What is the evidence that sound tracw q0yd:im 38yg5v+ co 8o dek/v-;xdhvels as a wave?

What is the evidence tha0wnuvdp5vb2wkn;68q dokf 4 8btvt,9t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attachin.tmv/ u3 h.x++vqbe7 fe:quzxg 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 .xqxtu:z ue +3.v qvh7+/fmbe 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, dokkp7r.rm4 gzfgwy( i5;k p0tl3 yj+ r6 you expect the frequency or wavelength 3kk l r47p.;gmrpygj56rw +(fk0tziyto change?

What evidence can you give that the speed of sound in air djsm- ogp/ +,z)bhgas)lto64 soes not depend significantly on ),-z gsmt apso4jlb o)sh+6/gfrequency?

The voice of a person who has inhalj/su4+q*x/xwzwf 5 q qed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitc1f: jttk(;hia,r gh ,ih of organ pipes?

Explain how a tube might be used as a filter to rl zue2e: r8v2veduce the amplitude of sounds in various frequency rangz ervve2lu :28es. (An example is a car muffler.)

Why are the frets on a guitar aj;/vrg(cs mis1c k13w21bi w (Fig. 12–30) spaced closer together as you move upcmi / 21rba( ;vcsww3i1 jg1sk the fingerboard toward the bridge?

A noisy truck approa ;0jdcsl jt;a*ches you from 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 of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffrd*sjjac ;0;tlaction.]

Standing waves can be said to be due to “interference in space,”h2g)b t+gh oafty) :n7 whereas beats can be said to be dubog 7))nygt2h:t+af h e to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were ntm:) 0 rsltw4 f,x8)y*z.m m5kavrinlowered, would the points D and C (where destructive and ckmx *tr t 48r)nivw0.lmy fa,s)m5 nz:onstructive interference occur) move farther apart or closer together?

Traditional methods of prote zvdpd)n 5 jyex4knbf09+p x te+hh19/cting 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 relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electrod+5n x+ p) pjn9v0txhe fhky/z49d1e bnically, 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. Each wave can be though8jj1n )kvu7us h*5 :apdkq:eq t of as a superposition of two sound waves with slightly different frequencies, as in Fin8j p:u5*u1hs v7:qq akdje)k g. 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 koi.mg yt tq5+ +h9:sathe source and observer move in the same direction, with the same velocity? Expsthy k.oatm5i +9g :q+lain.

If a wind is blowing, wiqh6fj jm)j99;jc ph5gll this alter the frequency of the sound heard by a person at rest with r)6jqcpj9jf m;59 hh jgespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mo*vxd9 yt )m30r2mlix onitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequenc2txmiryl d*mv9 x30)oy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a )k,gawn fez8p9 wm :z0lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the eegw 0ka8fmz, w)9pz :ncho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears pjvm5n :owk* l1d y4:fthe 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 signifdk:4ny5m:jwlop f 1v*icantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ai-.i1zw hktt7vld48aq r 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 of t xf* ew+2mpv(ouna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fi v foe*+2(xwpmg. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clx. v lth z1hnzox.x v5.9ftlz04w+d2s iff. The splash it makes when striking the water below is heard t h.lon0 x1vsvx f+dh4.lwz92x.zzt53.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, se:c :ygi uu7*roes a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they *:u7go :iu rcyare 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent e6s-fn,j ay*)abmw ,elrror made over one mile of distance by the “5-second rule” for estimating the distance fro)* l-js ayab,6en fw,mm a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain 01+6-7 l5u5bww bp;cctseyewr o 3lnblevel 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 sound whs:.f )x uc-zmqose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whek2m (oe1clkgp2f 9:n cn fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,:2po2klm e(cg9ck fn1 not dB’s.]    dB

  A person standing a certain distance be )dsdh6qr -lrs4+erm( 6ek6from an airplane with four equally noisy jet engines is exps -rqr e4dl+mrd6( 6 6)sbehekeriencing a sound 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 ratio of 52bb,uen ;u ( t-ykst6tf*c0q3dq x3io 8 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fo-2b tefsi y;btn06o k3*cxt3dquq, (ur each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speans)gls 9fyb-0 king in normal conversation. Use Table 12–2. Assume the soyf bg9- )lns0sund 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 eah: ik ei3rltx u*7*fs+fnn.6wrdrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modey-d n( -oe.e-r wp,t-h(.hk *vtphphast amplifier B is rated at 40 W. (a) Estimate the sound level in dechrp- hp-(d.t,k wop.eveytah- h(n*-ibels 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 j26.y p(ylcwn/lj8lv130 dB when placed 2.8 m in front of a loudspeaker on the stal v 8jc/p(nwl .2jy6lyge.
(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 souh,1k fistfw75 nd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [,5s1kf7hwf itHint: See Section 11–9.]$\approx$   

  If the amplitude of adoq(/ 0ts (xa 1qqk7ly sound wave is tripled, (a) by what factor will the intensi(qqlta kyx 7o(ds /q01ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves havevxh t/ode ;6;zgee* )a equal displacement amplitudes, but one has twice the frequency of thae;z ;x)6tev/ hd*g oee other. What is the ratio of their intensities?   

  What would be the sound level (in dBqne+09.l/5 xuwdq *6nzp svq d) of a sound wave in air that corresponds to a displacement amplitude / +q59d60xznq .qvuldewps*n 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-Hz tone thb x2ejkwltgdg )y 90.tn:n7/jat has a 50-dB sound level? (See Fig. g)b9 j 20el/wjyxd7 kg.:tt nn12–6.)    dB

What are the lowest and highest frequencies that an ear can detecwtzie*s8 hph 4g6 zdzm)m6l +8t when the sound level is 3edgiph 8)*w6z+l6z zs m84htm 0 dB? (See Fig. 12–6.)

  Your auditory system can accommk/wv (1pga-9hqrwy 4b odate a huge range of sound levels. What is the ratio of highest to lowest gp/a9wy-1 qv hwrk( 4bintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a viokix)0: mvsxb1lin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35xm v 1k0xi:b)s g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lon: /rn4nhz/+ry ptbq/zg. What are the fundamental and first three audible overtones if the pip z nzpqrny/+/bth:4r /e 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 fromu (l.q.m3,e reki.-l aa*bfln blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed i3eum .bl(qlkfa..ain- , l re*t was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of h5u 4gaj (b)ervuman hearing (20 Hz to 20e) jr(v gbu45a 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. What wilvpxogv2 n5e;n6;6cd bl be its fundamental frequency b2;nxe6vd ; co6pgnv5 if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E 3w+hkwfq- 1fgb(p3 bhabove middle C kfbb qf-wphw(3hg1 +3 (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe 1u:dv(q p-: 97iexpypvs vrf6m n:x4b that emits middle C (262 Hz) when the texbv9pi d 4q:mnp: 71e -x6ypru(fvvs:mperature 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 x(tln;qd 6:wx20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moul o vdhmcu3gp.49yqu9 lx.t75 thpiece of the flute in Example 12–10 should the hole be that mus.x 7594ldolmguv3 9q ct.uphyt 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 resonate at 264 Hz, 440 Hz, and 616 Hz, but not a bei ay rhu(qt pz)(8ildm) .-3,xyf,nt any other frequencies in between. (a) Show why this is an open(y b hid-))rumtpl(.fz8y 3iq,xea, n or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m lon hz+p*gc9yp2 bk8xj 8mg is open at both ends. It resonates at two successive harmoncjx 8ky8h+z9bp m 2g*pics 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 ox1r6) (sm9g9b sb9 ac6hkaas$^{\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 rantrtm3t *(78go 1jh-t rp oz/euge for a 2.14-m-long organ 8rtmtg (7rtepo3/ * 1ouj- htzpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. sah1nne jv1pvjkp +7 7;o2)uaIt 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 thev+ h1jukpv1 aj72 ;s)a7enpno 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 one beat every 2.0 s when trying to adjust bn;um /+g its1cemv69 two strings, one of which is sounding 440 Hz. How far off in frequency is u9gi 1/tn6c mev;+sb mthe other string? ±    Hz

  What is the beat frequency if midd :2s6w ;xz6xol dshsr0*guy+wle 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 (brand X) operatesvb ac;gnl;+fptl /,e8hb, z(:-wn ami at an unknown frequency. Inebg;lnfzha (/ vaw-8im:p, +ct,l;bf 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 produces9v2q8i deaaceavc1k (rx/ pq ((ajp :4 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s a2(pekaapc (a4d( rq:/ cjv89xiq v1 ewhen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunedom:uw zzv-b*3u;5w6mdfzm f : to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall * -fo w6zmzzd:v3 b;mwu5u m:fEq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pl q(8qfz:u zhc6ay middle C (262 Hz), but one is at 5.0°C and the other a:q(fq86 czuzh t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and x4 lih /4sp+iqC. 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.+ps h4l4/qixi What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A peo;mj x *sz16hf9uic l4rson stands 3.00 m from one speaker and 3.50 m from the ol1 h9jx 6u smzcf4*;oither.
(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 t f5 agfhd*wk g.aksg6:5 *kf40* k(f fnzty8reuner hears three beats every 2.0 s when they are played together. (a) sk r:*a.k4hkffa5ydfkfgg*g8n(e 5*f6 tw z0If 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 wavej6-xeqrql) :eym 1;,rk1 iv e8o6osq clengths 2.64 m and 2.76 m in air. How many beats per second wille q6locq:rmjor 1 ey)q; v1,i8s- x6ek be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’j( n2afu,esl 0(lkhph( .4brtn y4i: ws siren is 1550 Hz when at rest. What4bt,a uk40y wh(lp.lsnf en 2( i(hj:r 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+ ww v;-crhdt1d w66rme siren emits at 1550 Hz moves at a speet -w6m6hdr1 cdv w+w;rd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sounmt *e0zsf2 k/rce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Am/0zs tn2*k fere the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one ic e6towk6q). ab5h4y:lx zzodw 69 2-9kwvac ns at rest and the other no 6yvd h-99w k.weatc q2b56x c:z6o)lakz4wis moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives +l,u frm 3;pxs 7lhjm6them returned +lrshjm uxl7fm p;36 ,from an 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 apn 2uzsum0 6le)edw)o;3o : ia speed of 5 m/s As it flies, the bat emits an ultra:) a;6uowsepz)02i3m neuld osonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatsgkgk bh92 i1) trai)k 2gb s19ghkin 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 waves tov-n,i .14s.i/jgvtb c 1k7rdm lwm3*ir2 jqto 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 i ti1vjt74ji2 m*.3s.nov gr-kiwq/b ,1 lmrcds flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freque:+zbot+ ie l-b h.ulf4ma l8we+n,qvrz 2z9f*ncy $2.25 \times10^{ 6}$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. Whenlw;.0v04km(aemxch0j +2;k p x ylu pz the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, jup0( vkz00.;+k2; mh4lcpxw emylxa
(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 6 fo:vz,pg7a. erz:sk k)udl7 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 wi0u0,u 8/ htrrt8 4asc gmeup)pn8y;h0kt pk.here the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directionhr8e 4i 8/s,n).u0mtucphrp u 0;gtya p8kk 0t 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 of a planet where the speed of soundr*wd f23 pao0c oqh,el7-ljk* is o02-7hj,ar*fo clek3lp* q w odnly 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 o(f s lvcgj54k8cean. Determine the shock wave angle ic(s4g5k vj fl8t 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 1rki+8dnch .b*f8dovo;: mfn $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground u)zhajx7- /z zflying 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. See Fig. 12–34. Deter-zz7j hxu/)za mine
(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 s*i7)fs.p:b cuotdwha * (sdwf5 8h 7nw)ht-tfends 20,000-Hz sound pulses downward from the bottom of the boat8 f-i )7wdht( sh5tah:tbw ) cufpw*sdnf7*.o, 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 (in fresh water)?    s

  Approximately how many octaves are there in twkrx2l(p 6(g4 x r)m/xmmjz31dhbu3mro -x n,he human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewen(y9o9rozz0. vf1 prqufg8 b*r pipe symphony. It consists of many plastic pipes of vaffg0 zr byp19zoq ro.v9u( 8n*rious 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 :a xp0lg1oj-y from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound levjgo 0yl-pax 1:el of 1000 such mosquitoes?    dB

  What is the resultant sound leve;p. oftth6jpq.y 8f; ci+lnq *() mdlcl when an 82-dB sound and an 87-dB sound are heard simulta . tnom.q; i djf(lp t;+6*cqlyfhp8)cneously?    dB

  The sound level 12.0 m from a9;7ewtd 5* sedns e)plu (ymv+ loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?pvd we+7ed*nue lsmt(s)y ;5 9    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thlyi8vn sc/tk . vje8 euv+4.0ne power output drops by 10 dB at 15 kHz. What isty .4v8nk vus 0i/ v+e8j.nelc the power output in watts at 15 kHz?    dB

  Workers around jet airc7 m e.ga2qp m6rtc5w8atdi 0(sraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is td. taq6r8(c emmw gap570si2 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 sys m0y+/lx1r, pz zlaww0tems, 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 :pc;+utlg)m dtuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violino45-r exc*ogf is 32 cm long between fixed points with a fundamental fxferco4* og5- requency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fillepeqz6fy;a-baw 3 )g-ad with water (Fig. 12–35). The water level is allp -gb a6aeafw;y)zq-3owed 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 ju5fi +wbo7o7 that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resona+ uf7 boo5iw7jnce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res 5z6dkgsskj1e)e3 kd2o; wc 0uonate 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 t8kf vkxhwm4*3iw z/f5he 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determi5wkz h34* kxim wf/v8fne exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz u0 *di r*h)djkv8u:t cwhistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whak:ru *8j*tvui0d)h cdt is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you ivi/wqho;;if i-3 c:vts 538 Hz. After it passes you, its frequefw-i;tvv ;hi :q3 /coincy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can +d0 6hwgg2wq et6 n23ynkdij+estimate 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 straigh2w ije dhnn0q6gw6y3tk2d++ gtaway. How fast is it going?    m/s

  Two open organ pipes, soiod 1gx 5zskc)gn.aem w; (4x9unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thee;xgz1 .w dxcns59(iao g4)k m other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p7 vope*mad*kts);9 )w z(sy ziast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is ta;7dzs9e tk*s)w(yo v)*mi z phe 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 7yu*nl9qd1d joqf+dhm-/ c0fbeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assuo0 dmdyfq*9 7hl/fdjcn1- qu +me that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speedad2lttql 8; ;287 c s.toln4pwho0iwe 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflecctpea ol2hw nq ;204w ltid8 .sl;8to7ts off the moth?    kHz

  A bat emits a series of high frequ+s8 7f bos9 ky3tsn4i,zbmrbmc7 p(;wency sound pulses as it approaches a moth. The pulses are approximately 70.0 b38mckiz ,os;7r +7b9ypnsbs4(m w ft ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once 91g solxnc.3kused 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 flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as3. g91 oxlkscn an open tube.

  Room acoustics for stereo listening can be compromised by the presen ckw9 p44vtgs3ce of standing waves, which can cause acoustic “dead spots” at the locations of the pp49 3cs4vwgtkressure 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aluminzoabggf3 *qa: v7r7 2fum 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 s gzga 7:bfv af2qro7*3ound. 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 f4oo 763z 0l ep-oebnhaor the human ear at a frequency of about 1000 H06-n47eol 3opzhba eoz 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.b,4(q d imtqt 0;+qjcc An observer on the ground hears the sonic boom 1.5 min after the t cc0b q(mdqij4qt+;,plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ty;u,90g5nwn usl* vkja0 a8 dis 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