What is the evidence that souoa,lyvcw7a3 4nd travels as a wave?

What is the evidence that sounp8g:ldj,x1q, xdd h8c d is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a s5ktdawzm4-41 nbf+ba tring to the bottoms of two paper cups. When the string is stretched and a 4w-a 4dntkzm +ab51f bchild speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freque6tn 6wkv5 pk8v*ux.qlncy or wavelength to chan 6p5 xlt*nuk.v8kvwq6 ge?

What evidence can you give that the speed of ro/c jwsss,bb+8h -t7 sound in air does not depend significantly-sb7 t,sohwr8+ csjb/ on frequency?

The voice of a person who has inhaled helium sounds v7h71 uemt3 rhzery high-pitched. Why?

How will the air temperature in a room affecttkk0nt, 1;cqn the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the qry jp7*7(u7 vqlkax; amplitude of sounds in various frequency ranges. (An example is ( 7uklqr*av 7yxj7p;q a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clx8of3n) 2)y -jchqi jcoser together as you move up the fingerboard toxfi3j2c -nh qc8) oyj)ward the bridge?

A noisy truck approaches you from bek:y xb+rqdb*b ne,7g dbu862 pg)ujl- hind 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 noise. Explain. [Hint: See Section 11–15 on di)6u kbbg*82 +e:yg7xu q-jdbbd,prlnffraction.]

Standing waves can be said to be due to “interference in space,” wherd6 z4jio;kwy ,eas beats can ijy4;z6k wd,o be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the rp,o vr0(ftxl pq:f2c7 duj0-points D and C (where destructive and constructive interference occur) move fartc(p u-2 l0: pj7r ,qxdovft0rfher apart or closer together?

Traditional methods olezglh 60 zz-fqa:+8lf protecting 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, headphonesl +ql08zhlzf-e:g6a z 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 waves shown in Fig. 12–31. Each wave cany/ w.akb;0qw0hsn fmclro/5* be thought 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), /bk* qh;0ns0/5. yoarc fwl mware the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sour6 x)xxx zh(9poce and observer move in the same direction, with the same velocity? Exx69) (zophx xxplain.

If a wind is blowing, will this alter the frequency of the sound hea qgz -t1mx6a/ecjo 8r,rd by a person at rest with respect to the source? Is the wavelength or ve6x 81ezj-m ao/trq,cglocity changed?

Figure 12–32 shows various positions of a child in motzb5 zqmcw8)d *ion on a swing. A monitor i8*wzb)5q mzdc s 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 reasoning.

  A hiker determines the length of a lake by listeu)g;f*tf ue: yning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 ;:*fe)utf uyg s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below thd.w r0nqrll)9 e waterline. He hears the echo of the sound reflected from the ocean floor diren q0)9r.l rdwlctly 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 wavelengths in air at 8q-ldsc f k9,75n burp20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schoolqlaq 1*j)a8nmy:d*hv of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfiren)dmyjahl*q1a 8q * v: is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top ofc e*vnfkcj4r6aq: 0 b) a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thk)c: 6 anrj*b0 vfqec4e cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr85n*dega o eb 2f7j4qbete pavement. A moment later two sounds are heard from the impact: one travels in tho287nba 4ge*db ejf5qe 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 l vt2 ox83l3w4: 3lpzs.2 -8uvg cku1fyetv plby the “5-second rule” for estio2vll 438 f1ul3scvetz3py.uk :2v8x tgw p- lmating 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 dBismq* ahz :abd*n +8.v?    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 irnyqj9 th7er,nn.rpxyv,++z1z c6 3lzl 30t m s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousjpd g 0t7mj3+mv6j:xvly at a certain place, what will be thegj 3 6+0 x:j7mtdvjmpv sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance yu-4hp. u z0gim5ai.p from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience ihy.z m i5upp0u4agi-.f the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said tca kc1hrasppf+ 2),f1o have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB.)kc1sfp+ a,r 1 ap2hfc 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 power549hfim*jc/m f z d*gp output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered fd4g9*hfmiz/* 5jmcp 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 eardrums 7pz90 )lx 4xw8j,jqte1jt ut 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 14n8d8q zwr zwmore modest amplifier B is rated at 40 W. (a) Estimate the sound level in de 1zdqr4wwn8z8 cibels 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 dB met .uzhy9jy;f8b er registered 130 dB when placed 2.8 m in front of a loudspeaker on the sbu 8 fzy;9y.jhtage.
(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 detecaa v) f4vbwu5c+eg +g6t a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lev+a+cgg)5auvw6b4e f vels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by 3b,m rqdky 78st8v0au what factor will the intensity increase? Increase by a factor of t8var dy8q0,3 7 bkmus   (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dispce ofxul + hnt+1*9:zmlacement amplitudes, but one has twice the frequency of the other. What is the ratio of their iz:*ch+ tulx9 +fo me1nntensities?   

  What would be the sound level (ly4pd+mfo7m iw+m m8 -in dB) of a sound wave in air that corresponds to a displacement amplitude of vibratf m7+8 dml-w mpymi4o+ing air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to 3*3yw ecrrdyacx2ka e4t2 ;c3seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12a k 2c*yx wc cr;d2343ye3tear–6.)    dB

What are the lowest and highest frequencies tocgw+;w*f ,sbix vx// hat an ear can detect when the sound level is 30 dB? (S+sg/f oi,*xbcw;v xw/ee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l:*vjlci +u+zbevels. What is the ratio of highest to loweu:c+b*l +jzvist 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 frequen1.z qhvue m4yl+n w-(ag w)bc n8*1kqjcy of 440 Hz. The length of the vibra(j.ngwk41 vc -yle8*an 1whq) qm+buzting portion is 32 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 am/ y)3ni *z7g9htq mdqre the fundamental and first three audible overi/m9zq7g* n) qydht3mtones 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 youc0ror5 ;us gc,4*87xdrekb6 /ynt p gi expect from blowing across the top of an empty6t8sgo/xdp,n7 0e4 r bu rrk;* gcc5yi soda bottle that 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 pipnhdfben3f3 ;awj-o 7r . mq:4te organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipeso3;dnafj4q-r37nhmb e t.f:w required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 54 es1n0.,euej p yfnz0+y.frh90 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengthne 91f+p0.sey 0 fynrz hj,.eu of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abov4ztf /)y,k0dmhbn m9qe middle C (3dy9 /0 z 4fmh),tqkbmn30 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 open0.2v4s 6fhtjgdowk w23-zxn j5go +ni organ pipe that emits middle C (262 Hz) when the temperature is 21 jnogd2o3i-x kz45.f gwh+n2jt vs w 06$^{\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 a b,f 0eg(o2rkmguzma,ue6 7 z+t 5z*wlt 20 $^{\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 hole be t gk1ijrdpzksx6y4zg(9+1ec . hat must be uncovered to play D above middle k jy6p(gk9d z g.1+ez crisx41C 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 8zp/odw/wx2 g resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thpd2zwog/8x w/ is 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 1.8:.ra uz+b, rnjf/jp/m 0 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 H jjz:u,r//nm.a+ fp rbz. 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 r3p3 xw5n xkv,$^{\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 ork d,at62: h/a: ht7k-jbq6umnhsg o 9ue5*lbtgan pipe at/kt*,a6 h2-u7:hbnh sku blaemq5tdj96 og:t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim8d :pcy3u /jddswe-sv4ug(.v ately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in th- 4 e8d:3(uys pwujvcgs dd.v/e 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adju8tc7x, j9ujnc 7 dqj,zhtq,a 2st two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±,jdu2j,j, x7q7zqtcta cnh 89    Hz

  What is the beat frequency if middl8 elb8evy)0guqi s0 3de 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 anothedvag/ 7w m7d9ar (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are play9wd ad7/g7vamed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s4q;/dp bpx /ltj 3gcpm9 ki32r when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hji9gpcd2t/p x;m pr3 q4klb/ 3z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension ina6ze9 ae2lx g9w/xtq- one string qxla99 ex /a6g-et2z wis then decreased 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 iyoc 4qx(-u.oeuqk 9y1c4 8jojdentical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0y qj4yx. jq kec4 uu1oo-9o8(c $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whenjq e4sikfx 9bem2ms(+j,i:m: 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 frequencijfk(qes:xm, e s +mbi 294:mjies 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 one speaker ac8dfpfs1ht*// i 7t n4w0*tiaf9w ruend 3.50*ii 0/w t f1e4tthsfwca7n/dfp8u9*r m from 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 vx.s q6wfk,ijy9qn oqji. +-l +ibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132ilxik, y.qfjo-j++qn9qs. 6w Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many9 du*ac((2qw r 4tedwk beats per second will be heard? (Assumec9wwd(u4 td2qarek(* T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’so n*.3vzvhqwh2bv/tlk(n/6 p siren is 1550 Hz when at rest. What frequency do you detecnvvt//ohl (b*h w36z.pv qk2nt if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fi/:z yn5zkfg-ah3. bnb re engine whose siren emits at 1550 Hz mov n: f5/hzzgbb3.y-a knes at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift inyq.3m 0nhnrlgv lsq/b.4*f n3 frequency if a 2000-Hz source is moving toward you at 15 m/s vernlf0* n q 3.r3nvbgm. y4qlhs/sus you 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 horn. When ocn0xg o (l(nn :3l *tngcl3k)/ yd)yozne 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? Assume T = 20 c 0 l /nnd)( n o()l*n3ogytcy3k:xgzl$^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz jt:k 4 vnh bfg11k*90( wejekh:muy6land receives them returned from an object moving directly away from*: kv16gjf:4ehhk ulwb0j(1km 9e nty 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/s As it flies, the bat emits an rp7 / ,yl*oxrha1qh u4ultrasonic syola *xrq,4u 7hph1 /round wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuprxjqy n1/0xune -; 0/;t 6 sydkc)shvba was played on a moving flat train car at a frequency of 75 Hz, and a second identi k ;eycuny1/0 6snq rs-0/; x)jhxvdptcal 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 ulb 8()xdcv7 ouatrasound waves to measure 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 soun8 x(dv o7bacu)d source?   Hz

  The Doppler effect using ultrasonic waves of frequenl j-nwq20h.f.)shm hncy $2.25 \times10^{ 6}$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 ev b;- )n:jn:oo 5kgdsof frequency 570 Hz. When the wind velocity is 12 m/s from the north,b:goon: d jkes -5n;v) what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed a+46n1d u/4 lbhdf,umoh+ru4h)o / cjgivew;ft 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) k/0:/bsd ufznue6.o 5rp4t b5. cllcjWhat is the angle the shock wave0tceks5ro 4l/ c.5.bj/ 6:pu ul bzdnf 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 atmosphere of a planet where the speed of iev0 iz9 ij96xsound is only about 35 m/s j9izi9xv06e i
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine th3+zfp:eddgkz 3j p gt8sv ,39me shock wave angle it prodj z vz+mf dk83te:3ppdg9s g3,uces
(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 zptz* e:vd))bbun- 7e$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pl/5 yxp z9sd ukv)vl-c2ane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has lcup)d 2/vs5xyv9z k-traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward frott h0q9 hc-5wgpeftj0w v7:o: m the bottom of the boat, and then detects echoes. If the maximujt5 qhe9 7t:c:-0 opgwtwfh0 vm depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangei8kdsy3t2+74wi2pl(dd xou x ? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy mq6c w0 y-bzii66ekc-uic; t.mphony. It consists of many plastic pipes of various lengcc6i6;w -kiz.6uytmq 0bic -eths, 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 mcp7, wnm *chwepl6co/)0 b 5im from a person makes a sound close to the threshold of human hearing (0 dB). What will pm5ch*ipc)e/w, mb c 67o0lwnbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-xgpnrt)/dbpq 2v 94 kz)8ml;tdB sound are heard vbz t9dp4q2tmx8 / l;nkg)r p)simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thehyz/b wqasot/1x/9i:r g 3( vw open, is 105 dB. What is the acousti/aro1yq/zw wi9 (sth: bv/g 3xc power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output x1mb(,ynv et(pas/; r/) z lxbat 1000 Hz. The power output drops by 10 dB at 15 )tp,z(mn(vxe/ sbby 1/l rax;kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircrafr- b)u78 kj0bwjvab(c1b 2xgit 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 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 airplair 7bba20vuxj)1k 8bj-b( g wcne engine?    W

  In audio and communications skt+te cp2 v6z*ystems, 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 fip6o,p jyn(tlc22v-l mo rs) f90h7oi requency 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 loxoy7( n- u;aawng between fixed points with a fundamental frequency of 440 Hz and a mass per unit length ;wa7x yn-u o(aof $6.1 \times10^{-4 }$ 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 setqya l)0id;2-fffmd g ) into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slod 0ilfdafyg-2fq;m)) wly. 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 xj (-)rsha(xz9e , ltxthat is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resoxhx(ea 9,j ts)lzx-r (nance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate ad.v9e 2 dsegct c21mi;ipsl- 1s 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 the 500–1000-Hz range comif.3z 4rogtah+ng from two sources. The sound is loudes4raot.z h+3gf t at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stvss+2h vwld/7e ci0 rs-+nij/ationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movi 2nsdchi/ +0 j/iwe+s-sv7v lrng train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H:zvu+g -*)c foyucr *vym b*m3 88kbzlz. After it pasm uvm3c8)o y c vbl:rkg*8zz* buy+*f-ses you, its frequency is measured 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 listening to the dh28zh1 aeq3maifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frmza138hh qe a2equency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togethe.:suh 4 hy/gqnr, produce a beat frequency of 11 Hz. The shorte nhh.uq/4gy:s r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposizk:o(l m 6*/oye3cj oste ends of 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 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 yo3*lj :z (m/scoo6ek 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 uz+pid r uuc8d 6q5)(vis normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel wi)d(ci6uru +vd8 zp5 quth 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 itj)2t) +urvxs s flying toward the bat at speed 5 m/s The bat emits a sound wavx+)jur2st )tve 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 h 6.7 rxfzy4taw8wf/ idigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the d8wf 4/aw6 i y7.ztxfrbat 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 sig72p *s5ugrldjn 518fn-xpeg dnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called 7fr n -gl5dxe2j5 d 1nps8up*gthe F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the potci+8o78b4 kdaaghy4t- e2w resence 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, an48otb 8 iyakc d egwha2+7ot-4d 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 “sig55k+9kcvhy,hpoq+g5itt r,nging 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, ringing sound. For a 90-cm-long rod, tri hhktog+ +559 kqy g5,,vpc
(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 4dse r4/aoun ;afua5:of hearing for the human ear at a frequency of about nau4s;f 4o a5u/eard: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 observer on the ground hears the sonic bo u:n kj,ja+s3y zse9yt8d)6ixe+ zk6g om 1.5 min after the plane ne: xy98 j6 za3idtkue6+js) sgzky+, passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo* r4(25sf fbpvck5wa2inp(f7dvhw b( at is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h