What is the evidence that sound travels as a q +2q 2xqrgku,(ef+r j3se* sfwave?

What is the evidence that sound is a form of en4)a5p6 pmmxofc odw.(ergy?

Children sometimes play with a homemade “telephone” by po3iwa . r47cqattaching 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 tr3 oq7 apic4.whe other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passesfksb ..2c-vhsy tui.y. r1s,k from air into water, do you expect the frequency or wavelf.v -s.sib ,1yc . uy2.khkrstength to change?

What evidence can you give that the speed of soundbl 7uuko8ik90 r+qt) .frv/ bb in air does not depend significantly on 70+vb k.)iutq9ob8f/u blkr rfrequency?

The voice of a person who has inhaled het7,h p bv0ocj6lium sounds very high-pitched. Why?

How will the air temperature ihjr 8ka,vdlg.5i* j( 7yyu;hnn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of 6czo yu .mbxqsv;a9mn1,h) z0sounds in various frequencyzh asxnmu;vcbz6 .qo9 my0)1, ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as ystmrnvdj008pmx73it c9k/qj wbz qr)vu 1+ )-ou move up the fingerboard toward td cvi07)p0mr/tk x 1 rtubwn3zjqv)9-qj+m8 she bridge?

A noisy truck approaches you from behind a buh7.33yrcwgz rilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffrrc7rhy w3z.g3action.]

Standing waves can be said to be due to “interferencl2to3 be;mp3kg/ m/i6xc* 88 wzpezir e in space,” whereas beats can be said8i862m* w ltppx ke/ zg corbm3;z/ei3 to be due to “interference in time.” Explain.

In Fig. 12–16, if thh yh33ytx 4yj9:7uumxc(+zs te frequency of the speakers were lowered, would the points D and C (where destructiveu9 7t hxz( y4s: xyc+uhty3jm3 and constructive interference occur) move farther apart or closer together?

Traditional methods of pro9w+ n 6oy5 vg*9pvxfiatecting the hearing of people who work in areas with very high noise levels have consisted mainlo g* 9f95v6i+np yvxway of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves16jg13*ke m3 nw;4xihcu+px v/aew0 f z0dmd l shown 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; ip3df4x3m w *cvjd/zem 0ak1uh+ 106lngxe w. 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 soigb*ri c/p(tij;( v k5urce and observer move in the same direction, with the same velrt cp ;(ib(i ivj/*kg5ocity? Explain.

If a wind is blowing, will this alter the frequpu(vg7 t107ly kzrkhv2 ), tcmency of the sound heard by a person aty(k0kv u) zh2,c1gr ttvm7lp7 rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moncc)khm- h/gks 15zgr-itor is blowing 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 rea-)g h/mrzkhc g c-15sksoning.

  A hiker determines the length of a lake by listening for the echo i8mc 42l k/1jznal6kaof her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lak n1 4azllm/ 2i6kcak8je. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wat-bh mu*z5i +;jjoic; xerline. 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 spuo5 ijxhz ;m*c;+bij- eed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths6 ka:cjn:q+x p 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 dri*jl8.a(llx d cfting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much clda(l *.8 xjltime elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top1 kx7rswllrk, 1v9d (p of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cll 17xsr9,1pk w(r lkvdiff?    m

  A person, with his ear to the ground, sn21 grsw7m9wj ees a huge stone strike the concrete pavement. A moment later two sounds are heard fromng1 mjws9w2r 7 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made o530k p1srcu5i d r3xzves:3cgver one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is ep13svgd:rkcsiu05r3 35cxz(a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundybo 0lkp36r -t at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whos/uo6dzgxz264 yalf z,e intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 94dtmm km 1vjw-((4lwxsi9(f+a x ly i95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hit( w-1lka+ 9x v f mi9(mi(44mlwyxsdjnt: Add intensities, not dB’s.]    dB

  A person standing a certain distance fromoa6 .ine1 aeet5ed 8j5 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 c8 ae ne6jetdo aie51.5aptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hak3mhcoyg 320l ve a signal-to-noise ratio of 58 dB, whereas for a CD player it ickh3o0 m2gy 3ls 95 dB. What 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 h jqzy8boj t.68on7iw5c p yn33by:+ta person speaking in normal conversation. Use Table 12–2. Assume the sound spreadsy 3 oiq7+n83 y.jbw5 yb8:tz6johntpc 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 ar n2xs/cj6nzi;g- e, ylea 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 dyvl d -;a0oioj/+pn1B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m frompl oin;/+o-vy dda1j 0 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 registers0w/ .dtyo n ceeg(65hed 130 dB when placed 2.8 m in front of a loudspeaker on the stasco6 5n0wed e(thg./ yge.
(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 xmlwcuoa8jn:q/.q j. vf5- 1pdifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels difwj.:/acv- q. 8onu5 m jxlfpq1fer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorkl pen+o4 dv)* will the intensity increase? Increasekv4)lpe +n*o d by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equats n11* gfhjt:zrsu( 8l displacement amplitudes, but one has twice the frequency of the other. What itj8st1g 1:hfrzs ( nu*s the ratio of their intensities?   

  What would be the sou17: 55+ xpuo,bzsqjp t l 16kzgb6aommnd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules 5bo a7ku61o1zp lgs,z:m5j6+x qpt mbof 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as nhf7p-7) ,pzwd7q(s zs uz)vq j7z:rjloud as a 100-Hz tone that has a 50-dB sound level? (See vzw-7z uj7()7jds zs,p7nr zf: hpq)qFig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the xob6-yj e0 sz x:aa;gh2sw)m2 sound level is 30 dB? (Seea: hazg- b)6s;s2o y2wm0x xej Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l9b-l )koy7lbtv 6u6dagy*3buevels. What is the ratio of highesta7tvuu)66 ylok -ybb9ld3gb * to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. T .ftjuy p3-gy7s a qt;1/kvaw2he length of the vibrating portion is 32 cm, and it has a mass of 0.3ypgk vs /f 27aa3j;qt.y 1-tuw5 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threwoecr +b/sd- x/6 *dure audible oveuo cb-*wdx/r 6de/sr +rtones 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 bl3j ww.dnk cz3e3r*0c auci xze op98/)owing across the top of an empty soda bottle 3o9epu*ewc/.zxick3 nrjazc8 ) 0wd3that is 18 cm deep, 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 with open-tube pipes spanning;gj;ip pdob3jw3l 4:e the range of human hearing (20 Hz to 20 kHz), what would be the range of thjw :;4dp;iglbo 3e p3je 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 thirdqu(r2h;q * jx; .hgtzzk5 xa/d harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lhxuh x5r/ g2 q;(kz*dat .zq;jength?   Hz

  An unfingered guitar string is 0.73 v( 3ieotu r1b8yl*r s7-cy0 ejm long and is tuned to play E above middle C (330 7e0c jylv* orb1u-rs83iyte (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 Hab ) cfgoek)d0.jo 18uz) when the tempera)ek)do agf.c o8j0u1bture 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 20b sfakql e02soc r4mxnl*ge;lk qmw97 ,6(i83 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl0cg(p l wjd a.y z2:x;z1jthy*qqa5c9ute in Example 12–10 should the hole be that must be uncovered to play D abo y 2cazqx:0*d 5waj1 (jpchlt;9g.yzqve 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 reslbx4+/w +poegw 7ymu 0onate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show xp/+mbly w47go+ ue 0wwhy 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 pzxgn* 9*fv q/is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzg9x/ *nq*vfzp . 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 :e*hqyj(cqd9ku0 43 +znkijtgdiv5*$^{\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 rangev kqdy(cx(re9pv+s3 1 for a 2.14-m-long organ +cvyk((ds xv 13qr9e ppipe 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:+yyfp )t yt(q 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 inpy:)y+(t tfyq 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 tryiygs6tya925ws ng to adjust two strings, one of which is sounding 440 Hz. How far off in frequencyw ays5g2 y9ts6 is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) annl+caubn j) 06*7qdz xd $C^＃$ (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 ( a,v,ohn,qtbm eep :c*smy5;: 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 :amt : byhe,c*e sqopmv,,;5nthey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string prodbdw r7aaqo :e,9p, fqlck 7dyn,6 r :qbaj(9j-uces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. W pn(:e,ja q,r,l 7 q9dc7of:96-rk jwba dayqbhat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 29gmde) x n4i7b14 Hz. The tension in one string is then decx i7g4n)mdeb1 reased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each anwkl,2hyz,5 try to play middle C (262 Hz), but one is at 5.0°C and the other at 25. hyal, ,kwzn250 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork 31;eblnorh;putskq;m d39 )l,i m w 48l fznp/B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hzhwkme/;;9z,lr314dnl 3m pqpf8)bst ;inluo 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 from oned:q )ie/, nikw speaker and 3.50 m )/niiw : ,eqkdfrom 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 at 132 Hz, but a pi-y+-(whk vlld mr8r-v5 5nojnano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what muvr-r (jw5yomvln-8 dl5k+h-nst 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 air. How many beatu+ sg l+iv,dae8 jq.9ms per second will be heard? (Assume T = 20 ,gv+lmu . aqsd+ej9 8i$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of ae4ao)c dcli 31 certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s lceo)ac4 id31
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a( ,iz515f ehzb7sj(xkuocdv2 fire engine whose siren emits at 1550 Hz moves at a x(fsub2,oc j1k ve (hz 575dizspeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if st 8o3k;-a vxuia.( bfa 2000-Hz source is moving toward you at 15 m/s versus tv. (ua ibx8k3o;s-f ayou moving 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 hos7x 6/seb:n(v wkkgqmbb;2hu-+:j k trn. When 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 Hz. What is the frequency the horns emit? Assu s6s-:nbt:2uek ( ;khxvb wmgk7j/qb+me T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoux0hejq1 hj/ fr1bep*e1- pv4 nic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the- 0rpvh 1eeexpf /11jhubj*4q received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emg; a/qo4umo(mits an ultrasonic sound wave with frequencyq/4 mug mo;(ao 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tdtfex.r+l;r /uba 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 rfler+ td/r.x;est 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 mead8,td 5fk(j 8 utf2g,o;5nlj m7dwnsy sure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound sfmlo 8d2j d (n58udjnsk;w t,7ytg,5fource?   Hz

  The Doppler effect using ultr)ggs2i wc0 s8pasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. Whepeu1 xro/e 7p,5 4z -tlmypr(yn the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, rt pel4mzr up o1-pye/( x5y,7at 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 20 (1t js9xf.(hwj zd1gt $^{\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) Whatkd:1q 1y0jpqm l- )cftxr y+r- is the angle the 0r +qt1-c:xf-qylkjmr) y1 pdshock 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 n/q3u tf2yl:ive f 7 y--acb:zthe thin atmosphere of a planet where the speed of sound is only about 35 e:fl -b ucfa7vtzy-y in:3/2qm/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.,fnob1f n di1+)gtbc0;my8 1wpbu i 8o Determine the shock wave angle it produces wy01 fmio n) ,;1uin1gbt bcf8dpo 8b+
(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 mj(o (l1mk3 uw$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove na7x)twhx9i.ocvh5h,8 eri , rhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. B) xc95i,t 7,viewhhhor.8 naxy 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 so)sz74rvf .uqq nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed t.7 vq su)rfz4qo work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many q,n )y1qj/x smyqs) -coctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe )g)q ph0og4 cgsymphony. It consists of many plastic pipes of various lengths, which are open on both endsogp)g4 h)g0 cq.
(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 al7dfsd*lf 9 y) person makes a sound close to the threshold of human hearing (0 dB). What wi *d7fdyf)9ls lll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound lev(c7wywjb-d 2a el when an 82-dB sound and an 87-dB sound are heard simultaneouj -wy(c2 db7awsly?    dB

  The sound level 12.0 m from a loudspeaker, p9 (ygtp. *vemmtha+d*laced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiodg(+he.*a9y pmvtm*tns?    W

  A stereo amplifier is rated av7;by mc5/ sygt 150 W output at 1000 Hz. The power output drops by 10 dB at 15 k ;/y m7vbc5ygsHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wekps v78wxddg35d2 kwn2wgm 64em0xw *ar protective devices over their ears. 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.d6w*2d smvdmwe2 n ww7xkg 548p3g0x k0 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 communicati3tfz6t 68kbstb 4n/nc ons systems, 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 t ix.y:mcugsl .dkc2 f* 7-1nmwiwkk00o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long jl., i8 l:l8mgj3iybc between fixed points with a fundamental frequency of 440 Hz and a mass pe j.8glj38:i ,cbmylli r 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 tf,yjq nlt8+;lube filled with water (Fig. 12–3 fq+yn;jl 8t,l5). 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 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 tha/d; *c7s sa/ np6drgmut is open at one end and g a6/d7pu;nmrsd/sc* 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?    $ \times10^{ 2}$ N

A highway overpass was observed id*3 4hi43d ;;c-(abr gmhtj iy+hzic to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in thej). o ena- qw1bw9;e uu)ibzq9mxikj1h 70s)m 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequenk 9jz)eei)n bu;9q 1uswax17 oi ).wj0bq-hmmcy 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. One train is stationary. The conqp( d .zhd0r(rductor on the stationary train hears a 3.0-Hz beat frequency when t.(zqdhr0drp( he other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yoim *a,rai1.*ir1 ajaa u is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (ass *aaa ri1majir*1i.a,ume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the d *3r07f 3yv q -lh2xg0pxaf3yqwvz9cbifference in pitch of the engine noise between approacvvcqgxw *py ya27-3z0 9flf qh3rx03bhing 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.h.+ pl:i+v xml The shorter one is 2.40 m long. How long is the other? p ih+llm v+:x.   m

Two loudspeakers are at opposite ends m18 wm9vez1pvwya mnob 1926aof a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz86 awpvn9vm ybzw11ma1 e2 m9o, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bnq w oc/nww :25+hgwc4eat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from ch n:w5+o2w/qw4wgncthe red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the uqd)*2 t+ agszmoth is flying toward the bat at speed 5 m/s The bat emits at gq *z+s)2uda sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequehhm8 g8 . +hhiiaf9a9ency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms l+ifah 89mh ah.ge98ihong. 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 sig m- vut*if. /wvy+1ntamk0u2l nals 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 oavf1kn/t*.wu m2-u ltvy m0i +f 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 list z oun):l8g7u4kuaqz+ening 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 room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequenugz)u qu+4nkzo 78l a:cies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenda x4yhzhl/c+ 0er 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 made 4hc /+y0xahlz 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 at a frequl6h vn, o:aip2ency of about 1000 H,i hp6ao l2:vnz 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 observer4vi; v n/j)pzo/ nmy(p(-hcd m on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? vh;o4n)pm ndi-cv ((/ mpy /zj   $ \times10^{4 }$ m

  The wake of a speedboat i:gd/i3 s)s 4flci1e. cg+xxe ls 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