What is the evidence that sound travels asado tmcabt3/fqqq**9g5n2b0 a wave?

What is the evidence that sound is a form of energy .rf;ct 8xtr.j?

Children sometimes play with a homemade “telephone” by attaching a string to the( da-zzr6,xu) puq8ry bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can bq 6 x-upuz,a)r(8ryz de 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 exi8dpr8n07az av m:eu.pect the frequency or wavelength to chu mrz.e 7adav088pin :ange?

What evidence can you give that the speed of soufxx2 ok0 +,dugnd in air does not depend significantly on frequencyk uf+,x2gdox0 ?

The voice of a person who has inhaled helium sounds very higziy1 e y(d,z.2,meekqh-pitched. Why?

How will the air temperature in a room a7ay :dzu/ni+ nffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the uv8pm7gn55k ;cf7 qngamplitude of sounds in various frequency ranges. (An example is ;gmfv5p78 5 g7qunncka car muffler.)

Why are the frets on a guitar (Fig. 12–30) spak m)p 9bbibup 5*bez7y98lt2nced closer together as you move up t b il8np9b95u yeb7p)k*2b mtzhe fingerboard toward the bridge?

A noisy truck approaches you frov yke/,fav2 4dm behind a 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 oa vk/24 feyvd,f the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencwv7(qvy gp-oo:pfe+f4/1z to e in space,” whereas beats can be said t/(p47yefgqfz: +vp-oovwo1 to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers werewb+6z wyv0;ei4 z: hx9lyil 2b lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or clol0z wbxzwv:+hyy li;b9ei 462ser together?

Traditional methods of protect6 ed z y9yt( hq+z,,sbbeyut(+h)d l)qing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a rela+byhu)l )q e9ttsy 6+(dd (bz,eqyzh ,tively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves sd gbmys4e7b)5(vcr 6whown in Fig. 12–31. Each wave can be thought of as a superposition of bc (r sy dv7w4e)g6b5mtwo sound waves 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 so 8*0bagpta she p-,p0aurce and observer move in the same direction, wp,hb*s0te 0a8paa p g-ith the same velocity? Explain.

If a wind is blowing, will h-7.ffxa)p rm3bwyoro1xs- : this alter the frequency of the sound heard by a person at rest with respect to the source? Is txo.)-bpy: 3 w -1ahosxf rmr7fhe wavelength or velocity changed?

Figure 12–32 shows various positxogz5)t4fie7s9xq l 2rl.o5o3 h9qmu ions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequ)4xt7h5fqq.i3 o sz 92lxme5rolguo9ency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout r-*dzz4k j9 n)mcymiv*eflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lim* j)9km4-z*dy cnzvength of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the dul4 ywoq2/ m4mrq ec0) )/w:bllnx0recho 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 seawa :mw2rc0lbdwlxeon4rm/ )luy/q 4) 0 qter is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at6kboo za,;m3 l 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna onu 7p8c /1i2 h nd.v3lgd-qytwk a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muchu-.d2/8g inwqlp 13vy cdt7kh time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top ua.6f + cbx5qd omkradkjw89i/r:1l) of a cliff. The splash it makes when striking the water below is heard 3.5 s l5u.acrdxajf) 1 :8bmrk/iqw od69+k later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hug,/unotgl-rnusjn / ma). -s/re stone strike the concrete pavement. A moment lg njrluma/r /o./-n- su, tn)sater 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile m 9th/sc2 1ni d2gs5nvl 8/xxlof distance by the “5-second rule” for estimating the distance from a lightnings8ig n9stv5x/m xh22/ 1dllc n 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 120 d 23whl9txa7 ysB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound le4eb6 u4(bsvc cvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at6x97dhwo8y: h juue;d1j apm 4 a certain place, what will be the sound level if only odp8 hyo7 eajx6:wm;1u4jud h9ne is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi xt(7fqe lusg7lb30 (csy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person f (7l73eusltqx 0(cgbexperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a siqxun/xma h 2+-uj g ,0fzy0p*ygnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal andm-2u,fy+xapugyq*j n0zxh/0 the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power out/dlg ,lx ;k5ksl(sr v9skx.l8 s8t7 ohput of sound from a person speaking in normal conversat l/h,7gk88tk9l.k sos5 l;vxs r(sdlxion. 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 strikes an eardrum whose area sp te7,lihp.ai-; p18sklk s.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 d2) c2rlbb:s 0jyz.pwis rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in b:.pcdsw0)b y jrlz22decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 135w4x36:l xl-t f fyjvv+y *qbo0 dB when placed 2.8 m in front of a loudspeaqxfo536+vlbl tv:4-jfx yy *w 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 level of 2.0 fo5c6s+b2e gk dB. What is 52 6e+kgf cbsothe 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, (amq e djm;-7v:m) by what factor will the intensity increase? Increase byd-; m:7vejqmm 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 fziafc0 c4upwn 2.5gm3requency of .24 uc5 ipc0gma3wnzfthe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in g-t l/kmjfun*d jd n6)/b8wl:air that corresponds to a displaceme/bkl6 / *-tmjg)ndnu8jdf l: wnt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100 bsk w rc2mury87,23ue-Hz tone that has a 50-dBwk eum8sy 2u 23crr,7b sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequehlcf0 fdk r0 30zvym);ncies that an ear can detect when the sound level is 30 dz ;dvkfmcy30l0f0 h)rB? (See Fig. 12–6.)

  Your auditory system can u3w *w(vf: rl*8: 8xpdkxar.hu- aawnaccommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at:dfpu :-ku v83 w(*al*r8xxhrww. aan
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentalz,yx94 .osic l frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under .4, oxszi9cly what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundam9vx6 ub nuf cisy.kqk.hmwb8)( e*y0 ;ental and first three audible overtones if the pipbc;u6bx(e )vim89k .*n w.yq sy0fkhue 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 ;3,-z0r fmng (tvu ngnblowing across the top of an empty sodanfz0gng -vurn,( t 3m; bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tubev2 69 oov*bbf(zo3abh pipes spanning the range of human hear o9 *62hbv(3fzvbb aooing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz alpc *0 ef-0i4/jvqq tmq-* ysus its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orig 04* fqspvq-t0c-mu/ *iyjleq inal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E)2ylcn74c tlp ( umo kkr9(*ut above middle C (330)(tc mk n2p(uol kclty7 94ru* 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 oruf1vrb. (6o xf an open organ pipe that emits middle C (262 Hz) when thob6 1rvuf(.x re temperature 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 jdf/d:a:if e. 6c1jnvat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thz.a2.g+ zbeu m n47ef93 j*xv(5iqqlosq2bnke flute in Example 12–10 should the hole be that must be uncovered to play D above middlk5jn bqo .*vzsme feqqu2nb9g a.7(4lz32xi+e 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 pi8l;qc:6- oe6owudj-gx pvxs -pe can resonate 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 pip-;wxoq6celvpod6 g su:-- j8 xe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m x, xagl 53wn*olong is open at both ends. It resonates at two successive harmonics of frequencies 2,5*3a lxxwogn 75 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 bd;i . r(,n ae l9roazy4t9,ye$^{\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 within the audible range for aews/dwzt- mb:2m+ *4 nig 9eee 2.14-m-long organ pipe at /si- :2ngm*4dze+ etmwwe9be 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. I lvb5hf bq3xl- h bz-32)kl:lat 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 rela)aflb-2 : bzb3 qlvlhxh-5lk3tionship 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 strine+k b9b jeqjrp;k8r- 8gs, one of which is sounding -q8keb 9j kbr+jrp;8e440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency tr1h6en* qhx. 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 (br to9)cndk v+m1and X) operates at an unknown frequency. If neither whistle can be + tdnv1kc9 o)mheard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whelfu6c;/ co;9e32)tseu f mspxn sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the m;t3us2 o e; c9x6clp)/fesfuvibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. iz1xuf2 fsc)+6 gv +afThe tension in one string is then decreased by 2.0%. What will be the beat frequency heard w c+ffg xs zf1u)a2+i6vhen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryg .)ytfnnuyd 0ch3 2w7 to play middle C (262 Hz), but one n7n0huy w gf2c3y.d) tis 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 freqydyndv4zx 5noclubr* 6m c;/ (pw95y*uency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounde u *d9y ;dl5cby*wzmpn y6nxo 4c5(v/rd together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1(sbfd9bomh( l;f2- xo .80 m apart. A person stands 3.00 m from one speaker and 3.so dl ff;x29( hb(bm-o50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hear:zmi54d dq6( u4 8yr)5ue vla/nvaieps three beats every 2.0 s when ta mqunidv d5r (/5au4epe8)y 6ziv:l4hey 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 2ptmf 6-j;adf(jsht)fa ;1( uk.64 m and 2.76 m in air. How many beats per second a(h j6t df;j)u; am-sf(k1ftpwill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire mk1t /5z esc*hengine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a spe *mks /5hztc1eed 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 fire eywcs4 +hpcenzz+ 8*.w ajyo+1kx+kp; ngine whose siren emits at 1550 Hz movese+.zpokcw+ w+njxzhy +1 y;s4* 8apk c at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sor14jsk 0wb1bu*r5b wk2dr3 x durce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freqdbx 210rkbr5w*r uj kbdw 341suencies 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 frequency )+ sm2b7cfzjohorn. When one is at rest and2mscj7fzb+o ) the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends ou7-6ee y7 yt6kcwjo8 zot ultrasonic 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 receivejwytoo66ye7 k- z87 ecd sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ati/g8q (7pcr; b .dohg:itq5n42o /unb: peuh r a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectngt;b7h5r/ n48r2c bdigp:q :equ/o i.upo(hed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fh*5cp c-whv( ylat 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 apprhpy(-c 5h w*vcoached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usev**:)c qztfc as ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries q *z*v)a:ccft at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrason( nglup6.8bqw)sn / d;wjt 5chic 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:wso gke 3)jw8 the wind velocity is 12 m/s from the north, what frequency will obser wg8ew s3k:oj)vers 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 movinkhq -)oari25a6z*n b pg 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 where the speed of sound is 310 m/:7 x/; ha9w81zoklg v dt)hoevs (a) What is the angle the shock wav/vht8aode1g w; v)9xhzo 7:lke makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosapg:7ucb8:hmr zug wx70 :z0yphere of a planet where the speed of sound is onmaz7:c7gzxb: yg0hp0w ruu8: 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 m/s strikes the ocean. Determine*0h l4y)duyr glys2 ,i the shock wave angle gr lys)* y,hdiy042ul 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 vr7 gop4fp c2s:n)f eo f1x+kivz6+/o$/theta$ 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 aa/s6 * ey lftaru;u1t:bove the ground flying faster than the speed of sound. By the time y ;flue1*t:a us/ay tr6ou 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 20j).mskpd6 1ja ,000-Hz sound pulses 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 minimum time between pulses ()j msdak. p1j6in fresh water)?    s

  Approximately how many octaves are there in the human audible 5wym)(b2fjalx(fnj )aw n9 7xrange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon-f rz5mliu 5:/ow5se8-w mdioy. It consists of many plastic pipes of various lengths, which ar -ewom:mi/fr-5d isowu558lz e open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of uce4g m 195k,fwr*mje human hearing (0 dB). What will be the sound level of 1000 such mosquitf,j ukm4e* c5wm 9eg1roes?    dB

  What is the resultant sound level when an 82-dB +q7ujm):aernt2t tom20 jj5 jsound and an 87-dB sound are heard simultaneously? tjamj:ujqnj)5er 2t m 072+ot    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whatm)9f qrub rei +c0)6 mxrqp2d8 is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions qrdbup+x)qf ecmim802r )69r?    W

  A stereo amplifier is rated at 150 W outp(vye n:ei9,oqqxo m/-ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHo-qovx(qney m9/ :i ,ez?    dB

  Workers around jet aircraft typically vl xb b8-pik g c22vy- us)2kb9gy:i6wwear 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 2.0b--pkiwx8 kg2 cg )2yv9s2l bvy:iu b6 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 sysvhvn*9jc4p ki.pr .c(tems, 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 frequency 1a ky n6c8pef)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 h3 zmuk 3*lnb5h bcf/li2p6c7with a fundamental frequency of 440 Hz and a mzf bm3/cnk*l5h2 pbh37ul 6 ciass 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 vertif26x a4f;txxccal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowlyff 264txxcax ;. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one l-h7 6rexwy 8,-fzr8 k:hdb ncend and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itsh erxb-zn:-k8dcf8, rl7 yhw6 fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o glneij d4.hfa(eb7h+w- vl* /ne full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rak)4og :wf,m ldnge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactlydf,:o )4klw gm 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 tr s fkjqr7px3,eejp 5t-e8rss9 . ec:2he stationary train hears a 3.0-Hz beat frequency whe -ekf: r, 9r3eep x s5ps2rtj8qces.7jn the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whisth +erdyw1*5(v :zg lrnj8c)bz le as it approaches you is 538 Hz. After it passes you, its frequency is measure rhzblvg5+ d)e1c(rz* yn:8jwd as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listqfw +z ,dj (fxz8 s+2yila)r*rening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a fxy8) (zjf*+z2rl rqisdfw, +aull octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce ajwg ,::ttjuz9iofl:s c, 2d 7 do6g2ay beat frequency of 11 Hz. The shorter on2 f w7 ,o:, oyjlugaczgi2tjd 69td:s:e is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car j;4*xc*g9j n *xhfocy as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies o xo n**ygfchxj4 ;*9jcf 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 what be 9v+w1gbfi1cu hz 80 ubd(jnds l+1cx*at frequency would you expect if 5.50-MHz ultrasound waves were direcuhl1x1 dv*f+ c9b8 01 gscju bz+wnd(ited 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 moth is9kp*1tlh dt+iy/ bp30x s/roh 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 detected by the bat afr // pobxy*13lhhs9 tkt pd+i0ter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as -ttye gmv,36c6gz q6m8x:kac it approaches a moth. The pulses are approximately 70.0 ms apart, and e-z 8 ktct6, ygmv 6c6e:mq3gxaach 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–teiehc/ 0x l4s)+ (jnr d0vdsb;r8op 538) 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 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 flarl0 8ebdxs)n+t 4 c(/e0jp s;d5 hrivot) 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 x g6kk:v2,pgk j2l pczk2w +;mcan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m hi2 2z2c p:+pxkkgjg ,6;lv kwmkgh. 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,”som5r-qje((se i - gg; 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 9eejgq -s (rs5-i mog(;0-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 e/0.4s cjb8gtw*qo ngj p q8kv6ar at a frequency of about 10 c0w4.p kjojnq8/86q ggbt vs*00 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 yjdi.lb+7s8g observer on the ground hears the sonic boom 1.5 m7ibs.8lgy dj+ in after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1y m8ulvc w/pw8 ;wd1l75 $^{\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