What is the evidence -0vii-*im ygcthat sound travels as a wave?

What is the evidence that sound is )( l 7da 2e(dczwk8c l.)hwntua form of energy?

Children sometimes play with a homemade “telephone” by attachingigcosr .z48 )pf/0zz dj6 bro3 a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explai z.4i zrr b8 c0s/oo3gz6fjp)dn 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 freqi) v c:a5xh)deuency or wavelength t:avde5x)c h i)o change?

What evidence can you give that the speed of sound ish6,x4/9t0 yux2r fmoxv7d cqn air does not depend significantly on frequenc7r04xdumt2xho cq,/fy s6v9xy?

The voice of a person who ha)qr3r/1yl my51 ddwla tc fy2+s inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch :/0ymm9 i;top czsjw;of organ pipes?

Explain how a tube might be u)6/f8uduzsf osed as a filter to reduce the amplitude of sounds in various frequency ranges. (An exampzuu8)s 6o/fdf le is a car muffler.)

Why are the frets on a guitar (Figzm3dpk f )gm3/rh0 )xsfczr,5. 12–30) spaced closer together as you move up the fingerboard toward the3x)zmfd)m3 f c0k szg5/pr,rh bridge?

A noisy truck approaches you from behind a building. Initip; ahm858 iuujally you hear it but cannot see it. When it emerges and you do see it, its sound ii8juu5pa8m; hs suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spac4 *48d bsceq-lx:es d51qzzg de,” whereas beats can be said to be due to “interference in time.” Explad lz*:zd 8c1xqq5-eedb4 4gss in.

In Fig. 12–16, if the frequency of the speakers were lowe3-(q g:yxc:fg*ka63c kgms tu red, would the points D and C (where destructivgm6 cfg3y *u k:c:g -saqtkx3(e and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ofydxhst6 c o/snr31 9f 2:3dnzd people who work in areas with very high noise levels have consisted mainlhn rd1x:y3 96/cs3zstf2od dn y 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. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31.i )h0)txh3z2xqv8tmb;q 2y td Each wave can be thought of as a superposition of two sound waves with slightly different frequenz;ix b qm)ht2xq2y h0vtt38)dcies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dire9r)o (v*hefu nction, with the same n *he ufo9()vrvelocity? Explain.

If a wind is blowing, will this altera ctpj6mv(bph -d1 p3 ib6;n)z the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed p;in-cj(3hvbp1bdmt6 z 6a)p?

Figure 12–32 shows various positions of a child in motion on a swing. A monito2w jmp w s -vhggzc(nz;i 3z:66b+0wtor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hzcvo ;jt6 s3g(z-2z 6whnbwipm0 w g:+ear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of r:v x/45xdqj 7.qlavy t a7wy41 c)bura lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. Sy vdr jx1ar4.xb /7wqv u)l 7q5a4c:tyhe hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side ofq4tk+3u bcym c1 rrh+5 his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly wbck3r5 myh +4+1qct urith depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aid) y/0htsqw,ur at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school vfdvvl4x0,hss 9pmggj - 6 )0s 5voz8qof tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fishvh-,zdps vsgxq8 v)s vm06fg 49j0lo5 ,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when str( zvbl+:m-tv4jg gi r5iking th5 zigl:4 m (+-vbgtvrje water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hundhtw(: y3cp3 )vvv) ykfm 90yge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one dyvpc tw0( mv:3yfy)9 nv)h3 ktravels 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 on (u o h,pl;go8bspy7t5 cm93aue mile of distance by the “5-second rule” focsp;ty g83o79,mopb h5a(ul ur 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 sound 5k:yxw0k( p*no7zc f upq)9vyat 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*mxi9o* 3znp nudvw4mr*va( 1 a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9 zttv76r w 5byfj8xp745 dB when fired simultaneously at a certain place, what will be the sound p65 v yzjxf7 4ttw87rblevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certaiwe:w+z0 ju5lx schhfn t/:)7.eo t -jpn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What t):he 5+ twlu pszhj.x/7wc0n-eo f j: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 ratmrhn7e* j7 xibyyj44g /ye4o)io of 58 dB, whereas for a CD player it is 95 dB. What is thejo*7yenrhy/ b444yx7jgm) e i ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conver7e:,rh2gza2 wo c/njw+3wkll sation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere c lw+2 ,rw7jch3ozlak wg:/n2eentered 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 )zn mel.z850 k puoe j,4xv(hiwhose 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 g;y1 mv,ek( p+k if(smmodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connm;(k( g1k+ ymvspfei,ected 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 1 wzws9 kgq0pfc+.:,th30 dB when placed 2.8 m in front of a loudspeaker on the stage. p f0tqzw, g k9.+s:chw
(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 dB. Whatagp cv .gx-6z* is the ratio of the amplitudes of two sounzg g6.ca*x -vpds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ib4aev , hxdh(1ntensity increase? Increase by a factorb,( x ve4had1h of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have ew:vide fqu i *c.*b :tlpq0r(5qual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensibeqcd:rpil *u.wi *0: (vtf q5ties?   

  What would be the sound level (in dB) of a sound wa/xx*z7j,khhy:b dqfl7zu*cic1k- 6k-v8ae ave in air that corresponds to a displacement amplitude of vibrating air molecules of cjuf b*a-qkz ixk7z 7*8cd xlh1/yak6ve h,:- 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100- uzxd w( v0y)pazd,o1hqr;e,*Hz tone that has a 50-dB ,uea*dzwhx(1z )y q;dro, vp 0sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear capkkdhei9 ;dl5f5v) e4j+ 4m fpn detect when the sound level is 30 dB? (See Fig. 12–4m9dji lheve d)455;f fpkk p+6.)

  Your auditory system can accommodate au hf-;y1 zhn2xv(a0 ow huge range of sound levels. What is the ratio o0(;1 hwvuyfz- 2hax nof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz.( fnye (;hla)5fo p.jf7 ttb9k The length of the vibrating portio(n. b k)jt;loh57p f(f9 afyten is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibl54gphama g.p)8cn i f:e overtonpa :hcap)5 n8 4gfgmi.es 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 you expect from blowing across tph1x 1ab yi+5ohe top of an empty soda bottle that is 18 cm deep, if you assumed it was a cloiyp1x5a+ o hb1sed 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 sp qab cmmx+o/)qo 4e+l+anning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p+maq cooxq)+b lm+4/ eipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third hanv,3efn * jc10 rbkzi1rmonic. What will bein1*z01b3ev fjc, n rk its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string n6glh/qe( *hj*ag. cu is 0.73 m long and is tuned to play E above middle C (330 Hz).lu*c*a6gg/. h j(eh qn
(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 em8 +r 4 ijg)0zfs+vcw dlk3t(kvits middle C (262 Hz) when the g+08c3ft( kzi wk4rd+)vsvjltemperature 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 20ze*z ocv+ 8(fm $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec.rt k p-,zx5xie of the flute in Example 12–10 should the hole be that must be uncoveredx.p xzrtk5i -, 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 aayeqwyj *1, xq bhusy/b,:9z 9)n nf*et 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or ) *uwq1fxezy/y,e*n,yaqb :j bnh9s 9a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It o4p; *-xa i4kw:tbbceresonates at two successibk poa:tc*e;b4- 4w xive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 dkpd + :,.02rkulahrxqyz m66$^{\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 a 2.14-m-lo.apyh4s rs;*m ,c poe* 0suiz*ng organ pipep**msh;,esr.c* aoui ps z4y0 at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelyw:6 xh: z4,t7qzeex zj 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 thex :we,hj xzzez6:q 74t standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears on o3+f:vnsabw2x .*u qse beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is tfw .sbo+ x*s un:3v2qahe other string? ±    Hz

  What is the beat frequency if middle 0naulmh*0;3ehpzzw ,oz q+w0C (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 h p3s eov y9vee5+a;ia13 uvo)(brand X) operates at an unknown freve3 h p;eaovu3oi)9a1ye+ vs5 quency. If neither whistle can be heard 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 when sounded with a 350-Hzgjgj* f6) r az5k/ejkg-h1u:bhbg 44m tuning fork and 9 beats/s whfkg b6zk:/ h44 a g1g -u*ebjhgrjmj5)en sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hfhj7b pkn/ ;/ mzdc.q+z. The tension in one string is then decreased by 2.0%. What /;dp + 7.jkq mfcb/nhzwill 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 flutes 8b mqkg;qdv (n60ud-m each try to play middle C (262 Hz), but one is at 5.0°C and the othedmmkvdn qb6u(gq ;-8 0r at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B l1;sbl 6sck(z;,qvnk 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 of A and C? What beat frequencies are possible when A and C are sounded toge s1bc6,(lv lsk; nk;zqther?$f_A$ =    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 s *.to)r7hmhy z9fdn6kmyum, m5 gi+.apeaker and 3.50 m from the dh7 g,n . trm9y*mhmafk +z5)you m6.iother.
(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 cn62y*z/oc dz- xcgz -ku.q/; ge c+ge132 Hz, but a piano tuner hears tcq+-xugzg e/ *o/ncccz6 -yk2z.;dgehree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m avw 6/) ivldx5d0vg3i q3epyf+nd 2.76 m in air. How many beats per second will v5 vp 6i+e3yfwvl3qx) d0/gidbe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s si0b9 fin.7 g gnn5:gy*n0djao(gr pm d8ren is 1550 Hz when at restpdr.jn9gf7mgngd00b* y 5o( n8 gai:n. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whos t2i 6 +g+fj,zi)jtsrne siren emits at 1550 Hz moves af62tjir+nzigs+t,j) t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2lp;w q-j7m)y)vw x pj8p9f5y+ bl+yqokrvs /4000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are thr9by )px ;-wfvpok45ll jqs7jm8q++ w)vy p/ye 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 sa/4lp 4(ej m(wdlw+ ylyme single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fm4e/pwl+l lw4yy(d j( requency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoni32zg 5ekato 8* f3ki/wfft x*ic sound waves at 50.0 kHz and receives them returned from faik38e3fxwf5o*t / 2t gik* zan object moving directly 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 fli cm/k6dd egh8+es, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequdem6ckd h g8+/ency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubay n6hbl6 qc5ne(i3e8e was played on a moving flat train car at a frequency of 75 Hz, and a sei en(3c8h6eq6yenl b 5cond 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 meterqzb)8i78ukkbov3u9 d 3i ;ee k uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sou kvzu3obieq3ib ed7)k9k; 8u8nd in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi7yyp g4g 6+xlf*fi12yq 8svya ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind ve*zkfwdqgc4 5y2wxa/ h*g 31n qlocity is 12 m/s from the north, what frequency will observers/*3 k2 x f*cy4wn1wg q5dazhqg 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 if its speed at 20hh6e 7wr9uwp; hc6a fa5eh(g8 $^{\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 whermgc,n5l (l z:we the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airlw n,5g :cmzl(plane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the 60 1cod4hgrlaspeed of sound is only about 35 m/lh c4og601 rads
(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 stri 6qnzhy,7k;m ap*obq, kes the ocean. Determine the shock wave anglen,7pyqok ;m *hqa zb,6 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 9 l9g zy:h70i pgj.nhq$/theta$ 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 th2i yh-o35k5phy) qo hre 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 km.p3or ioh2-5kq h5hy)y 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 pulsewo3 m kz*d7( k k./pdhhc1wpk8s downward from the bottom of the boat, and then detects echoes. If the maximum depth k8c whkw3/ddo* .1kzp(m 7phk 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 human audible range? )h b) v6zh5(k99 mt7nfsuymic$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sfxc9i gvxi:ogs4u i 1*1r +pgt51o tl-ymphony. It consists of many plastic pipes of various lengths, which arei1up*5g:xgoio1xvsgt fl 9 t1+c r-i4 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 cln g/ xlf)yg1/bk/a7r yr0i st:f/j(ufose to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mos/syffn lg7k)i/t 0jfx:byu( 1/r gr /aquitoes?    dB

  What is the resultant sound l3enoa 6cr3i *qevel when an 82-dB sound and an 87-dB sound are heard simultaneousrn oq6a e3*ic3ly?    dB

  The sound level 12.0 m from a loudspex5zu h :z5h*n3mwht n1aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equalntz1nxhm h5uw h35* z:ly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output d;(1juksk (se xrops by 10 dB at 15 kHz. Whak(u j1s;xse( kt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices o 6krzm x./v,xjjm.kz0ver their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 mx .60kzx j.rz,k/mvjm, 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 systems, tp 1spgz-p0o f8he 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 (,ui)8kd8;xgz*r0 gair hoh r 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 findhl)jp8b18 j -3y1zz4os0l nm0xz smxed points with a fundamental frequency of 4 8nnlz h010y)-l1dj4 ozzpx3bs8j msm40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical 0wgia gvq9s-/c 97 gjxopen tube filled with water (Fig. 12–35). The water le vgjg/wis-ax7c99 g 0qvel is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at oneny/ i xe4v- w3f78yrmji/g8(wmxw01 h9p mmlc end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in it(x3rme -x fmc4/w/ ih9pn8vmjyww1ylig7 08 ms fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was 8g;lx-i py wb3observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-H 4ne 3j e8q5cm +elytl5pt9gq:z range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the + ng3epj85c9lq mqe5eyl 4:tt other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the s(1awsy2dl p8h tationary train hears a 3.0-Hz beat frequency p dya s8w1h(2lwhen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam shh:i k:9xry: train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? 9y:hr:hkxis:    m/s

  At a race track, you can estimate the speed of carsy)b. g9cm2i hs just by listening to the difference in pitch of the engine noise .ymgi h29)sbc 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 H+ 9nuzo;k9of nz. The shorteo 9knfn+uo 9z;r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statimkc0rf 2f;g mrm +;cy9onary observer at 10 m/s as shown in Fig. 12–37. If the speakers+; c29c;mr mgmy 0rfkf 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,5y qmca1tzo+ ec4 if-p f kgjsv4v)91s normally about 0.32 m/s what beat frequency would you expect if 5.50-M 5j1acqv,io9kez tffmvp4g-y sc4 1)+Hz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying h/wtutc*tv9(m o+q 6ytoward the bat at speed 5 m/s The */o c q+u6wht(tv y9mtbat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses a 8a5h; c6uoqjof 2;vues 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 be detected by the bue5f;aq2 u o6o;8 hvcjat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signalflxy 7tozud/lq di7.r nbw r;6s:4g83s 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 flat) horn. What g6 l.wz f8iutod7:/yxbrq7nl s4d;r 3is 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 compromiseyeymt y6;u:d)is4 /ipd 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. Cy:y/)iesm6 d;4pitu yalculate 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,” involves a long, slender alu,e *lzews,/ omminum rod held in the hand near the rod’s midpoint. The rod is s/oew,z *m ls,etroked 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 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 a2rahsnifos22l48k b(c x9 k 4at a frequency of about 1000 Hz isn c i8so22s(4k xarhl4ab9fk2 $I_0$ = $1 \times10^{12 } W / m^2$ 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 sonitj 4aan.o2+nhc boom 1.5 min after a2h j.nto4 n+athe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is y9zgyp27 bb(mx8p .bj15 $^{\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