What is the evidence that sound travels 7q9 j : pzties)g,z/he-5.tjnmst: qras a wave?

What is the evidence tha -pjf9bzz wnrtqz,+ p*krij :1lk6g06t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attach6eztb6 xg ps 7)7wim11nwy- muing 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 traey -bw 1p17ug)t 6zsw6nmxi7m vels from one cup to the other.

When a sound wave passes from air into water, do you expect :p; olo1u tcc-sm*k t3 owy .lu*0.yucthe frequency or wavelength to change -lc1pku.;cmuy uos3 w.tyo l*t 0:*co?

What evidence can you give that the speed of sound in air does not dependtq+vb.zuh3o(ge-w, 6uw:c 2: mv tn(igj 0v zd signifijb,q::u(o h nuv6zviw dc+-gv te0mw(3z2gt.cantly on frequency?

The voice of a person who has inhaled helium sounds very t iain((fgl m5h.(7oy high-pitched. Why?

How will the air temperature infngqmqh:0 zy+k;r 3h:sv8 w +a a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplituzfeq8:e+p , qjf-ul7jwlv64ade of sounds in var ,-6l 8aqle+ f7wjup:e f4jvqzious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo-ynm.qcb5d9/i in5t2ga 2p ztser together as you move up the fingerboard toward thtz / icb92t5gnin.am-5pq d 2ye bridge?

A noisy truck approa.woun(/ zkax/ ches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency wkxo( z un.//anoise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said 4c4el mqsr-qfwty6.* to be due to “interference in space,” whereas beats can be sai-ms4fq4r6 t. yel*wq cd to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of cy6y2p1 yt9*th g4+th7z jxpl/ n giu+the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer 7pulj1hzty ytpty+64xi 9/ +g2*hcngtogether?

Traditional methods of prote0r u,4mnv jwp*cting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching t0*j rmwnp,u4v he ears?

Consider the two waves shown in Fig. 12–31. Each wavzb0:sfk0kpd/hdm 5e1 e can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–15/:zdp hd0ebks m1kf 08. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in 25ct+,hadmh nthe same direction, wiacdnm, 2h+5ht th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the srgzl 254omg xql/ b9c-ound heard by a person at rest with respect to the source? Is the wavelength or veloqlzx2-bl m4rg/ o9cg 5city changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monit gyo*u n(6;roeor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highesy oo(nre; *6ugt frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lh6u gac) kdvvpv mc 09gj-3jl(t/j0,length of a lake by listening for the echo of her shout reflec)j0lu m-tvv,c a9g 3/pg0(v6kjj hcld ted by a cliff at the far end of 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 shiptolly7901 *yrh/y :otsi ig p* just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in sea:s/ **lg l r7hpoy0y9 oiti1tywater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 0(*yzktcu1g6w8kr wjw+8p sx 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 i)tn9vi;o bzm /k92srv s drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (F;z9s9rk 2no/i b mvtv)ig. 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 frotibn-ht b+62h m the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. Ho-+tth2h6bib n w high is the cliff?    m

  A person, with his ear 6b89 b (duobeaq )ip32nexdft t 1,z5mto the ground, sees a huge stone strike the concrete pavemen,qd9mn5(dt 2ebxa1ue io6 bp)tb38z ft. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rulrg9td l,sgg729.pe c je” for estimating.lsg2 cg,epd7j r9t 9g 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 pathjwcw0q+f:vu5l r.ggg 0 h7 ;in 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 whose in;1 n ldzfjm70xtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95ot9x ,n8db 5 cwmne9n9 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded?n5no ewm9c,9dt8xn b 9 [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with g-grg6qymng se9(1zt8:nm )xfour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What soundyn 16g: g gte qmx9s-rn8zmg)( 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 gc lmline/e: *e coeb3qc i+3-v809svhave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What isnleib98 cc-ol q3e+igv3/ cm: es0ve* 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 in0g2/n r obp:kw normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cwnok0 :br/gp2entered 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 arf) 0urg)vh8 y+mgcr9m ea 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 rbsg 0cbj-9+sk) ux /nA is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspj9 b )s/+brgknx0scu- eaker 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 placed 2.8 m in fron2x:h5 l11p gbu6jh tmnt of a loudspeaker 2n:tujx615 lh1pghbmon 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 difference in sound level of 2.0 dB. What 9akr r87)w kwwis the ra9a rwkk7rw)w 8tio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripl/i7uy vel 5yqnxj4v(5ed, (a) by what factor will the intensity i yx5/(7 uvvej y4lq5inncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq:tjny8w -c +neual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their ijcn: n8 t-wy+entensities?   

  What would be the sound level (in dB) of a sound wave in)o * c)bjn vnvbu)u3c8 air that corresponds to a displacemeoj)ub)vu b8) *3nn ccvnt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soundj,x3 qss2la6,wc )ylwv w 4rk bluc,9, level to seem as loud as a 100-Hz tone that has a 50-dB sound level? 64c2v,r)qkbwwl3, 9ua,lslsxc ,jwy (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detec5f ggld,3ylte 7l+ht0- :wrb ps1kli2 t when the sound level is 30 dB? (See yf25-et 01diwl+hlt sg7lg:p bl 3,rkFig. 12–6.)

  Your auditory system can accommodate a huge range ug m .o.jvkl50+ op)fiof sound levels. What is the ratio of highest to lomkf.+ ulg5jp.iv 0)oowest 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 frequenh6n8zci,pfy uzk)./e cy of 440 Hz. The length of the vibrating portion is 32) k6.hnc8 epzi y,u/zf 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 three audible3x f1 d39ssqnl8.bvw e overtes ldf.3 8 nwbsv1qx93ones 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 blowing across the tos bt (6q2caxukev; *j/p of an empty soda bottle that is 18 cm deep, if you assumed it was avexj(q/2tucbak*; 6 s closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of huq3khd+wlq; * jman hearing (20 Hz to 20 kHz), what would be the range of the lengthsqdl qj*;+3wkh 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 qqz 7pnjy4h8k k +c4u*third harmonic. What will be its fundamental frequency if it is fingered at a length q k+c84kzn7yp u4qh*jof only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above pa vmf99)ekm8 middle C (330 Hz)m pk9)mf9ea 8v.
(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) q0dj i/qtwv4gjl(k-3ro-0d+k - vb xkwhenk00q+4k(r-3vkj wg d it/ dj-ox-qlvb the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 k1w6g benw4-xqt oo .8$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hjl8,yphca +(mp) ; k2 xsyg-rnole be that must be smak ;)-jc8lhr (2gynx+, yp puncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 612re-rx s:j00w /ghmhn6 Hz, but not at any other frequencies in between. (a) Show why this is ar2mx:/ es-h0 rnwgj 0hn 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 botu)y 0lj imi;t9h ends. It resonates at two successive harmonics of freque0 9ji;um)lity ncies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 3q 5*p6j gamgj$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long organ 2d2q 4 ntqnls ogjq(.n wu(fy356mjg4 pipe n5 qjf(mwudosq342gn jl 2n.q 6yt (4gat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5dfw.7g,3)li w fau7 s zocvss g7h.r,7 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. 7sg7,v d7uzf.gws. ah)o,3slrwfi c7 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 ev 8; + 9ywuw,+pso hyjle8xsw.nery 2.0 s when trying to adjust two strings, one o, +j98y +usn;lw h wpex.wy8sof which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequen6c,u*v x i(4cos27v;8xpwfixssabw 1 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,aj 7 w:j7v5swp while another (brand X) operates at an unknown frequency. If neither whistle can be hsp77 wja5jvw :eard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and . /ouybvnb,jp 5tb/ vx+gp. ,u9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of thu,p. g,ovyt p/uj bb.5/xbv+ne string? Explain your reasoning.    Hz

  Two violin strings are -x4 ;edkcx zrn( :z1am31tmmv tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard we k1rmn(-c za dxv1;t:mxz43mhen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicalhzv sdmd04ja; 75. zvf2d h1j cyjs/-w flutes each try to play middle C (262 Hz), but one is at 5.0 dvjsmjzchyh4d w;f-2.a57sd1j /zv0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of+,qfxg d0gpqha /8m /i:ru e2 dep;i)i 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 ber+h//eem8pq)0ig; uix g2fi pqd:a, dat 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.j ka2xe7im4p99 oyp6 *ryjw u lgl0p);80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the op9lp4gwlyjrjyxa 9*;7 moe0up i k)26ther.
(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 suppo3zowf(s mu :-wsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are plufw(3:zmos-w ayed 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 asgcqyx6a (e n2;u3q6dnd 2.76 m in air. How many beats per second will bsx;3uqcey66d2(n a gq e 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 wtp/ hfpf2n i,xkh. gue;)t lk(kf/.::cesv:phen at rest. What frequency do you detect if you move with a speed of nx.k,ple:k:f//vt(h ff2s t.c) hup ei: kgp;30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fre b-n t8xis xq/d,m(9qoquency do you detect if a fire engine whose siren emits at 1550 bqn(s,o 9 8/x-qmtxidHz moves 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 source is moving towack5vg ,5blws; rd you at 15 m/s versus you moving toward it at 15 m/s Are the kv,55sl;bgc w 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 frsg3dn;b/ b-6lg356 sfsc fllals3h/qequency horn. When one is at r-c;bs 6s3ns/lldgla6gs/ f lh3q5 b3fest 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicrv6dj a+gu3cb e, g.xktpr3/ 4 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 rece 3eb.rku t 63gdax/+rcpgjv4,ived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of pmodnq0 pj; drzj)/*7 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected waveq)r d/pd *p7mn ;zjj0o?    $ \times10^{4}$ Hz

  In one of the originalnd*s tq5/m7rt Doppler experiments, 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 trtt mn/r7ds5q *ain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speedsd6 ;s)to s+tsj. bf0zc. Suppose the device emits sound f)6+0st ojds;s cz. tbat 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 frequg ft0 obgkv +jyyda45zrz1jl9 t+7v72ency $2.25 \times10^{ 6}$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 freque kqe:4)n9hkwpncy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at restqkn:h4ekp 9w ),
(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 movingqkx 2g1j 3ov8m on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2rew9 hg92 rqu2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s9h re2qurg2 w9 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 thcerm0 iew -m.9e thin atmosphere of a planet where the speed of sound is only abou wr.m-ecm0 ie9t 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the o 0e:zhpxxfk., cean. Determine the shock wave angle e x.fh0 k,xzp:it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle +t4valz-fmlj 2pbv9z 5cr(+j $/theta$ 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 groun m, pifclz 854c5bszzq(.(ntnf *qaj do3*. nnd 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. za.*ns(z5clo bi qftm f(3*znpnq d45j,n8.c 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,pnk ai58c- p6b000-Hz sound pulses downward 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 tk85a- ibn pp6cime between pulses (in fresh water)?    s

  Approximately how many octaves fvit;yjxrw e(58 w3-ep 8y;igare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer / doam69rd;eq+4 li)ju0odrq og)2yh pipe symphony. It consists of many plastic pipes of various lengths, which are open on both d do4 qqi+ )gj/ro9r2oal;u0 de6)hmyends.
(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 fr 9fxe11wc bx-rom a person makes a sound close to the threshold of human heariw xbcf9 ex-11rng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8*dz aqmei 7-r(3ftm8s(h+qau0t .dc v7-dB sound are hea e(07(q azthsa.3dd8r v+ tcmq *fium-rd simultaneously?    dB

  The sound level 12.0 m from a loudf0bd .zr,gpe/speaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speake 0r/bz e.,gfpdr, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The xwe;p6bcfb* n-+s ite82q 5a ppower output drops by 10 dB at 15 kHz. What is the powerfc8x*tp2 q b6a-bwes5 +inp;e output in watts at 15 kHz?    dB

  Workers around jet airch3n e+s js+i (b/( 5qhltd/tryraft typically wear 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 tha +isn+h3(rl ttd je/5s (yqb/ht 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 systec(3y8ofgp f,thyb4 j(ms, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequw 1l);jmjnrk cdf 78cjcxl; -hlp0,k9ency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between f+ lxvh.rjkz:33nu2 ysixed points with a fundamental frequency of 440 Hz and a mass per unit le+z3r 2 .:yk3vhuls xnjngth 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 set9yo0oe/trw k + into vibration above a vertical open tube filled 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 fo k9/w0orto+ey rk 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 o lx1e+ mww+.cwf mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonancww+cew1 .l+mx e (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was -;aj s0 g ptcpskwq(zc3.s 1j8observed 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 pure4upxf(3s,fm1:l*fpx6 iumg n 7fj(m qe6zgb; 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 freq6nu6 m (7 z1gx4b( :fmfse; lgu,fpxm*jf3piquency 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. Thlxnqv9ungcb v *1(+dkfa .e)6e conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spn1kveqa*fb9cu.6dg v l)n+x( eed of the moving train?   m/s

  The frequency of a steam train whistle as it apsz hz4+n;m 7zyproaches you is 538 Hz. After it passes you, its frequency is m s4zz+7m;hynz easured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by ey81 6nj5c xe*uf ,hiplistening to the difference in pitch of the engine nois8exe5,iyc 6 uh *nfp1je between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pr. i30une r3ysboduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the 0sry3u be. 3inother?    m

Two loudspeakers are at opposite ends of a 6i+wyycib5v-sjt *3h 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 f y5bscj- vy*i +wt63ihrequencies 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 C?

  If the velocity of blood flow in the aorta is norb9+, dfck(qn7x2t+e iv*tfjh mally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directedd hq(etfj fc,n*b2vt7+ + ki9x along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is fly 6 ,7bgcb3chozing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after c67bhz3o bc,g that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound p(asbu zz2zig r :79-hhulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo f9:za zugz7 -isb h(h2rrom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villn7hxo exz47w7ew)w6 aage 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 alpenhor7 ee7axx4nw6 o7wz )whn 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 /arhe:y5 th+l- xq)urlistening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Conside5-x)/rhe r tha y+qul:r a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singive;.sp.mke5m8dq ep. ng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringinq8.m;.dp.smev e 5kp eg 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 earzu(7yw1 wzho0 -+iypz at a frequency of abo y7ozzz0wy- wu(i1+ phut 1000 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(7g hf,o8i ahg observer on the ground hears the sonic boom 1.5 min after7(hgfoi8 ha ,g the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ib)oapt 5 wi-2qtd47gm s 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