What is the evidence that sound travels as;1tqoby,/yd dx:j /b p a wave?

What is the evidence that sound l p3bq2 vd;pn4k;ne3c is a form of energy?

Children sometimes play w*m yp3va-2lvemi *k-vith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is - 2myv* vv3-aek ip*mlstretched 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 wate+ 6j;5tsjb hoor, do you expect the frequency or wavt+6o bo5j ;jhselength to change?

What evidence can you give that the speed of sound in air doy:yd ew/ipo9 kh7egc 0s)+y: jes not depend significantly on frequedp )wiosgh 70y::ky +c9j/eeyncy?

The voice of a person who has inhaled helium sounds vekcmz, /q);uy cry high-pitched. Why?

How will the air temperature in a room affect the pit*fs);qn0 c08c w ewrjjop*wc-yc+9b xch of organ pipes?

Explain how a tube might be used as a filter /pc;+yz5 wqz2k +almr bwky,1 to reduce the amplitude of sounds in various frequency ranges. (An example is a 1z+5ml w+/ b ,awrcqkp;yk 2zycar muffler.)

Why are the frets on a guitar (Fig. 12–30) bzb1hdsl.(el9utt e +1f t0:pspaced closer together as you move up the fingerboard 1ltuz(0b 1.se+ 9hb tdlp:teftoward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it *xqasw qh(d e( /j.i*bbut 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 xa.(s/eh(*qdiw qb* j Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be2ft teed+d. w 0:hcz(aats can be said to be due te:. 2w+ztd 0(cetdfhao “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would tha0 -su ) s:q2nwije6rze points D :0 r a)unw2q-zj6siesand C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protect:q :th;- l bmocpdj9b*ing 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 dej b:;t*9- hmdlp:q ocbvice 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 ss iw;f45gj ;aphown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, 4 g5a;pjfis ;w(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thenrla x1r/ 8*ze source and observer move in the same direction, with tr8 */xen1arlzhe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heardelducg b.)f 9l cl2 (81cs0kdc by a person at rest with respect to the source? Is the wavelength or vee8d fllcu0(b12c. sl )cckg9dlocity changed?

Figure 12–32 shows various positions of a q nlx3ik)wyj ufn)(+y,is( a)child in motion on a swing. A monitor is blowing a whistle in front of the child on the grouf iyiwqla +suk,()n 3jx)y n)(nd. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the leng,c 0 tix.ran)bb 5x6u:u/lxxy(i zm;y4 jas s*th of a lake by listening for the echo of her shout reflected by a cliff at the far end :5bnla 6xs;ia(tu* iscj.u0,b/ yxr xz m4y)xof the lake. She hears the echo 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 tg q.1gye pt ,7,4 rqos.6uisethe echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocuy6,pe e 1r.is74gst .qt,oq gean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ln4s5cfb32a/c yztbu ..n5vi air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. Wiw:ugi592i7)cmep hkt.7 ny f othout warning, an engine backfire occurs on another boatt eo.:cp u9mw7 2giy nf)h5ik7 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clqa/e e/typ qud2 f(j; +1ij0dyiff. The splash it makes when striking the waj/+tpye fd2u(/0; dyj1 qq ieater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pj jz3m;c3(ip.b uw vj2avement. A moment later two sounds are heard from the impact: one travzbciv.u (j2;m3wj3jp els in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rep*)exo ykvf15 ;t4ca ule” for estimating the e )cty*5a ke1pfxov4;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 at the pain 4jk0 d6 1engx0u13px8rewrw i 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 aoc fy3c-ikix8 .d vb-b3 l*oi4 sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired szd*/k k7wq +xck, ilz4imultaneously at a certain place, what will cw dl4k/x*+ qi,zk7kz be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distg8p,pe25g1p6aw frv */w js lo-y bw-mance from an airplane with four equally noisy jet engines 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? l-, p -r5vwe/bgw fswmjg82pp 6ao*y1[Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, where+s ldm(qt*o; aas for a CD player it is 95 dB. What+qato;* (d lsm is the 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 normaaq-nn:o c9sh7j6 a6of l conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou9 -nscqno ja:o6a 7fh6th. $\approx$    $ \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 r ieuod)1e,kf(44x8s:dwf uk 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 modest amplifier B+,zur5yketg1 upds 7,ue z/.u is rated at 40 W. (a) Estimate the sound level in decibels you would expeezke+g,rspuu , t7u 51.ud y/zct 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 130 dB when pp7k0 ;fbz4g8nvt p5mllaced 2.8 m in front of a loudspeaker npl; f4m 5vkp gzb07t8on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a diffe0hj4 tqq+,zlzrence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this h4z 0,jt+zqlqamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (axj.yoowjti ;0q *,) fd i9sdh.) by what factor will the intensity increase? Increase by a factor yjhq .js;fot0ix.d9d,w) i* oof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dlnch o9 7bivk. p4u*7iisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their in vp497l7bkio* uh.ic ntensities?   

  What would be the sound level (in dB) of a sound wave in afm3c hb 50qdv-;u8oac ir that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at ov-q 0m8;ucchbda 5f3300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that 9q9:ogkn u fu.has a 50-dB sound level? (Se.n kfgo9 9quu:e Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear canv3(t6,zv dq,gjgn lyw f i,7r4 detect when the sound ,q46vg znwl f gv (td3y,7i,jrlevel is 30 dB? (See Fig. 12–6.)

  Your auditory system cxqp9hqr)(fg d;k4n e*xbx/o*an accommodate a huge range of sound levels. What is the ratio o9*4)xxk* f qnq;gob(hx /r epdf 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 violi,1 nj4m3gbub m.*bz0jq ed6 bkn has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32bd*43bb6k.eqm g1uj0jb z , nm 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 thred8vn t6:xn5 u8of;uoey4uq+q e audible overtones if the pipe f5qeqdnu+v4 :o8tnuux 68;oy 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 the top of an 7mh)-i it6kjh ;s dgf/empty soda bottle that is 18 cm ddf )-shh6jtk7;mi / gieep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe o wk/u7h) 6t.r8; ed b;mrqip/.jdtpm brgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pip.p/q)tp6b;bmdk/8e mwh;dr .t u ri 7jes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 54 0v7fwzf 6i *7xuku ryyr(5;u;nbj1zc 0 Hz as its third harmonic. What will be iyk1bvy jwx7c6rn 0;z(zfrfu u; 5 7*uits fundamental frequency 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 play9 0 p.dzr3k: sjlk-pp6 ihmki( E above middle C (3id0:j6 k9-m i sz3h. p(kkrlpp30 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 pit l,wl-qg 8kv;pe that emits middle C (262 Hz) when the tempe wll t-kv,q;g8rature 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 rg90ta;r)3-d5eohbh 2zd klt20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in n(eg ,earuj lg /o83,oExample 12–10 should the hole be that must be 3 ( ,e8 /lnjagoerou,guncovered 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 a j+i9-prs 0hm dw-r-zyp5s+ bkt 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between.+sbh5k -i0 rdmpy--rpwz js9+ (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two s: fegkyqnzr2hd 29w-8uccessive harmonics of frequencies 275 Hz and 330 Hz.-28kn z:yg2h 9q drefw 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 pk 5yn/js-0 iby ld18e$^{\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 *b qphqik rck30l8zd ge1,/o9for a 2.14-m-long organ piprd lcqqho3 i1b,08e9p kzgk*/ e at 20 $^{\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 outside andm*o9ggj 7py oz2cjaj+l: i6+ r is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) 2igoprjm*6olj+jyc :z ga+ 97of the 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 one beat every 2.0 sjya4s q c*8v oee5c3a. when trying to adjust two strings, one of which isc .qs3e ae oajy5*v84c sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency it/rxtb:; jo7n,qgr4ew g, ,rff middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (braszc yha( eoj1i 4 g*-4ilug4q-nd X) operates at an unknown frequency. If neither whistle can be heard by humans when played ses *cu -j14g e hoyq4a(gziil4-parately, 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 355 v-r jy4he 1imktbl;ksg7gge*p5*c+0-Hz tuning fork and 9 beats/s when v ktg7l*g p+ji g1 ce-5y4*ersbh mk5;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 Hz. The telc2kcl; d( 9+lg:beq ynsion in one string is then decreased by 2.0%. What will be the beat freque(gqlbl y elc2ckd:+ 9;ncy heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middlew(*yaqhsoc/7rl .rebzg4 :m 2 C (262 Hz), but one is at 5.0°C and the other at 25.7b/z:roeh 4w*mysr( 2q aclg.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has (,x24tq,+afv)rtw okjjsu 1 pa 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 arew(,2 , j1atxrokvjp)uts+4qf 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 from one speaker an072fsn-c. kwfc-qs1cn f;a brd 3.50 m frosnbc.- wafk c2 sfcqnf017;r-m the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating it67acy4 m mv /.r m+/idqq,-bzgw*cjr u4c6y at 132 Hz, but a piano tuner hears three beats every 2.0 s when am.y6r/ 4vu i,7gz-tibw+ m/d6 *c4q cyrjmcq 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 and 2.76 m in air4v 4095pk3rc /vogpyz5eljan. How many beats per second will be heard? (Aprvkle39gnj5o /v4cy z4p 5a0ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire e ,ju:3ss( ;uybcg yf(zngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/yy (jc3g,(uss bz:u; fs
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if p)xyuqv(ms a.if7qbak:e3*sh e4e ,9 a fire engine whose siren emits at 1550 Hz mo* 3pxa9ifb7ms, aeyh: )4(qqev k.eusves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hzg+dpj/a 3u4 s 8d xch6h19dmm7l.lluf source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Ar4 d lm.1 l ulm/uj7a3sdhgxch896+pd fe 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. When5bwq52 zeroh)9a.a b9x:t ah a one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hrbzbw2 xh5to a)qa ae:h99.5az. 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 9: b+vhsfz8j:.hkk t8 qtm*vqand receives them returned from an object moving directly away from it at 25 m/s What is the received sqvm+s:jh9f 8*8thbk tzkq. :vound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, 16j2fhuiv8obzxarq7 )g/qp 9f/f0 zy the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What f9i //7rjvu b8)a 2zxpzqfq1yg ffho60requency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expem/cl ajeg(jl 28afk47riments, a 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 car approached the stationcl gm4a78lj2/ k (fjae at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedss:y 8rhcojnlvc ,z cz:56n: -w. Suppose the d: z 8cowzjn:,vhy: r5slc6-ncevice emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr eo iu fkk2vde8j9-7ri/j2ry 1equency $2.25 \times10^{ 6}$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 velocif,bgp o1 el jn)34tqdps:r,v)ty is 12 m/s from the north, wh3bljo ) 4p ed)pg,snvfr1q:,t at frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2/dxvwip j) n*10 $^{\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 soundd;7 ymkblh ph.-0:c rd is 310 m/s (a) What is the angle the shock wave makes with the direct. yl-k:;cb pd07mrhh dion 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 atmospsm3.5eii yk1 d+8ize2 nzq1uvq6d(mghere of a planet where the speed of sound is onlygn vie (5+3ik d281 qdmqzm.zie1 uys6 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 wcf68.ggm keqt5 , 9sonave angle it pr,5 9f.t6 congke8mgqsoduces
(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 tz66gl q, 8lx n)k+jnk$/theta$ 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 gro3mic(qw nfwuoj:7 z9lch :y- :cr r2(ound 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. See 2(j:r-zc u :m r (coohw3qc9lyiw:n7f 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 pulses r 1av7t*gw5 qldownward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in frqatg 51vl* 7wresh water)?    s

  Approximately how many octaves are there ini; x stu/:ph8swt t-c: the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ;v nsxakn)(2 rcalled a sewer pipe symphony. It consists of many plasna(2 ;vxs) krntic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to t ,h6 0.xl igt1n-rla6 0xaeniahe threshold of human hearing (0 dB). What will be the soun an. h-i06a1tnxxgel0 r, ila6d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are h,wh6v: cn( jpgeweb9,)o+tlleard s+hj6eww(og ntcvl )l b e,9:p,imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10 7iz gt:tis8-p5 dB. What is g:tz7isi - 8tpthe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powe0 tfi/qt sz1p en4-u+vr output drops by 10 dB at 15 k/q4+-tunp0if tves1 z Hz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protect s9 7rm(lar3adgjk,btn 9ra*2ive devices over their ears. Assume that d s3,t9rr72lba9(ngmak*j r a the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the m s5 073zrbtpfgain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1cy3c+v 0z)c uk e 1blh(zqs))x$\frac{1}{2}$ 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 fixedixxk4xr ,a:vcck3 +n51l bb) r points with a fundamental freq5n x,r4: cr kkai31b+ xcx)vlbuency 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 t,iv* k.w3 rkkky+e3rc z0y 6gvube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air ieg33vrri6,k kz+c ky0 yw .*vkn 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 ara4 ;aa1t ov(ls8ybkv*yd 33 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 the tube?;3 oak(vr3yat v8 ads*y 14alb    $ \times10^{ 2}$ N

A highway overpass was oba v).qp 8x6bdtny*xu ,served 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 6)kc23ywz*l7(f dl:,qz jadb bf idb/tone in the 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 finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is th: lb*),bz fdcl q2jfd7w6(dzky3 ia b/e frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Oo 4qiy * ua7nody ij:x 5/tq)gt*cu/9rne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency wheudiyg/)tjut*q io*qa n5r9c:/4x7y on the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After s14nwml zg co g1btiu;-eb2( w ysb4/4it passes you, its frequency is measured as 486 Hz. How fast w eybw4si4cb g4/sb; (tm1z21o-n uglwas the train moving (assume constant velocity)?    m/s

  At a race track, you cimh0v7mjz4) r an estimate the speed of cars just by listening to the difference in pitch of the engine noise between approachzv mm0)47 ijhring 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 Hz.;v 1cu fjpr*9oq,m/om The sho,orj1/m9* vq; opmfu crter 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 statildy*+o7 qj6c myncb 0 p; 5(yei3pm7hyonary 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 hears thh 75ce0y nm7pd6mljo+( bypiy3;cyq* e speakers after they have passed him, at C?

  If the velocity of blood flow in b z. 0ysy), y*jvl6 ;e7ptgi2zn2sxwdthe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel wi)lzit y7b .v2*jys,6zg n y;w 2sedp0xth a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth 4m 2xysa4xs*sx5 :-ad)ludqw7 ;rsh2fn dj/q at speed 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 tsqdhj7xx2w-2naq s ;y/* a5:mfrdss4l x4) udhe frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of(qr.r7u h.bqf:ke yo; high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eac (f:oku;hb7rr. eq. qyh 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 used to seqvse6 fo i6ml2 c5;1nind 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 ieiqifcv21;6 5sl6 nom s close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stan q0y;o kl(z9j7z4 zoglding 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 inlojz4 z gk9(0qz7oyl; this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”w 7yy2fi;f0zm n6 0uxl 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 littlef;lmun xzf6 iy27w0 0y 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 osyj3z87 4saye f hearing for the human ear at a frequency of about 10sja z7yy 3e84s00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An obser wu0(sdake 1;lh (p8xe93h fdkver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead.( 3de fsl0uh(dk918; axk ehpw What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatlezx;l0-k r e-nb2 :dt is 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