What is the evidence that sound travels as a -q*k7 8b )bzbbm7jpt7 1znu:a. vfgrcwave?

What is the evidence that sou9lzhggqqt js v zi(gk;2, 267tnd is a form of energy?

Children sometimes play with a homemade “telephone” by .n6k,yrr/ hkuattaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, t /rukk,n y.6rhhe sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequencyehdczy ;9 c,(lwsx1dx)cp)h0 u f,c(p or wavelength c( ,xph;) e cu)c hc0(9lwds,py1fdxzto change?

What evidence can you give that the speed oo9s7 ;d(bcdvaf sound in air does not depend significantly on frequen (dv;bdca97oscy?

The voice of a perso(2+r n:rkyr 3cga+3 xrb pthn*:hztc,n who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipe1a3 btg)u )gjis?

Explain how a tube might be used as a filter to reduce the ampl egn*p k+n.j2rx.+j,emw6z uf itude of sounds in various frequency ranges. (An example is a car muffler..nk jmz+.fx u2+w6pee *,rnj g)

Why are the frets on a guitar (Fig. 12–30) spaced closer tosja.gv ;1 vft1gether as you move up the fingerboard tofvj;vs tg.a11 ward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but co.e6. brrcgfu(m2wdf q d7p9 *annot see it. When it emerges and you do see it, its soun .fq g7u9.dr*op 2bdw(efrcm6d is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saieva2grjj- juio ,a1g l m2);npcn8f ) v2h;+wmd to be due to “interference in space,” whereas beats can be said to be due to “interference in time )i1hjm2wc) j+8 v; ;vgg-p2lrj,nm au2ena fo.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points Duwhql02 fmxs+v8x4a ge 1*2au and C (where destructive and constructive interference occur) move farse uux 4+hfxwa2m1avgq l 80*2ther apart or closer together?

Traditional methods of protecting the heari fge09gz b42tmng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones 9 zfm20t gbg4ein addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 121y3 uoib h,mh/–31. Each wave can be thought 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 component frequencies farther apart3b i umy1,oh/h? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourwwvij;usr4wh6e 44 .bcc5 s 1mce and observer move in the same direction, witces54ww1hjwv;m 4 rc.us6 bi4h the same velocity? Explain.

If a wind is blowing, will this alter the 2;empe94uryupl w a66vna2y; frequency of the sound heard by a person at resaypml29n er;a;e2vpyu 4u6w6 t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil9i7cfx/q7bui (tt;33jlgnw ed 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 freqgfj7 c3ei/9w xt 7q nt3li;u(buency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by 5egbje2r1tj: p or8cbg h2..dlistening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afeotrep .j5 g gcb:r8dj2b.2 1hter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belowxu*vj m -stz.g6l+* ww 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 spee+gwjslx t -**v u.z6mwd 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 inz-nyk, .ta1qk 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 boa bqs-1(5hkot yt is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occursqoh1- stb y5k( on another boat 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 th4 j84ql hu:gzu 3,ev8hpi2zxd e top of a cliff. The splash it makes when striking the water below is heard 3.5 s late84gv3x e4z 8u:jiquhphl,2dz r. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike tvt* fxzf7oak16s j ou7) 5xmi6/c+ bjche 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 thf+ 6 x uk77/xa6stboij)5jmzco*vc1fe impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by theix4 vf+tx1-t4y q mxb/ff6.lf k l*rg3 “5-second rule”gf+yf v3x1 rx4lbl 4mt/k fqi.f-*t6x for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun21y stbt5 b+sm:n* rcld at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a soucyee pnzqf/uaa( 9bl, 50g7. ond whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneov-v9fb 4us-*d* xew5vd)krcwusly at a certain place, what will ef d 95sdcw4-ku)*br-*vv vxwbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with ef4/i qbzj0f8 four equally noisy jet engines is experiencing a sounb qef0 /8izf4jd level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rad 4-3jsm0ip 2b 6nyqg* 9grmiftio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ea9b3gn2pism6 jgri*q 4fm- dy0ch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output k,/msp: svmn/ h0x9onof sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphkp /nvo/ s9: 0nh,smmxere 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,a ofr.4c12fe lr 4ftc 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 morr+3m4 )t3p4+hxw q7whz k qrzee modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wou443 xhrmwth7q pwqzk3)ez+r+ ld 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 mxn7-rw w mkcovbn3cfc5l 8,,1eter registered 130 dB when placed 2.8 m in front of a loudspeaker nb15r,oknvlcm- cf8,w w7x 3c 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 diffcr ae+qs 3,cg/erence in sound level of 2.0 dB. What is the ratig ce +/3rq,caso 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, /a;kvp z;blj m:k0tx. (a) by what factor will the intensity increase? In0j /a;xz tpmbk.v ;:klcrease 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 fdaev9k 6.e) zl mk6dh/requency of the other.dekl )/z 9.e66hdakvm What is the ratio of their intensities?   

  What would be the sound level (in dB) hf4os di4k:(m of a sound wave in air that corresponds to a displacement amplitude of vibratingh (4 :o4fidsmk 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-Hz tone usknke p+2dsqf ..z5mr x+j8g v+.xs9that has a 50-dB sound lf ux 5zedm+.vgs+ x kn8k.9.qs2pr+jsevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tharh8-dnb px)sl+q- xzy/i u1,kt an ear can detect when the sound level is 30 dB? (See Firdx1uyb--n/+h 8ikxs,zlp q ) g. 12–6.)

  Your auditory system can accommodate a huge r8s -nprg5l.,bqu(n yc ange of sound levels. What is the ratio of .c8,(lrq uy5n nsbpg- 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 fundamentalo5 /et tkp1h9gvtc,q 76f8rqt*bd w:z frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? ttt8 ,hpkqf7/oqegd*v91c:t 5br6 zw   N

  An organ pipe is 112 cm long. What ar5v eyj ;ho:tb jvzxw 5799hyv.e the fundamental and first three audible overtones if the tyb9j7h jwo xh9vv 55;vy:.ez 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+,4o+sdbq)uo er bi 8b;9gsco you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assubeorg4 bcd;9u+s )ob8qs,io+med 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 s5*2-wumn, g/fqzog; zg :numl,cr*dz,:c s en panning the range of human hearing qwd5g2g:l zn*e:*m n;os, gur -/mczuf,z ,cn(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 as its third harmonic.dj metrr v .ccz)k/:;. What will be its fundamental frequency if it is fingered a/v:; d) jkmrcte.cz.rt a length of only 60% of its original length?   Hz

  An unfingered guitar strin+9r7x1lqpearevaqpgch u3 3rg -,(7 yg is 0.73 m long and is tuned to play E above middle C (7,gepqyv lc p3uehr+r9 q-7 3xgra 1(a330 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 oruzz:ycwiq4fz - 49ltu;:u ;sd gan pipe that emits middle C (262 Hz) when the temperature ::4;y;u94z-zulc dustqz f iw is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2ey1+,baoivu s +. cjh,(2p9bzvuv4xc0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in gk 00oai)enyrmk;l 759xsi01m)c rph,0f cat Example 12–10 should the hole be that cm k1s, xo)0 70 tgirr5pciy0h0lka na9m;)fe must be 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 re b pf/iq+ 8fs)2j.wlcwqg(vy *sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any c/.ww8)*ipql2sb(vf+ qfjgy other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.rd2z)wgme 6lo(4 bmc4 uj1e;n )a ,zia80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. W;jir6cn)4be o m2wzzm4,d e1a)g ua(lhat 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 h5:(q2ynpfz4 n 5gyqv$^{\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 preugv9 9tguh-:c sent within the audible range for a 2.14-m-long organ pih g:tuu- c99gvpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is gi80gjs--c qv7vb *mcapproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear-v0qm8sibvg- gj*cc7 canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears on3qok0 1y.x)air m s5sfe beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Ho01o fiq)5 ym. sark3xsw far off in frequency is the other string? ±    Hz

  What is the beat frequenakhi5gr0h p+q s(r.l)cy 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 23ndn 8mk0v-oh mripx+chf* )5).5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separa)vpi h8nmk xr)fhd *o50nmc-+ tely, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz cn05lt1qt :bttuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string?5q1:tbnl0 ctt Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in on)u6; aqyh4*5 -uiqyqsptq2 hqe string is then decreased by 2.0%. What will be the beat frequency heard when ;q6 uphht4s a)* 2qqyyq-uq5ithe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tx0d; z hx df(6m/hf;dnry to play middle C (262 Hz), but one is at 5.0°C and thef/h6;d ndz;hxx d0f m( other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Ccwc; kb*0 uzc 6icew t+ty2i2w::ve;z. Fork B has a frequency 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 o2* wt zzc:cc 6:e;k0uivyeitwbc +;2wf 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 3.00a:4v7-z .r(ftk:y u2nrp erqi m from one speaker and 3.50 m from ka r(in4e:q-zr y:7p.tfrv 2u 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 Hzaxr0lxh-+511yy f -avyt ;6wzfjrv: d, but a piano tuner hears three beats every 2.0 s when v 51vydzf;j-xrhw+ xaf y 0y6-1a:trlthey 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 2.6nm2w mc(baxg8d3c)c9 x55myj 4 m and 2.76 m in air. How many beats per second will be heard? (Assu55xd8 am)gc3 mc92 b njy(wmcxme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequg xwtl*w,9,ce k;nfp hufk0(/ ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 mxh9fw ,;f lwe (0tkuck*npg /,/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whpcgu 5q/1rdgx(/jp u( ose siren emits at 1550 Hz moves at a speed ouju(x5dcp(r / p/1qgg f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in yl.acvvg9o 2 0grlj*7frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two ca0gr.*7yj9 g2 vl volfrequencies 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 horn. When o2j1wt7 pbn1ou ne is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequencyb11pjo7 w 2ntu the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out pmj2 t; 57n z3bvjyrg qrl87ok 9t5.zxultrasonic sound waves at 50.0 kHz and receives them returned from an object moving divlj5.trmb7gyx opz5 3297tnzqjr8 k; rectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits a;azd f;cck o5u ensj*5qc.7/zn ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectj/ cf;*znez.c ac qko;ds7 55ued wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wasvgpb eo1 0i5qspsyc (1-uc0t 4 played on a moving flat tr5s01vu(1byps0c4cogp q i - etain car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wa8q6r 9nl5 r6h*d,xavvzrtsy pha(.1vm+6 bzzves 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 at 2 cm/s dir(9s*vn,thrazdzlpvz.y66q vr r +h6ma 8 1b5xectly away from the sound source?   Hz

  The Doppler effect using ultraso ek+g4 reqs;x*vr)5yjnic 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 frequ)fuioip ;wzhr3zbyv *) i/g.8 ency 570 Hz. When the wind velocity is 12 m/s from thpz )h8/vb.)go iyr 3 i*zuw;fie north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an objecs;xn3: pu8thgazw0b+c;m18 3+sej fcrw 4q ket moving 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 p4tf m**savfy2)ixy8n vo .w( Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle th 2 a4styi p8*.nmowfvx*fy(v)e shock wave 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 atmosphere opup9w p(*uye zc y5m+l*(xi4cf a planet where the speed of sound is oeup((ycx ci*u95*+my4 ppwzlnly 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 oceat)n i 3t6yc-f chxo)6mn. Determine the shock wave angle it pro6i mnc3 )t)xfhy-t6o cduces
(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 *i0zt2xcrr/s+0 jmdz$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhea2h; 15k8xyrf q;chxjpd and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 kp rf5;yc;jh 18 x2xqhkm. 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 2hos6m4 u .:k59vl jphk w 7ixkdt6v1kw)8n av,0,000-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, what1 .:ihn , 8k k96kalsm7w v6vpdok5w t4ux)vhj is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in :ye(srt1zv1dr1alw* 16hjh+( m5l s pfig k*u the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sym1b5 wzu/hbbhj) iw+bp95perl yo81 c4phony. It consists of many plastic pipes of4)w/1+5w5p98bzol1r bp u hjb b heyci various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresholpu/ ec 2mfc s7wf 9zv-re3va2/d of human hearing (0 dB). Whefaz9evs3 cpf27wv/- 2/ mrcuat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and2xb9u ,d / k)qtum xp3*tstf6y an 87-dB sound are heard simultaneous,sfkxtb*2tutm) u pd6q3 x y9/ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whzqn:mo xjb sh+4dj+7b73lhf: at is the acoustic power output (W) of the speaker, assuming7h:4+j blq3z7 fd: sj+nmobxh it radiates equally in all directions?    W

  A stereo amplifier is rated :bbties:g9gwp07,5dk1mt s hb 5g +hd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kpsd7 1s hkgbg+ 0wb:tmbh i,5de:59gtHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.c(4tl elo .p.lfwj2h4 Assume tjp4ow(.fe4 2.ltl hc lhat 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 distance of 30 m from a jet airplane engine?    W

  In audio and communications systemz0pzmbs.u a-* s, 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 t;l g.oxic :l7mo 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 funda/ xd/ikfp9w)smental frequency of 440 Hz and a massw s fdk/xi)p/9 per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled w, ur*-iqqpom 5ith 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 theu o 5q-iqp,r*m frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is ;wd87 iyf0skig7mv(mvq j/ u1 near a tube that is open at one end and also 75 cm long. How much tension0ikq; iw7g7jv 8mumy1dv(s/f should be 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 bu00- qr7m7wey ,aihg oyr-q8as 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 500–1000-Hz range comingvg+7pn lx4 oc/ from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal n4 7+clv g/xopat 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 whist;rrb 4 x8kvxop*8yac 7les. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat fy47x8 vok*a cx;r pr8brequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachess +3q3mmpd3j;z)0hd z,sytz e you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train hm pm,3+;d3sd0zq3z y)t ez sjmoving (assume constant velocity)?    m/s

  At a race track, you can estimabb akhc-/hn(:gd*vvv k 64 x-mte the 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 (frequency halved) as it goes by on the straightawkag6 :vc/k- 4v(h -vxbbd* hmnay. How fast is it going?    m/s

  Two open organ pipes, sounding together, pr v rhced1 (p,nd aj1:xd0l bwe33bh2h9oduce a beat frequency of 11 Hz. The shorter one is 2.40 m lobcd(lx3v:h 30 ed1 1ne hhpd,baj92r wng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past amru1jtmlvj:; afq1ul* u;*+ z stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencr; f*+qal*l: u umm1tjvjzu 1;ies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboun+o/iicd +,: p,dqxtut 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? d+,d/oi,txiq c:p nu+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 is flying toward the 0l,1im op 9e5g9i+nj kqrli8u bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Whpu9i ki +g0e8il1lojqm9 5r,nat is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freq:k a3jrv;t,sm50cgoi uency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth b0,rsva 3ct:g jo;m5kie detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) d 6vt4;qe-uqwwas 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 deepv6-qe 4u;dtw q 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 cof80d t;xh6rl ,bae p-gmpromised 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 high. Calculate the fundamental frequencies for the standing waves in this b8ed6 r laxf pg;,h-0troom.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a longyh3jfr+1)drtkb u 25 a, 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-long rodkbd a5rtf1 ry)+uh3j2,
(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 thh7i g5 va s1wian)*)swreshold of hearing for the human ear at a frequency of about 1000 Hzhs5s )wi71wvinag*)a is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boomn 4; gmo03 8bby;sh*qf/e prij 1.5 min after the plane passes direhqrmjn*beg8 iy p43ob0;;s f/ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i p4yt-42fuwo m 7/bl4.kw jbtis 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