q d 8aould you expect if 5.50-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 6.5 m/s while the )5s 0b;v1 qvudde-juon 4fxvmk(1v2 ymoth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency oxvd1bvj2 v)s de u( qnk5 m4-uovf;1y0f the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.mz ge rs2loq0x :c7cf2b**w, e The pulses are gw xcer:m2qezf70l*b*2,c o s approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sengmi5aeturj : . r1-:cwd signals from one Alpine village to another. Since .m1iju e:r t-5agw:cr 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 presf j fjkqwim(:n2t,h 1;ence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living roo jtwfn,j h;kq1mfi:2 (m 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 “sj2gn+e(c omsw, v,, rfinging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-c,sw2enr +gv(, fmo ,jlong 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 fa2 t(9nqqs: 5w:nia cyor the human ear at a frequency of about 1000 Hzni9a 25qc wt:q(nas:y 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 amez 1/b t**yolt Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planz *lbmt1 e*o/ye’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 153mfdtkwvx t p7d2+-i- $^{\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