What is the evidence that sound travels as a wave 1x;nf7c3iv ut8x+sgl ?

What is the evidence that sound is a form of energfr3tl 1nlm3l kpn;g,k ,a1j7n y?

Children sometimes play with a homemadel cc(bc5+8e vapmd+c 2 “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 cav e2+5 b+cac8mplc (cdn 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 f4i ht*g8jpj-es 6 c/nmrom air into water, do you expect the frequency or wavelength to change?thng6mjip8j4es -c* /

What evidence can you give that the speed of sound in air does not depend sign fxn4(zp5u y0d m+p/huificantmyx0(uuh4fp d/nzp+5 ly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. ij9 ;;v xx)e3oaqr+fr Why?

How will the air temperature in a room affect the pitl fd, ok* ;ik:ie7glo)ch of organ pipes?

Explain how a tube might be used as a filq rf*cr94suu0ter to reduce the amplitude of sounds in various frequen4ur qc*0u s9rfcy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30md t4l *;m.ouq) spaced closer together as you move up the fingerboardmqo4 m.ul;t* d toward the bridge?

A noisy truck approaches you from behind a buildi8giv3f5z*m d yng. Initially you hear it but cannot see i3 z5 8ifgy*vdmt. 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 diffraction.]

Standing waves can be said tujvn)fx0:4emr k,vv 0 o be due to “interference in space,” whereas beats can be said to be due to “intek:,m) v xe4j0v0nuf vrrference in time.” Explain.

In Fig. 12–16, if the frequency of the speake0 e9vbm2 / aoyv+cwe od,9yj/drs were lowered, would the points D and C (where destructive 9 a0bdvcodjy /9,me2vy/owe+ and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wi+,bs er d-b;xoth very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. Howd bs -;ex,o+br 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 gpve10 afc /daz9pv6t8k0d+ o of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two com1 fge+o0ap8t c vd9vpkz/ad60ponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer m ell+ofxnp/s:7 kfc2 .ove in the same direction, withl 7exo.k:ffs/cp2 n+l the same velocity? Explain.

If a wind is blowing, will this alter th5o:-a ntsk:c-4cbrf83 3yb r+n clzame frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velo83+-b 5cmon-nc sra4 y:zb3f ark c:ltcity changed?

Figure 12–32 shows various positions of a child in motion on a swdr -xn*m 6c3xding. 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 fx*c6n m d-d3rxrequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo 37bcy2/.f s ejtk8o3y5eqrx aof her shout reflected by a cliff at the x ya83cyqk5see./b otf 27jr3far end of 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 his ship jus6 zye0ncf-8 ct8x* 1qr qh0plft 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 y01frcx en08qp*-tl z h86fcqocean 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 rz.nt*ne d,/ din 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 s5.fnmy mrp(3 ychool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muny5(yf m3p.rmch time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frtqdt4em60nvwb/ 1fs 5om the top of a cliff. The splash it makes when striking the water bel tv4f/t5d16 bnws0eqmow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone str )g ux:o4djax;r*. nq k*3hmjzike 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 Ta3znjjdo: a gm*rqhkxx; *.)4uble 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distahy ;(,bw :dmqance by the “5-second rule” for estimating the distanc wd(;: h,aymqbe from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 8tzb*nt t k;r *uc7hq0 ze.fa1120 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 intem+kjetmj /y(6 )n)5)hm4qxdh wczo lj iy3+ 6ansity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atrf a ttdp,e:vhjs6j/2gk7d )1 a ced/rt) 7,s2aevhpj1gf:jdtk 6 rtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancen8d6ur qsgv42ez /7yl h.7,)qhtr czfn8)bxl from an airplane with four equally 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 /)hhrzx ,teq8f8y.gur77 vbzs dn2)46l q cnlone engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tk m sq k+2-i1ox-*uasto-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of in+ao-t 2 1kk ssium-xq*tensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power (qp49z-omcybkvtt;mb 1zlz ) rps3 2,output of sound from a person speaking in normal conversati4kp 9)zq zt3;cmy(,o- 2mp bvzbtlr 1son. Use Table 12–2. Assume the sound spreads roughly 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 strit3j ygtq jp2-jv:) s)mkes 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 amplifier B njkqp3;spwvqz e,x95ph v7og/49i,tis rated at 40 W. (a) Estimate the sound level in decibels you would expect at a 95s p7q ov ek ,/qg4j;pzhp,3xvi9 wntpoint 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 when placed w tpdo( e*/pn92.8 m in front of a l/ep( *pw n9tdooudspeaker 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 dif7 yydfus 0 o28 po+ncpsv)zi,)ference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels ,nc7o szufs28o)pv)0+yp d yidiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tril q2i4om2g-6vdzo+l-g r:wd n thv:c: pled, (a) by what factor will the intensity increase? 6ho-+: -dzmor:vw vgl2 gl4 2:cnqi tdIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frdruvyhl /)5( pequency of the other/h(5) ulyvrpd. What is the ratio of their intensities?   

  What would be the sound leve*lm 1g 3rgrkha 0d1-ayl (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.133ky ram1g1-d0 gal r*h mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzlw3j3efx8d vs b36 ()dqdus3r tone that has a 50-dB sound level? (Seb3wrsl j8df x 336s3d qud(v)ee Fig. 12–6.)    dB

What are the lowest and highest freq lnu*z 6*k*st xo6-eytuencies that an ear can detect when the sound leventu6zo txly-*k s*6e*l is 30 dB? (See Fig. 12–6.)

  Your auditory system cz7i192 qlqtg*6u(alw5 mqj* cqcw k/ qan accommodate a huge range of sound levels. What is the ratio of highest to lowest intenlwj/6q 19mq( qz wq*c q7*tag5uki2clsity 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. Td2o g) y1b0jidhe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pl yo)2bgid0 1djaced?    N

  An organ pipe is 112 cm lcjo3fhkr6g sqm 8hf*01s2d8 t ong. What are the fundamental and first three audible overtones6s3k *2j rmto8hc8hf0 qg 1dfs 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 vsgqv cs7u/ 8az9g 6:ayou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assu q /vg:zg6svc9aa8 su7med it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the yg lykz8y,9c+range of human hearing (20 Hz to 20 kHz), what wouyyyl, 8+9g zckld be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thm9g8 rem en 1nv+so7db3 h)xy0ird harmonic. What will be itshxrd1 eyne87903os+mv mnbg ) fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string im;3w m8 ov:utxp2b3 yts 0.73 m long and is tuned to play E above middle C (330 mmuyxb33 w8tp :ovt2;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 emits middlecp q) hmk:geq/p(r6dg: r:w0o C (262 Hz) when the temperature is 2cmk0 g qg(r/: 6)horw dqepp::1 $^{\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 a6jpt 9jm2 zn(o2)rv,hjf4ykn 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 szn( 9yxp-s* n9da0nhthould the hole be that must bex9s z0 *9 hd(ntpnayn- 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 26qko2n1eygirkwd3fxacw ;32 x )8y-c64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipa3xroen22gkc83 yqy i xwc6-1); wkdfe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m dc*(b(g(gfnpeq) -ut long is open at both ends. It resonates at two successive harmonics of frequencuqpg-)edbfg( ( c(*nties 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 xg +3f h8yi-ub$^{\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 a9dvy , sp:kns80: wk k;2;dbe jfqf5hyre present within the audible range for a 2.14-m-long organ pipe ndkj8fq w0v;y5:pehkbd:29,y ks;s fat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It isbouq:s:6/t gd 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 relationshu b6/qsod g::tip of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two string3h .mg - k4swrb(.+jtjnpgh9k s, one of which is sounding 440 Hz. How far off in frequency is the ot t.n34shhk-p(9g.bmrwj g +kj her string? ±    Hz

  What is the beat frequency if middle C (2c,u(9adg+rij: ms/p g62 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 opera;;lemc*m vsq ,,,oqb/xq.rkt tes at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, r t.,kmsxc;vql , ;b/,o qm*qebut 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 tun/ eg 7yc0o 2k t)(mr.etekg*fhing fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.f y.e 2)ecg(0mke7rk toht/g*    Hz

  Two violin strings are tuned to the same frequency, 29c57 zi e.1e0 wgrub;zb4 Hz. The tension in one s0 cebb 7uwe;1.gz5izrtring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu )-ho4o r 9wckib3i az,az:1gjwnx/ u,sftq/(tes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 cj /zaa,wb-gtwhi1:kqs r3zf/4o)ui, n( xo9$^{\circ} $ C?    beats/sec

  You have three tuning fvspznztu 6.f 8s b/,y.orks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of/p b v nts.fu8z,.z6sy 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 stands 3.00 m from one speat2 ni8w)d9v1iyev hi )ker and 3.50 m )8iwiid)yvh 1 tev2n9from 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 piano5me 0d+x)e ycr tuner hears three beats every 2e+ ) 5e0rmydxc.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 ofb(.vxtejs /r7 g(*rd u wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T( stv/e drj7x*ru.(gb = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sira22gpo:okwsas i:6je,5 gsg1en is 1550 Hz when at rest. What frequency do you detect if you move with a speesgsw,se g: a k5jpo221og: ia6d of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.w9*(kw /rpsnpa 1gw(a What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at wasg p91(wk(r / np*awa speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frj f/46m6c7cs p)xv uac++wwz kequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving 6a/fk w6+c)jvz+u4pm 7xwcs ctoward it 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 single frequenih.uey 4hnj+:kef 2l0i :ffk,cy horn. When one is at rest and the other is mflh nfy k+,hj:4uei: iek2.f0oving 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 ultrasonic sound waves at 50.0 kHz a5muoz0 cmx *5ch 29wwfnd receives them returned from an object moving directly away from it at 25 m/s What is the receivedcwf9o h5xm*w cm50zu 2 sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a yr:) wlsk k-g.9e+gd*3eydj mwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in th+9e. mde-lywkrgj)gd ys*3: ke reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on k+ t4 9qd:yirqrnyj4n13o oe7a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whiler34qt 7qyor ok9+e:nij n 4dy1 at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppodosq u**m(jnc 01wzyp0f dcj3: :ivl-se the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to 0f1* :ldu v mjosyqc0id(znc 3w:-p*jbe 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 .v t7aboi;ga9yv.pd 0ultrasonic 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. Wh1j*j:z08 gs v9nbbiid yq6aa9en the wind velocity is 12 m/s from the north, what 6ajb* 189s0dn i jagvqzi :by9frequency 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 moving on land x)le 7x;n np)gif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 31nr:*8-ge 8he;04rxt yx uaivh0 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s moea;gut88r-0ixn rvy *:hx 4hetion?    $^{\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 atmosphe o*7fhv;. .hxk(.zyjm ggupp1re of a planet where the speed of sound is only abouz*h(;. xv.mup .g kp gjyf7h1ot 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 stfxl p:8z(bpn7rikes the ocean. Determine the shock wave anglefpz8xnp7:b (l it produces
(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 sxxap x8 2+ /1lpb,lkh$/theta$ 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 lkj0wlp+g,v2; x 5d19ej 6y)idx1 rhugcfn* ethe ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontpygu,g )dhf5210rn1xld+vjcjk6 e x l9we;i*al 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 sound pulo8k3h( kfe 08,v njui d/oif6ases downward from the bottom of the boat, and then detects ejnif0,8vhi/3a( ok ofk6eu8d choes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humanv55dbvtc4(s99wica jx/b)m l audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disp wr bv -;cmvweop3-25flay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are operm ; -ec 2-f3bop5vvwwn on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes ael10nhqql+ 4n sound close to the threshold of human hearing (0 dB). What will be theh1l+leq4 0 nnq sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whenj*ekxp .n5jtd;./h pm2 gfwk1 an 82-dB sound and an 87-dB sound are heard simultaneously? fxn/;k 5 2kep*wj.1mpgt jdh.   dB

  The sound level 12.0 m from a loudspeaker, placed in the xa e;1w2 qpr)nw mw20ih np26sopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it rawnsme) ;2 x0 pw26r1pi hwqan2diates equally in all directions?    W

  A stereo amplifier is a3* j.d bdrzf.ld3+g b7iidg0 rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powd gb * 0 3ji3dg7+dabzilrf..der output in watts at 15 kHz?    dB

  Workers around jet aeykf7/8 cgn+/0iqgo6 *t tb gfircraft 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 ave fgy*t qc/0begi g+87/fok6t nrage human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gazjk+c: ew)xicr 2zfx xs.2m-tej*7+ain, $\beta$ 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 violin5w 39qsfzoj3 f is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundameikle8uap( ,6y ntal frequency of 440 Hz and a mass per eayk pu,i8l(6unit 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 cgq- xaoc/l*5v ac 7r2u;ve/ v7 ufaw,6u*wkytube 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 tkgq*vr ayc5,vuoc e6/2uxav 7-ul7ww a;c/* fhe tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open 6ynyf4- d au5nhq8:rb at one end and also 75 cm long. How much tension should be 4da yhufbyq-6:nnr 85 in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loodc kv)a+13yhf p ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rangxf6 odv 3h9b+l e6:jfge 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 3+ evffb j6 xl:6d9hogfinds 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 o.ax1yldhg3z u ym*e3 ,n the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is thea3* 1gy3h, dxuy mlz.e speed of the moving train?   m/s

  The frequency of a steam train whistle as it app2y jwlwyk,5 ;oroaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veloci jk,w52yylow;ty)?    m/s

  At a race track, you can estimate tha,pd2 r(mtx 3y/ev0 mte speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequtt2rpyx e ,0 m/(3mdvaency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency / 4kt wp2f4slp5hth+oof 11 Hz. The shorter one is 2.40 m long. How long is the ottk os52h4wfhplp4 + /ther?    m

Two loudspeakers are at opposite ends of a railroad car as it moves paste)7 a5 bgtby/v a stationary observer at 10 bvg/7 te5yb a)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 i uz/,0u xvx;-ju nxf:vw51 nals normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? A u-wa1vxuz ,/ f;0j5u: xxvnlnssume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at e abxoz0iv/s3(dvl1 8speed 6.5 m/s 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 wave detected0 xb81d lvz/av3eios( by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches gybc0j81 dk*o1 fi .qla moth. The pulses are 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 chfko1.d8y0* jbl qgi 1cirp is emitted?    m

The “alpenhorn” (Fig. 12–3al n um9e.c2xr) dxh)2f( 3fjr8) was once used 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 alpenhorx3m()2hcljradnu 2) e. f9rfxn 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 th e0z35mcg0qc/ aifinr 2a dc432-blj me presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing war0 adi cac2f5l2 nz-gmb43q0ie3jc/m ves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender znlnz-:jb8 zb3r(m -,4o vdrpaluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the ro-rzd 8(,pnzrblbo4v : -mn zj3d can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of pml /yoh-t)y y(g (qn)abou y))phlt noy/g(q(ym- t 1000 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 sio8nq- +:dkg)kv )k 7rh mr/dMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s al ndo)v/mk-8hikr+q g: )rd7sktitude?    $ \times10^{4 }$ m

  The wake of a speedboat is bh-wa322ewwkpo 5w :o+1yem x 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