What is the evidence that sound td:k9 b ,j 4enm*h7bvbu3iez,hravels as a wave?

What is the evidence that souqn,ubfkf-( zzxl +4s1 nd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to tg;fy:yozmy2,)laz3emq)- k rhe bottoms of two paper cups. When the strifmeky )r,3 z2o ;gz)-yqal:myng is stretched and a child speaks into one cup, the 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 frequency or /( m44hg6aalpdil w-nwavelengp/ wgna(amlh6l-i 4d4th to change?

What evidence can you give that the speed of sound in air does w ;fhhja lcn9ic8i3:7 not depend significantly on frah: i89lhc w;fi c7jn3equency?

The voice of a person who has inqlaq;c+ ira qe)xu+8( haled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of q9y d n;xtqk qf 8246eett5r9uorgan pipes?

Explain how a tube migh. v f92snqgzp55n;jml0 -iqzot be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An exa2z qvnpjl5zs0f5-mq.9; gnoi mple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together j) t utqs23zjj--:i o ofu-v,yas you move up the fingerbt:to fj)ouq3--i-y2 v,zjujs oard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but c w/ i9m/ylvqejq(x;a- annot see it. When it emerges am yl/je / v(xqiwqa;-9nd you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be qua jl7z.d. u- jxokajb l0,i4dr:i+8due to “interference in space,” whereas beats can b:dj0dix br, aio4jk 7j zl.+-ul 8qa.ue said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spea yhb4 4-mm)ajrz*s*jakers were lowered, would the points D and C (where destructive and constructive inte -m jrsh *a)azbj4y*4mrference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people d mx:w8ebq l hgd:30nle.f :,1i (nwpcwho 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 in addition to the ambient nnbf1lec q lw: x,g:md(ph.w: 0end3i8oise. 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 tho9u) n0 r5zetjlux6 c.hught of as a superposu6jt.n 0uxlh95e ) zcrition 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 apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sl w2p ,zf)ztrmy.73yeame direction, with the same velocity? z23 le,p7wyf). zytrm Explain.

If a wind is blowing, will this alter the fre0e x ;4,pnwzg/xm elv) 39fhcsquency of the sound heard by a person at rest with respect to the source? Is the wavev )0 3esnzwgm,l/hx4xfe cp;9 length or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mon)+3b ikb43 mivp: jcxqb*c5 :argw(xpitor is blowing a whistle in front of the child on the ground. At whi5)b4(+j mbr* : cp3gbawi :qxickx3vpch position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for tz 2 u)/dlc1jruhe echo of her shout reflected by a cliff at the far end of the lake. She hears the /zjd21r ) cuulecho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jus ek9vxj)r5q 6vaz 8,hk.b..xthv3xt hqj 8,cq t 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 kxqxht h.aqb3kj65, )z qe,cvvh j8t89r.. xv seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in af6 nhj) shc7eqh3)65mhotj/ tir 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 tuna on a foggy day. g dq(5g bx u--2b9npn;8 s 3i9cyczrenWithout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backf g(bqe;2y cx8r9-pnz35i dunbcg-ns 9ire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.-. ddu: wik:xy hq(ap7 The splash it makes when striking the water below is heard 3.5 s later. How high is thead (wqi.ph kd7 u:xy:- cliff?    m

  A person, with his ear to tqmt; t pa64jfb,wp 78che ground, sees 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 are 1.1 s apart. How far away did the impact occur? See Table wf4b7ap,q;c ttjpm86 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of +dkmyty 5q oc9h9u0 d.*ui i-.vbca ,zdistance by the “5-second rule” for estimating the distance fzucd+a 9i- boki. tu mqyh59y0,vc*. drom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 ds: 5qk3 ky9qo 88bbbb78qwx uvB?    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 s ftkq;)cy hu7p6/2pis ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d9a0e9ezt. ytlyyvy 7*pgsjnt*. h*h+)wmc9n B when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add inte zhh97yjv ** 9 at)9 e0ynptcg+*t.mw yls.ynensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally k yumw*vy-*m96fy;lw noisy jet engines yvl y-6 wkmwfumy**9;is experiencing 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 havenrth ,bn9-ppv: o+ p;sp.nhi+yc7 eo- a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitirs tbp7: nc+n9o,h-v.hn+py- pei ;poes 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 s o ,t(zso 1u3k he+ys jhzvvt3k*8;3fdpeaking in normal conversatihdy(jvt,* s8+13 3 ozzuvtko e3sfhk;on. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area i3 mdl pnc)ige/ x-sbw.gi8i 2/s $5 \times10^{ -5} m^2$ (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 An qe1s a1lxr95 is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 1es9aq n5lx r1m 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 registernp c)9*g4hkcr ed 130 dB when placed 2.8 m in front of a loudspeaker ocr) *h cgp9n4kn 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 4 q)hj/n4pu ludetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudesjh u /4nqp)l4u 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) by what fkd.jd (rb bn2;actor will the intensity increase? Increa.j dk(r;dbn2bse by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displsr7 a6w +ds43/tsave f*z sdj+,zmy /gacement amplitudes, but one has twice the frequency of the other. What is the ratio of tht z, a34 s* /jzgmdr+a/+s7s6sewf dyveir intensities?   

  What would be the sound level (in dB) of a sound wave in air that co wr+)g aq(m1gyrresponds to a displacement amplit+mgw)ayr (g 1qude 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 thaawqi 6;qf jw *dyvtv )h/6ys(;t has a 50-dB sound leve6fq;jsv y ;(a) h6q*itw wvyd/l? (See Fig. 12–6.)    dB

What are the lowest and highest fr u,0x782z jkjlafuxr) equencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6ukx,7l 0xjrj)8ua f2z.)

  Your auditory system can accommodate a huge range of sound levelpn3qv a3uq;ou /dar +,s. What is the ratio of highest to lowest intensitvq33;u+d nrauq/ ,opay 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. The lengtislr9 4ku+(4 kstsxes.k/v8o h of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinrli+ 4/uktk9sve4skxo 8 s(s .g be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audib0h:fws bpd l j9dki+ d3,hs2d/mg, b1yle overtones ifhp9dly h:dd02m3s+ j,kwfd,s 1b bg /i 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)ngt2x 2-f8ucr j*crp)k y+ nce5a;ss the top of an empty soda bottle that is 18 cm deep, if you axpj -cr2un2+ s5))f *rcnysaek;8gctssumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the ran2i-m6tsew c 5dzch2n0o dl 11gge of human hearing (20 Hz to 20 kHz)cih1md2 5e-nd twc l61g2o0zs, 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 oozxa;lbysiy2+. n*9will be.o+yzs biay9o;2xl* n its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is p9ls my:u )hw-0.73 m long and is tuned to play E above middle C-puhwm) ly9s : (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 an8mlob gz+ a*2pi )a5io open organ pipe that emits middle C (262 Hz) when thz la5ag8o+ *2pm iboi)e temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 :; 2utf/a wejz)d3 xas$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the az296u5dt, x xfg8 xsqhole be that6x9f8x atdz ,q s5ug2x 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 resonate at 264 Hz, 440 Hz, and 616 H/2vdv9u)- 0ot z ihq5lnp/g .cbxc.ak z, but not at any other frequencies in between. (a) Shouoz ag05k2 )9c .btpn.qdx-v/ licv h/w 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 1.80 m long is open ab;z/j j 2c 8l -qil*6rhek7ixgm h9i.zt both ends. It resonates at two succe9 gj*xiqlih m;z6kj7 8ibr/h-. c 2lezssive 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 wg9 n gb-/jur8t,fy0g $^{\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-longk 0-zly ww28sgl: 1lmp7t xym. organ pipe at lyp7 kt:w -lzx.ym82lwgsm1020 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsi ;l8c+7sqa d2lrsk/y ude and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear cak+7 u s/;d2l8rycla qsnal. 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 one beat every 2.0 s when trying to adjust22jajlsej,659bc d p2j( fpmvg4 ct4b two strings, one of which is sounding 440 Hz. How far ofj,j5ej2c(t 9mg4al 2 j4c v2f6dpsbpbf in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an aja0x: q9adir30.aha d $C^＃$ (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 oper)gtmd) n.kc);n x .20e)hel1b7k 7ya sffz dqfates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneouslyaz fkbh0 nfg.kmt) y x7)7cl)sqne1d2df).e;, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning ft6hk 5 oql:c/w6 m-zrlork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the zmt:- c6hoqkll 6 5/rwstring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenno9/e9irlp7 )l7il ue3-pa ovq b-nx(sion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two stringsppl-7 x ()qoia/bee l9r7nv un39-oil are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes es */pfyq zjuux. 84,wbuiz qq: o2nkm0,jo8f6ach try to play middle C (262fiqjszu8mk2bfz4j/u p n x*w 8qoq.:y,0 ou6, Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork udkga f3zu 0lj yz :v1qsl12.z l,iq6.B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency ofqjag 2sl0yuql1 6idzl1k,3:f. v.u zz 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m f(*-k8hj mjnb zrom one speaker and 3.50 m from the othem kzjb hn-(j*8r.
(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 Hzopqf:(v m 9sq-2ltnx4, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132: -qmopx(t9 4lnsqf2v 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 j*cto lh-,vi0.64 m and 2.76 m in air. How many beats per second wivt0i*j ,-clohll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155j isp 0x1ygg1k6x 6*op/r.naa0 Hz when at rest. What frequency do you det*yg/gxra sp66 axkn1jp.1 i o0ect 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 deteckb+ vfd(jzcr35e c h;xpx:3m) t if a fire engine whose siren emits at 1550 Hz moves at a sx3 b :)p3xv+rce cd 5mf(h;zjkpeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving 8 5-3fjvqf hobkze+qp w02 c je*oty6a9m 3o8ptoward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sefc2j htkayvz*w ep3m90j88b+ -f q3oqo5 po6ame? 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 horgapxsm e3k4t3g3ln(* hh h-1fn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fn-h3gp 3sf41ak xm(hhegtl *3requency 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 receivxdu b)r(* -yi8fd4 ) ;yvr8qeqlxdnd,es them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? (uxd-qx r*)l4 fbney8,r 8)qddyvd i;   $ \times10^{ 4}$ Hz

  A bat flies toward a walhuu;c9kg hea (r: a.x1l at a speed of 5 m/s As it flies, the bat emits an ultrasonic soundcrha ea .u9hg;1ku:x( 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, axemn:4 j;vrn+w ;u l(f tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train xvf ;e+ln ur:4jn;m (wcar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure )ya9 8 oy.yci1 a(bmajblood-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 arteriy(1j)cob a.y 9miya8aes at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ4bewhq7tyjq l0u )u 8)ency $2.25 \times10^{ 6}$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 windzji65 45 nkc5n9a vlzv velocity is 12 m/s from the north, what frequency will observers hear whv5 lnni5c 6zv9jz5a k4o 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 speed14v6s7saj ; 3iy qcerc at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) W /40k yejej9 me,ou5eah+k7fvhat is the angle the shock wave makes with the direction of the airplane’s ye+ juk,0ef/a k o97vmeej h45motion?    $^{\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 whejl7vu i,uq90*r i3: u .txvxhcre the speed of sound is olti09 r.*qxc ,x :iuvu7uh3jv nly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wavezj .hf8,i6+iq0ff z ku angle it produce,jif086+f fi zz.qk hus
(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 /e7g o2 xftqgj7l) m9j$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead -dum*imsz u6nb( -p;zand see a plane exactly 1.5 km above the ground flying faster pdm u uzm*s -i6bz;-(nthan 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. 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 u q d vylic: dz.9cd9e 9o6nh0eb4al85pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth ford vacecy l09zeiqd4o69895b lu: d.hn 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 audi 8oe)q mr++p7we:. u*evc xbkible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewbo3q0cv( 4bjz vg ge42er pipe symphony. It consists of many plastic pipes of various lengths, which are open on bogzvb 4gjcq vbe2o(3 04th 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 perso.cn9 wx)5 9udpf1t fbwazj v6(n makes a sound close to the threshold of human hearing (0 dB). What will be the sofz dtx. fvnc 56wwab9up(9 1j)und level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dvmtixmnsv2 , 7vy0u9,B sound are heard simultanmm90y,txv,u vs v7ni2eously?    dB

  The sound level 12.0 ,q8do rwi6k +o( m1wgsm from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equ ws wi,og86 kom(d1qr+ally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.ml x- f,gadd59y0-ksw The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1 x09d-f,y-5 adsgmk lw5 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thek( )fzszgr5cr. *2gbvir ears. Assume that the sound level of a jet airplane es (c*2kbgz5gv rfz)r.ngine, 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 s+8so bm s6w6k *pq.lut1okh5/qll/hmystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequp+gzj ;e-ihjm a5;csoy c9e-+ency 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 fundamentaricgb ik4f(vu;0 -qqx u36ttft6m1 e(fsx72 el frequency of 440 Hz and a (1643t-uu6fc20em ixtk 7qetvbq;xsf(gfirmass 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 with wa+rj: v da 4;iq)rpvz 1x3xy2dvter (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 water1 ) ; xviz4vdy+2 jpxv3darq:r 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 massjmm0z)oek 9/8x-h/sgkm-4l n1kza a h 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in them1/4- xl9ke/m0k8nhmjs aa)z- go hkz tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resona;d7+k 9aa k 4dgthnf)vte 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 thgm/y5 ly7 )iofe 500–1000-Hz 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 finyfm/il) 5 yg7ods that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. s5 i l:7(pojiiThe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the s pi:oisl5 (i7jpeed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz3ffb j .3uim4m. After it passes you, imfbm3. uif 4j3ts frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate theeyps,z+ ldd 6cv;l re -ta8u-4 speed of cars just by listening to the difference in+-dcl, tl;46esveadr p8 u-zy 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 straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce 6v,nps9snu t4 qyo-/ .p3plcy a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oth.nuyy o s6/l3n9,pt4cpv - pqser?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s w0k*nj : yb0qjoa6q.stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he heq:jy.0*b 0qj6 snwk aoars the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is krb68y os ,muyy+4 p3jza)i/7x .onysnormally about 0.32 m/s what beat freq .uo kyp +ix7,yoy 6s3ryb8aj)/sznm4 uency would you expect if 5.50-MHz 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 speedx);v uka8ir8p 1d/xfr*kcm6o 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 rk rc6v iadx8p8x muf)k1o/*;frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high fruorw6-qi)k fe8 ) y4zz/ zaos6equency 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 be detected by the bat so that the echo from one chirp returns before the next cu-48rqz)o/kf6z a iz6 yo se)whirp is emitted?    m

The “alpenhorn” (Fig ni5 hc) :p*fedr8uk 41rm-zrb. 12–38) was once used to send signals from one Alpine village to another. Since lh* bpf4) 8nc 1:5errzrku-di mower 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 as an open tube.

  Room acoustics for stereo listening can be compromised by jisdtm qnv/6j sg8-,,9 bkzyee) 2r9q 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 roo,9-) 9yis 2vgej6 b8dtq/r, mznes qkjm.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrat ;wzc;z n+0/2qhgu1qgsrp 33bv uy:t jion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be m / n12yq3svp zt+ hj0r3;cguu;:zgwqbade 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 attw+bx 3 xd/ne+ a frequency of about 1000 Hz idx+e t+bx/3wns $I_0$ = $1 \times10^{12 } W / m^2$ 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.unyt( 6f35:oq-7lxca 3l7ncif cq :hx0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’q73la ix-36 :txl u5cfqn7cf:n y hoc(s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat islqn.k 97x88hieza 3mhws i6g)j b7 h4b 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