What is the evidence that sound travels as a wan lvbecl*q 8ew++9w8wn08t 4mwgj9 ;bbj rq2ive?

What is the evidence that sound l0-qpb1 w0n deis a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stringay:t j 74jrr3ah.l kg 3lh5 djvf8*i(a to the bottor h(4 lv*l.ajj3hr:t7 j 3ay85gakdifms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o uu:vupb7 g/g*r wavelengtg7g * uvb:upu/h to change?

What evidence can you give that the speed of sound l yr tf2stqwhd2d*ye.10bs/. in air does not depend significantl.21hre/sb l.wd f 0*2tdyysqt y on frequency?

The voice of a person gsx/pid /y4o7mrn)ql cs8 0t,who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect tk)s f 3oj(i kf0g i0+ sdb)+r+ s06ewndmb;qcuhe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of u5zn 3zzh7thvx 9vg21sounds in v 9h x5z7ht2n3gvuz1zvarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30):ghr 8j1 xrb5jnz tg34 spaced closer together as you move up the fingerboard toward the bzrj8gxgrhjt :5 14b3n ridge?

A noisy truck approachemya -dg)p h tfnzh7/63s 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 m6h-3h 7 zgmdf nypa/)tore of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen w:*malclf - hk:sn.d4ce in space,” whereas beats can be said to be due to “interfere:cdk* f-sna:hl lm.w4nce in time.” Explain.

In Fig. 12–16, if the freqgo *-csvgliw- st 81-j67bd utuency of the speakers were lowered, would the points D and C (where destructive and constru dsb- oiwg -gj6-8cut ltv7*s1ctive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of pgw; fy7r h)i /keyf)+weople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levrh/ef7kg w)fy)i;yw +els. 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 waves shown in Fig. 12–31. Each wawdrzmk9fb5f46; g7s lve can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explab zlm;kff 94dws6r7g5 in.
(12-31)
(12-18)

Is there a Doppler skm;py1;/ idm edu *rv5wtm+:yhift if the source and observer move in the same direction, with the same veloy*y 1mpw i me;d m+tvkr:/u;d5city? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pgc677pg yms7s erson at rest with respect to7sc77g m 6yspg the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moqdg ;9yp28d-6xmnv k;d5xr irnitor is bx m2p;id vqkrdx6nrgy8 d5-;9 lowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echzqdc(n uye, (4:pee (6o) mmleo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate thzoee,pluy e6(:((md qmcen )4e length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juvzaev)ho+4qpy7h j3:4pexzu lp, .t.st below the waterline. He hears the echo of the sound reflected from the ocean floor dqpht v)o3z 7:z. p,e+ a4le x4juy.pvhirectly 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 indu(9lizst o6g6 5t py/ air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above ad.pnyd y9jxcy j5991c e*,l7t* wv4yv* veyan school of tuna on a foggy day. Without warning, an engine ba *d 4l*ayy95,j.y n* vp1wcte9yexy9dnj vc 7vckfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped froxdkvak*p yj:c9(kj (*u) gjp-m the top of a cliff. The splash it makes when striking the water below is heard-j*9jpak:* kyjd kupx)gv( c( 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground +0ziklrr67f04l ezx* ufu c;fvf.3nf, sees a huge stone strike the concrete pavement. 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 apark. zl +r*zl0i0v6 ex r3f47fuu f;cffnt. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of d 0-04dtlmajtip ,rg)xu z)d g0istance by the “5-second rule” for estimating the distance from a liz40gdg0tl d ,ru j- ta)p)mx0ightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundy3(z ,vmr ;y+ybw107 em0zx p(qrswmtszw-,p 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 lev vhq+wbv8qi ,psxe c3.u(o+x5 el of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sc ebprwb 5:x74ound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? b5r:7 c e4xwpb[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from a8l *fplypd (r5/k ob 1fo*v9dvn airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perso ffl*pr5 bov d*/pd8ylv1(ko9n experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fo,.r jzz-tj)4ty2 uy t)xhe q8hr a CD player- t eh,tqz)jzxy2huytrj8.) 4 it is 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 0(tr.: fivgktan/s3+wr.ilb from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over fiiv kr:.l. n0sat+tb3 rw/ (ga 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 ej-efb n,xecy0 b2g 4g/ardrum 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 Wa c. z4q9t:qkm, 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 loudspeaker connected in tu qmtk z:aqc9.4rn 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 regisowgo0z z xth,6z :h2y/o8nq- stered 130 dB when placed 2.8 m in front of a loudspeakerx/ -now tqos :hz20zhz6g,o8y on 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. W-vo/kr )hd(jp fubt-5 hat is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sp r vo t/uk-dj-fbh)(5ection 11–9.]$\approx$   

  If the amplitude of a sound wave is zwwb/;6p :vg*wefu 2ntripled, (a) by what factor will the intensity increase? Increase :b e *w62w;fnz/ gvwpuby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitud-:5w xlas-ow( y934fxd n nj8egrb .yhes, but one has twice the frequency of the other. What is the ratio of the wwyrn5elayg(ox3 x-jb8. - ds9n :fh4ir intensities?   

  What would be the sound level (in dB) of a sound wave in air that corres3/ rypw:m* )fjsa +4 fodun6ffponds to a displacement amplitude of vibrating air moleculd/ns6 *rw:j+ mayuf4ff3) p ofes of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz twyi6lm in;2e9l6/j sh( tn m1aone that hasisl6 1 t29am(ly6m h/njeniw; a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can j le:yof k5f,8;m nb5pdetect when the sound level is 30 dB? (See Fig. 12–6.)o8nylk5m ;e,fjb: pf 5

  Your auditory system can accommodate a huge range of sound -o14tzz zt8f d.z/a g nv/d1yrlevels. What is the ratio of highest t1 oy1 r-zdz8tz znt//vgf.a4do 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 ou+yjz9z 3tv gqn /o+h 5w(mo,fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension myw53otn m (o h +z/u,zovq9j+gust the string be placed?    N

  An organ pipe is 112 cm long. What arem* z/7tjg;)ksj5zzy76gmoa e the fundamental and first three audible overtones if the pipe is j5)zoz/g e gm77azjyt m;6sk*
(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 frequenc miy lg.k1d0zv*sj6/my would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assuml1 *.m/szvjdmi 06gkyed 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 wi9 ykuf(:tw7 ejth open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of p9t we yu7(kf:jipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5(p;ywtr- cxs5 o3ty *h40 Hz as its third harmonic. What will be its fundamental frequenccwth*yp(53y or st-x;y if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar s )2y2c bsqb pdlt8i2h0tring is 0.73 m long and is tuned to play E above middle C (330 Hz)p22si2btdy h0 8) cqlb.
(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 orr kww8i jg8i9(gan pipe that emits middle C (262 Hz) when the t(9jiiwr 8gw8 kemperature 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 a;bffz55wa(78ixb hpie9tld kq .t72rpr(*t ot 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 hqwsz3 1mgfo rc7x8 55mole be that must be uncov 5m1 xwqfc3morgz857 sered 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 resonat+ lyum 6:r thhh:ltf2a*k7y1 je at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pi mhk7f1:ry2jy:lh al6 +tu*thpe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates asy3ul uee v** .uq70mqt two successive harmonic0*el .*7uuqeqv3 umy ss of frequencies 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 m6i w1s;gfzs6 $^{\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. gp-d :mbwzip7lk */b-qtpje q9(w6 qa -jud7 organ pipe at-quj q b/w(zapm-k.d7:6-7* jgb d9iplwpetq 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longq pr lqb1v8hx5s3 bt:omu(04v. 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. What is the relationship ox vrq(ls0b8o :3u 5tq4bmvhp1f 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 c*9zrg 1 m/rlrg3)8cqy1fulxum 4 s.n when trying to adjust two strings, one of which is sounding 440 Hz. How far off i1q sgrccz4y8xlgn l f*u1mr).r/3 9mu n frequency is the other string? ±    Hz

  What is the beat frequency if middle C (a ow+j/5g kj3temj32vt40m kl 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 y)kzum4, y 5drzd2acq:j- :e foperates at 23.5 kHz, while another (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 daz4j rze-cku)y5y 2q:m,:dfplayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a z-dii*hf z5f- 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tun* zzdhf-ii5-fing 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 i;ao;iz(ue /8shd itz/n one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playeddoe/ (ia h;/ztz; ius8 together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hslg) 3bv-80 s pseq1ideard if two identical flutes each try to play middle C (262 Hz), but one is dq0 8slbvp) 3-eisg1 sat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, andtjc ; i+mnc0s; C. Fork B has a frequency of 441 Hz; when A and B are soundedc;+ i sjmtn;0c together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are ns8a(*4sjh xv1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. nx js4ah *v8(s
(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, + k2 o.pxf;yqe0rtqt. but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is y.qxt fk p;.+qoter02 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 2.6ulq822 cuhe2bc;; lcpxp ;k(o4 m and 2.76 m in air. How many beats per s qp 2c ;cu8xbl; ;2loep2kc(uhecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 155 tic;nje) 7,xh0 Hz when at rest. What frequency do you detect if you move with a speed of 3;)7,nht exc ij0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine wmt1 vg 5*ntqz am 8sy:i;;otl)hose siren emits at 1550 Hz moves at a speed of 32 : ;1*mv gan) ilmtotsy; z85tqm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a h.*l 2 h;5i0etztb feq2000-Hz source is moving toward you at 15 m/s versus you movingq5i*h zflb2 t.te0h;e 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 equc a;pqc85jid t6e)8d)tk( ozvipped with the same single frequency horn. When one is at rest and the other is moving toward the first ava kt5qt()cddc 8e;p8)o6ij zt 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 o4 hsr8ol0q e x 39rhwzh6g4b) ui8:tuaut ultrasonic sound waves at 50.0 kHz and receives them returned from an object movi 06839hq4xrbslu a:8)weruhi o 4 tghzng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/1bp yex 8r+5ebrj /gh zxwj:3,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 wav+p: j8r/w ,z ybj3rgxx h1e5ebe?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentt( pt8niud9rl secmt*p58- r:y*qw o/s, 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 statio/rpnr tdcq *s5o(8tt8 pew*lu:myi 9- n. 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 3/eyls*fcc )s to measure blood-flow speeds. Suppose the devil)f ss yec3/*cce emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulz8rp2fif)m2gyjg 0kbd:7 v7nov .6tgtrasonic 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. When the wind velocity is 12 vbs5d .ioou2 ,movuib5s., d2 o/s from the north, 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 spt d 2udeh:rru/d4dv4;eed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where thdq.9w,;me xb re speed of sound is 310 m/s (a) What is the angle the shock wave merw.9;m,x d qbakes 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 th 1o7ozn.6)ek hk6va-1dm pyr qq8 am79zgrk3ye speed of sound is only about1ag.zq km y 3zqo678 pd)ayk79hr-vke1onmr6 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 mwzm /vkl f,,-y/s strikes the ocean. Determine the shock wave angle it produzw,, mfkl- yv/ces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 4) karoen /g7o$/theta$ 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 e0 8t7wjn b :q+9 89x eyqz/oaktanpko1*t1ozrxactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the soa0wpz zjy179aq+88 9k/ t1noeo k*tr :xbtonqnic 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 socs5nwl 5 tcgx-)vu, /onar 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 uwc-t,cs x/nolv) 55g 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 audk3qjvcvbo xt9n(uwz. 7 d4, msp**m2kible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display callexuz h4kgzg.:s9klr .6 d a sewer pipe symphony. It consists of many plasticulzz:g g kh9k64r. x.s pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold o c:c)xe6rcl8x k0g dm;g4.rgkf human 4c); g:68xlkcgxrerk .gdc0m hearing (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 87-dB sound are he6 ve6 v.jyswtx,,kj d:ard simultaneously? ,:wk t y6sj.dj6 ,vevx   dB

  The sound level 12.0 m from a loudspeaker, pl gwtzfsd134;( 89ryh ung+nbtaced in the open, is 105 dB. What is the acoustic power otnwu 3tsr9;h+g (bfng1 4zy 8dutput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at/ ry* ;fq9bhohwxi3y r(r6+o o 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power ou6h/f+oy*;w x (o9iyr3rbqro htput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devj,u vpx clk0krs/:l*(ices 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 u,cskpv lj ( /l*x0rk:an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,7nm:ilh9 n 5gzqtsbjvj1 a+kwh18)h+ 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 f8 i: p;arqq6sjrequency 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 fixed pointss zcyeri7 7q.c6 97;x8 segmv)t dqm,x with a fundamental frequency of 440 Hz and a7iydz q; 7,xsvrgm9xe c.q)86mc7 e ts mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical t e5xz4g0ea 1vopen tube filled with water za10e5gv4 e tx(Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from 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 that is open at one ende6 -7hbo)ywy s and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its f-7howyey)s6 bundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatej m)/f (k3layq 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 the 500–1 069 irljeg**fi)ocyo000-Hz range coming from two sources. The sound is loudest )r0if6yo* c g*joi le9at 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.5a mn50o8 y c ygf;ws8hz4u0fd One train is stationary. The conductor on the stat yy84cg z fh5ad0w8 m5nus;of0ionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After ip(k gq0 9xkl8q hw,fy+t passes you, its f8+(k,lf90whqygk qpxrequency 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 bygl4jqc,1f no f*.cy5m listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it g, nfc foc5 1*lyq.jmg4oes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hy kww 4 *osbaxts*d9;,z. The shorter one is 2.40 m long. *w, ;as94to x*dkswybHow long is the other?    m

Two loudspeakers are at opposite ends of a dnk*+35mt ewq qbs07i 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 bq3d7wt*b5siq e0 +k mny 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 0zlx i9q)j(7g lus7n-i.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 trsiljgn-zl 9()u 7xiq 7avel 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 goee5 2pg67jjiuu.,tngf8 y2is flying 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 detecte628g ygjen,u7.g iu fo5j2etpd by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth8d+ wz vhwblw8*o;erp61i ns ,. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lon*i o , dlw1w;rv8+esw8zbp6 hng. 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.kj(z/k 4w/;df pvcdq 7 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds ar/(wd7jdkk vpfc qz ;/4e less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the preseigb yopw-dw,zpu2;m 4o3 m)4u nce 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 frequen o;4-pyd)b pzmmw wuu 2o34ig,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 lo3hhbv 18fw dmd/ zt+)wng, 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, ringingw/m1 vb h+8thddfw z3) 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 0s vv6pya pt(-ij k2,ymy0b /xhuman ear at a frequency of about 1000 /0 j-vt,kyxy a(2b s0p6ivmpyHz 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 6(cm6*5q0zljmhs keethe ground hears the sonic boom 1.5 q6 e hm*kces60(5l zmjmin after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15brh,g1;2s xc6mwj5xd y ssc*yld:g*x7 27hgo $^{\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