What is the evidence that sound fi w:g m*ty35e9vdt 6 :tc.aoatravels as a wave?

What is the evidence that sound-thub91lku*5-s fx3v vzr85f:ej y7 sbg8rfu is a form of energy?

Children sometimes play with a homemade “telep zy1su6t h:p:1w) fqn id (y(ycdag)k2hone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other1d (16ayswhn(:)pk yuy cgz 2f:t) idq.

When a sound wave passes from air into water, do you expect the frequency g.k lrzyeuq(q n v9)l /*-9pdfor wavelength tg. n vlfypr)9*-e qduzkql(9/ o change?

What evidence can you giv6 qdop.j1iyv hbe 1fruo4,,r6e that the speed of sound in air does not depend significantly1.efyq1 huj 4rd,, vporboi66 on frequency?

The voice of a person who has inhaled h+lwtvv +2 i1(3n xz.m*ztb ishelium sounds very high-pitched. Why?

How will the air temperature in a room a; - 1g(t+ sh;gnhzhu r3+k-cjfncfu9zffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude -mh 0 mdrc7;kfgxn 0:/yqi) aqof sounds in various 0ydqnc-)g mfh0/ kmq7r ;:xiafrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3us.n 6w; xem1v0) spaced closer together as you move up the fingerus mwevn;x61 .board toward the bridge?

A noisy truck approaches you from behind a building. Inr3 wq-crmqc0 q.a82zm itially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of th qqcrmr3 zaq .mw2c0-8e high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be2a(-ynp xcplw da.xd**4hb4 r ats can be said to be due to - ya*c4xdr l(phbxp n*a24 .dw“interference in time.” Explain.

In Fig. 12–16, if the frequency edrjb1iaz01) of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apab)0i ejr zd11art or closer together?

Traditional methods of protecting the hearing of people who work 1*np;)4 szf p6rcp(yphz1dyz 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,z4z)( pzs yndfph *y1c;prp61 a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thcf lv5 d:t,8xnought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two comfc:td8nx5,l vponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sou2wie9d:v*j axmvkiz+9 a , x3jrce and observer move in the same direction, with the same velocity? Ekm 3dwa jvzev*:x2ia9i,jx9 +xplain.

If a wind is blowing, will this alter the frequen4r -ra55cad j 7odm-bncy of the sound heard by a persondj-n bmac r dr-55oa47 at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil,xz sy 1y+8pku)ublg ,d in motion on a swing. A monitor is bp+gb,1u,8 kz )s lxyuylowing a whistle in front of the child on the ground. 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 length of a lake by listening for the echo of htt z38ktf 7hn1er shout reflected by a cliff at the far end of the lake. 1ktz8tf3t nh7She 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 hec om*n1lno 73oy+n3 mnars the echo of the sound reflected from the ocean flo+3ocmo 1non3n*n 7ym lor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavomb, o u4pv.-q.dfux8elengths in 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 drift4dfrn w*c q68fing just above a school of tuna on a foggy day. Without warning, r f4q *fcw8dn6an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes vn9dm*-o uy2: 4dd -fazdd 3n-c5i fvwwhen striking the wate w dndv5:-3c n-diayfd- zf4o9m2*dvu r 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 then.4nia9bo7/ jqztwg: concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the on:/9wb. zn 4jgqit o7ather 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 trz(9 wj vdhuvi q,;33rule” for estiz 3vh3r tdv;9juwqi(,mating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dy nk8 ei0 2ofj/j b4hk67fts,fB?    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 whose intensity is)c+ 0k 4:kagtkdf-dlu,nzzh+ $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslyp9*vt 3kyg7yyoc6:wvoic i- y dq440t at a certain pla96qgock c4-yo tyvw70 pd tv*iyy: 4i3ce, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cerh /1 ysy. 0 o.,gehic0us-unwwtain distance from an airplane with four equally noisy jet engines is experiencinn.h.01i wwg,/hc 0syuoes u- yg 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 58 dB, ws1hjzfq3j6r xk+3o q50lef m -hereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eachhz je +1rf mk3q5qjsf6oxl -03 device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in norzqk-j 3;zj1la/zw,85b qec+juci1j81 r cvvrmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mout3c ;rwv5ac,zzq eq/lbj+1-ij 8j 1kc1 u8rvjzh. $\approx$    $ \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 szh 8gzn u nwz4+sfv2xpyr)-/5trikes an eardrum 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 m+59o 9km pive a+jr)ccore modest amplifier B is raio+ k 9mc5ep+9vja)c rted at 40 W. (a) Estimate the sound level in decibels 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 dBtsh;dk ;o ,p5a meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the s5, apko;sd;h ttage.
(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 ddc0f5+e ,li c q,f9qtmqif 7o3etect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whq 59fc tidq0,cei fql 3m,f7+oose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factw 5l ungfzx*swyef(4* 9o(1lo or will the intensity increase? Increase by a factor uzn os*9yf*egxw1 5flol4(w (of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequnwl-/o)k 5db yency n-y )lkodw5/b of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sou42gtsstfw*h 9g:p nn 1p/dj/z nd wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.1gn:j p t//wht p sz294*dsnf1g3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100/n/oj ob/a jd*-Hz tone that has a 50-dB so/jb *j/oon/ daund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that oix)wtm,71gz e.(i7gqnu 0.g czxqx/ an ear can detect when the sound level is 30 dB? (See Fig.m,o 7ixc xgqiz/uexggt(1z) 07wnq.. 12–6.)

  Your auditory system can accomouv 6jj,6ny34 wpkgt/modate a huge range of sound levels. What is the ratio of w,6jug4ntj 6voy3p /khighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequed 7tzxssvl2h +zq)+)gncy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 gtvd7)x 2zs) +g+zh slq. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audp,l g; cqxtjb5.5xirgn81 n3d ible overtones rbl3x c8gndpg.i x n1j5qt,5;if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowinmi+ me0k efmb6z ).5pdg across the top of an empty soda bottle that is 18 cm dfe0zm+e) b. m5m6ipdk eep, 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 organ*v82k gthz40 iy+vlf3 hcl3sd with open-tube pipes spanning the range of human hearing vcv3k i23zlhsyl+t 8dg0f *h4 (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string habzi,3f,y 4 whnac:ra3 s a frequency of 540 Hz as its third harmonic. What will be its fundamentaa3w ,hif4c ra3b,y :znl frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m ; 5 j iis nmvokx/*9w,k1zx;ttlong and is tuned to play E above middle Cjtwkm;on*i9k1; tsxvx ,5/zi (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 that emits middle C (262 Hz) whnh)uvvlun, pfq 7np- ua,(.6h en the temperature h.(,nnapfu6lhvqp7, nu) -vu 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 ahq fv9 ; 7c(t)q;-w-yvogkqaet 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the83mar nn50l9)crtxr5 vo 1jma flute in Example 12–10 should the hole be that must be uncovervm jcr38t5r1l onr50ax9)mn aed 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, cm3yv z.acp +1and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pip1+v .3zc mpacye. ----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 rhkyq t1 6jg*j-esonates at two successive harmonics of frequencies 27ygth j1*-j6 kq5 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 nj* n4: r45 w4tes(zwfrwsms, $^{\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 aajv4hy3osm6l /mvr ( duz ;/.mre present within the audible range for a 2.14-m-long organ pipe.m(o/z ;uj smy 6lavv4mr/d h3 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 dua ;pqsi3fc gvxoa8.wux)4z3 f75 9nthe 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 the relationship of your answer to the information in the graph of Fig. 12–a v;i5xu4sxzfa3)ofc9nqupgdw 8.736? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying tofyad eo-0a; nt 6/2pen0fa;oa adjust two strings, one of which is sounding 440 Hz. How far of /np;2 n0d0a a-t6of;oayefa ef in frequency is the other string? ±    Hz

  What is the beat frequenvl ;uh05 nk87: 41jsiohnbbvl cy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) isq4h:9d 4*9uizumo 9 pw(z laoperates 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 simultaneously, estimate the operating fuqw(z l9:ipa io94h4s *uzmd9requency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fiadg i+eg7:(u , qn5 5xu.ldhfork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency ofu .ghxqgned7 (+:5 lauf d5i,i the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, ;s.1b-irgd( wrbl7ubkjdi:* pf0m4e 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 playi 1brl . 0(;*ksb7ju-edmr di4pbf:gwed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h *gigv* m/9q1r .zorna*p vd;ieard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C 1gv9qnirv irpz;o*dm */ag*.and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, agjfv 7z9foqj c0t( wyt9+7w0ynd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C arvj77+yf09gty9 qft oz(0jw wce sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.8s uxxc;bi(jz3;)f vsj2n4vvl 5auz2( 0 m apart. A person stands 3.00 m from one speaker and 3.50 m f 3(xcvanf)zlb 2x iujv;usv ;524jz( srom 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 /pvwv lnxl3ye/.ub: : vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when w3:vvx:/e. l p nulb/ythey 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 oq/+ddru.1 h q9culxi:*2 ukjt f wavelengths 2.64 m and 2.76 m in air. How many beats per secqh /2j1 q+ rui*uk.xucdld t9:ond will 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 1550 Hz vepnen7qyt t rb:a1zq6us 9; ;r110rf x*f l(mwhen at rest. What frequency do you detect if you move with a speed *:nv0 lrr1q9n 611etu;t pxmzr( esyfqba; 7fof 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequencymd,ac7k,3lo+m a2qej; zj8ph do you detect if a fire engine whose siren emits at 1550 Hz mopodq,k3l m,7 mah;+zej 2j8caves 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-Hz sb)5aa0pq ano h96g6vg:ws5 aqource is moving toward you at 15 m/s versus you m) aq s wa:v9gq6 650ghpaab5nooving toward it at 15 m/s Are 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,7fqa,z hk ah 7xio:y5 horn. When one is at rest and the other is moving toward the first at 15 m/s the drivk7,o 7:z yh5hfai,qxaer 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 ultrasonia:lsbo 7zqq8 j/37 nxku kkbh64f c9*kc sound waves at 50.0 kHz and receives them returned from an object moving dihk7zfj3slk* nbc oxb68kk:a74u /q 9qrectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/dg3cf-dv -6uks As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What fr 3dgvc -ufd-k6equency 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 flat o kh2*o0(wocztrain car at a frequency of 75 Hz, and a seco2( *zkohco ow0nd 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 to measure blood-flow speeds. Suppos*uw 7upgl-8 fu87lxm:g j+pdpe 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 largegp:u8l8 7 w-umdgl p+p f7jxu* leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waveq e po:rfvf4.4mdwp70 s of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 57eg95n8f 1 ka ohfyy1.l6h9jge0 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers ag18hlf fh9 kyoe19g6 ye .5jnhear 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 spee a.f7(1vwfb3af3co skd 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 +v9,iz 37myxtk ly/icsound is 310 m/s (a) What is t,xmkly+ 9 y i7vzc3it/he angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmospxn ge-0-o ll kad*kw(*here of a planet where the speed of sound is only about 35 m/s w(*okdl*e--akgl n 0 x
(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 ocean8(h:ve5pui no. Determine the shock wave angle it produ8n5uio(v:hep ces
(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 k oj+a6c.di63gx dp)ay6+hu 5bkkz (ci9 )irp$/theta$ 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 groundw:wiik09k uw1 +oxhe8 flying faster than the speed of sound. By the time you hear the sonic w hki+ ueiw9x80ko1:w 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-Hzr1pjl)ibfjav. -jdzu,c / l6 ; sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work /p1,rlcd;u - .)jj6l f jvzaibis 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how marldtm+ nb+c8. ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man,-vl:ro jo7g h8omri5y plastic pipes of various le7moi,holr:rj8gv o5-ngths, 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 closq zl r9-4 ogtj-0d(yvv1z wyo.e to the threshold of human hearing (0 dB). What will g(.vot-lzwv y4 zy0 1-9d rjqobe the sound level of 1000 such mosquitoes?    dB

  What is the resultan.olulf.fa -5ss tfa*0t sound level when an 82-dB sound and an 87-dB sound are hea5-f sl0a au*ls.ft.ofrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in ts48du5s :ljenns ;w,ehe open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally is8ne4d:ue ; slwns, 5jn all directions?    W

  A stereo amplifier is rated at 150 W output at t89xc4t fe pj ,(mb gp1c))cgqou h4r71000 Hz. The power output drops by 10 dB at 15 kHz. What is th(8oc)t )m qbxtupcf44p 9g17cg,erjh e power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.+-9axutmv:9ko+88n:r hqfi i3z x nvj Assume that 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 engiqhiv:k+3 j:ftn8x9- + a om uir8nxvz9ne?    W

  In audio and communications systems, 2a )e r05wtyl-eo jda+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 y 52 34xpcmrsq9u70jz +ouok mtuned 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 violin is 32 cm -v/pjdxtr:8qhw,3bf2r a *u clong between fixed points with a fundamental frequeh*f:x-, 2ua/ 8vwdqrb3r pjtcncy 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 fiklwdwvjnjgv()720s9xfkj4- qvx .s; lled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from th0.7ldqx) 2( wxg-jvv4k wj ;j9kvs fnse tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one e o7./ou+b: i6, zp(xnn2t5ukvxbpo v end and also 75 cm long. How much tension should be in the stno.:k+n6z( 2xp,uxuovvp bi o 7b5te/ring if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one npbferxx c nj.7u ,c 343ef7.idr9wm)full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two souq pp(;c,6wruea tb+k;11/z/k wsc husrces. The sound is loudest at points equidi6 w1/ e(s1su,r ;a/;wzptquck +pcbhkstant 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 the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Oizkr 8vgnw;3 (ne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train;nk( rvgwi 8z3 approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as ehz+nkfbs ,zjiu* 93*it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (k*ze* bn j3zihuf,s 9+assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bg. q chnzdr,p 3*c5,any listening to the difference in pitch of the engine noise between approachp,c,drqnhz .g a*n5c 3ing 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. The k*x;gay, ;, .hdztpir shorter one is 2.40 m long. How long is the othezrtg; ya,p.x,kh*i d; r?    m

Two loudspeakers are at opposite ends of a railroad car as it mn o lbgf2.d(cx1kfqt0ry6 -2 17 snidgoves past 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 the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at Cdf bg0g1 i7-n osc2.dkqrly2 61txn f(?

  If the velocity of blood flow in the aorta is not: ecsq(iz 61 j9vhuo+rmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directe(h : ztq6evu 1ojci+s9d 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 mox31 ds 1qvze*cth at speed 6.5 m/s while the moth is flying toward the bat at 1xd3qszv ec* 1speed 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 reflects off the moth?    kHz

  A bat emits a series of ;w;( ao rp.i :jnvmz,yhigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abowpm(:v n.;,r zioyj;aut 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 send signals from one Alpine vid8q.r1sal3 3mgl 4 qywv.4cbyllage 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 instru8wrvg. ql 1.4m3sl3cy 4bydaqment, 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 stu/jyo 0ja/q /cereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living ro/yqj/c oau0/j om 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, cacyljz*q;b h 3 6(fmi2alled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rahc*(z 36 ;fbyqlimj2 od is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long 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 rl-. h yf5q3v ik2by0dhuman ear at a frequency of about 1000 Hz is 20fr.qyl5vh -i3k ydb$I_0$ = $1 \times10^{12 } W / m^2$ 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 Machm dvhhr2r2*s d7w, y 8lzmr-3p 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altvr-2l 3 wyshh,dp2mrdz*mr 78 itude?    $ \times10^{4 }$ m

  The wake of a speedboat isc *u4rem ;cj*jswg8qj2l vm-4mit; n8 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