What is the evidence thal cu54f7fgqt89i4 qom t sound travels as a wave?

What is the evidence that sound is a foju/tytdu4n. 24j vot, rm of energy?

Children sometimes pla/g v b .2jj- pf14ektjkr)+q97aoz i1nyee;mg y with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be he k/re 2 j1-4jipe; 1anzj .9)gt7egvf yobmk+qard 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 intol0vbsw3, mtd .w cu;7p water, do you expect the frequency or wavelength toltwpcv ,0d3s7b m ;u.w change?

What evidence can you give that the speed of sound in air does not depend signkrmv-e/:7k d; m lx2fvificantly okk;l:/ 72revm-m dvfxn frequency?

The voice of a person who has inhaled helymg)xxni 9v86 k) tc;,w w6hxjium sounds very high-pitched. Why?

How will the air temperatufl3b35jk darp0agi1 ,h w(ru+re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of p yxd,9:lv il k kd.yvj+h9x/7sounds in various frequency ranges. (Ak .l7v/i+d xyvjdy : ,l9px9hkn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a. x+n-3k1ua w*oo/ qozal/ztns you move up the fingerox- kw.oa1nout3a +nl/z*/ qzboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hh;i+g) xr v3obz(;tgsear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequi )(s;rg;og zvx+h3tbency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b9k )g*nnr/ agpe said to be due to “interference in space,” whereas beats can be said to be due to “intn rpg9)ngk /*aerference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would tot l+.bkko fz+j87 d2the points D and C (where destructive and constructive interference occur) move bf oz2td+jkt k8o .+l7farther apart or closer together?

Traditional methods of protecting the h2) beo*dnhl t0 g*bqo,earing 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, he hbq,n*t*)gl2e0bdoo adphones 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 shownq+i3-i jqisq2 in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly differe+is-2 jqiiqq 3nt frequencies, as in Fig. 12–18. 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 the same direu4i x2r/) eyb:dld.dkqc9)bj ction, with the same velocidbd/) d.cxqbr uk)2j 4ilye9:ty? Explain.

If a wind is blowing, will this alter the frequency of the sound h/y,w 7f /la2ok:ne beneard by a person at rest with respect to the source? Is the wavelength or velocity chk/:b fw/ 2onlae7ne, yanged?

Figure 12–32 shows vq85t6lk v tz s0aht/1yq1ix 0narious positions of a child in motion on a swing. A monitor is blowing a whistle inqt8hn/51zqvt kyl0 s ax6 0it1 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 bd4ct6s/-ci 43, bzmgzg oq3 +h2us fojy listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the b-gso4zih3c,m dz43ug/q+t 6f2cjo secho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wats +r4,vvhpc 0yerline. 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 seawater is 1560 m/s (Table 12–1) and does not vary significantlycv04y,p hv s+r with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in azvie fo 9kyk0trbb1f40;4 s w+ir 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 jdph a6ocv-8q6( rpw7 just above a school of tuna on a foggy day. Without warninpa86- (cd7jworpq h6 vg, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cl 2q4hkq/ 3l0bt;fgpoood( p- miff. The splash it makes when striking the water below is heard 3.5 s later. How high is the 0o-2qo(4p tmpodgfkh;lq b3/cliff?    m

  A person, with his ear to the ground, sees a huge stonw gs16g8jdt.cxz(yo( e strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the conc1o8w(jcxgyts.d(g 6 zrete, 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 dis yn0o 9e-2r4dxfs g9zwtance by the “5-second rule” for estimating the distance from a lightning strike if the 40fde wrs9 -oxz 2yn9gtemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB/h7r1qn 0y7 mrxa9. kmiewog/?    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 who9ne- 02kf(5(canwsl p qjlas-se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelmu;dv/biue5 *7ueh- e of 95 dB when fired simultaneously at a certain place, what will be the soundubhme v 5e;7u-/ei*d u level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fo m d3apwt9(txxt5fie0t a)m2w;3 5 isjur equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pet5t0; fw3s2a am)9x3mp5 xdiiet(jt wrson 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 of2 pv)+mldf1ni-ms w4 b 58 dB, whereas for absdmn4l1 vi)2+pf w- m CD player 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 powel4(;d :),3bpw hucsz ojw oyqqcz0 +a.r output of sound from a person speaking in normal conversation. Use Tab lqz0.uas;w(b ycho3c od4+ :j)qz,wple 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eard 3.7zd-,obd( kcgat/vg)usy jrum 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 raq.ce*onl9g( cs05yrq2cerj3 / f yy4eted 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 fr4(0eyjny.fsrecr /lq * cy53o qe9c2gom a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 db)g c,k( cv0pel +cicybjt*q:34il*a B when placed 2.8 m in front of a loudspeaker on :(i* ,bc3pl)0cv l+taykb4 ic eqc*jgthe 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 levej5 : ns9v+j*ecoic0w hl of 2.0 dB. What is the ratio of the amplitudes of 0nwjc ohi:sj *+v95ectwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by1k,ps p vll8* o4vhpk,hy 7pp* what factor will the intensity increase? Incpvk1ylps h 4,hokp7**l8,p pvrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have e:r7crmcwxo j5p1h9(s,t rk0 xqual displacement amplitudes, but one has twice the frequenc:s7mc1chr 9xr rptkjw,o (x05y of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cr: f/xeuo (4sfe xd4x9orresponds to a dispf/o:dse(f94u4e xrxxlacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lo//drrhl3:brk3e c 4 5zoq ko8jud as a 100-Hz tone that has a 50-dB sound level? (See Fic58reoo/3bkhrrz kljq4: / d3g. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deteco1ffd7 la0 (5pez lk4kt when the sound 1kalpo dkfe l(05zf4 7level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accomtlo1 hbre-n.3 modate a huge range of sound levels. What is the ratio ornl bh3-.e1t of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental fr9,v h vuf 5g0sk+qef.f.csu 4oequency of 440 Hz. The length of the vibrating pvushfc f 45 k gv0e..9uso+q,fortion 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 are the fundamenksdxf9l; +zl.jzy 94jtal and first three audible overtones if the pizy94 d j9f+xl; .sljzkpe 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 top of an w z.5nc* * +r:ajgd8(rw)wobsvj3apj empty soda bottle that is 18 cm deep, if you assumeb.+jrw j c oa da)z (swg8:r3nwp*v*j5d 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 ph8e:fitgl* ), 3 :wa4tb ;jjecfnw(d zug 6w0nipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the ln(dzwb 8jiaw*4f egjw6e c)t; tnuh3f0:, g:lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmoniccv7i:y0wy 7ud5 xbj,1qt g6 gz. What will be its fundamental frequency if 0xvty7 1iuj:7wzdqg b, 65ycg it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middleck ;7 k:r0fcob:bw8 rojg4fj: C jo:k w8: :rrc7kbgj0 cb4;fof (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (2sox q7;jb4d+a 62 Hz) when th+jq ax7;s4odbe 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 201i+0q8 zfrslzlcs. yq.mm19h zf0yz5 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece tshv2pj1d ,518csbrz)s5 r uoof the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz?, jspr5or1 ct2bsz1h8s5)vd u    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 resonao)36)/yluh fv wak2y 9xso 1dite at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betweeh1 2x 6df/k9uv3a )ow)isolyyn. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It r:hexobprh - ulo y9x fw-2*5x2j eld5:esonates at two successb xe*:df25 x-w poohxj:eh u2 l-9y5rlive harmonics 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 g/+5gvxy5o+epjf u ml 0i2u yt -m2qr)$^{\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 r2j(f;qbnnj g 4ange for a 2.14-m-long organ p( 2 ;4nqgnjjbfipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelymilzwvo/j8 ,2 cfk u.54sus;g7 jznj) 2.5 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.znuc gfms2 w)jz8.57 kiuo/j, vj s;4l 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 adjust tw q4 k.twfj 4.a8bsav(vo strings, one of fv .4(jkw. s8t4avqabwhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlexuh qkf n:u uoc36bvx9c* v/(0m9)vhj 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 oper:;84x +ir9for tykgpoates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whi9 t rkorfy8gp;:iox+ 4stle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with */n j1vpm/5ywgxop/ p a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz v5oppym/jwgn/ px*1/ tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to 1f:d8.hd oo f,htdvps5c 1+obthe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be of.v o1h8h+d dt:s b 1ofdc5,pthe beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluscx 99e 2(mqlztes each try to play middle C (262 Hz), but one is at 5.0°C and the other as 9qzc9e2m(x lt 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f8 m++vmng:1 tphb e)gmrequency of 441 Hz; when A and B are sounded together, a beat frequemh+gb8mpt em+)v :n1g ncy 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 1.80 m apart. A person stands 3.00 m from one speakero*:xfuv.tye til m +,8 and 3.50 m from the other. t,yu ieo. lx+:tm*f8v
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tucoln(x sv -n-ng4 gl ;*vcu8cd-4j x0rner hears -glc-cvcxd oxnn4 vn(4*8u0 rs-lj; gthree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m andr on 0j) 7(u;oyv.ktmm 2.76 m in air. How many beats per second will be heard? (Assume T = ;vro.( tu jn0 km)moy720 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when ahkntgn 5k pr+dj s:au7;t- g8(t rest. What frpktnagd(kh-sn j:;u+t 78gr 5equency do you detect 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 fire engine whose sire50nwa 7qe9gex n emits at 15ax ne7wqe590g 50 Hz 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 moviz63 )nrxe,e5 2z kwvcvng toward you at 15 m/s versus you moving toward it azev5 x2zv )6,wcnkr3et 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 :dkve:c )t6m)ao1*m wgh w -mswith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is tmso-eamw vh*k:d)6)cm :w1g the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and rece2 8em 0;2arj hcj )uvy3ohez2iives them returned from an object moving directly away from it at 25 m/s What is the ror)h 8m32ju2jie 0; he2vzycaeceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speedvp/9:- kst4ytmo+qxkj l:s o3 of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequenj9s:+y :oq3/ stopxkmk-l v4tcy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experi - l6gmwry/;pwments, 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 train car approached the station at a speed of 106m;wgwpl/r y- m/s ?   Hz

  A Doppler flow meter usj; j8fix8zwm+es ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue imxfwjj 8+;z 8is 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 wavef9emc(wunox)4eq p *qao0y ::s of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits r h/ddkh- ;;hrsound of frequency 570 Hz. When the wind velocity is 12 m/s from the nortr;; k rdh-/dhhh, 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 mo(/jz. 0if jj:syuspf 5ving 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 Ma;w.wl+)h, a 4szk7bzpvf4 bygch 2.3 where the speed of sound is 310 m/s (a) What is the angle theh4f7w.s zkl, y)pbv w ;az+gb4 shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosph7-b t8r(exttsiem1 c *ere of a planet where the speed of sound is onltcmb-1x7(e* sri 8 ttey about 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 strike:-v li s73.vrsp-btff s the ocean. Determine the shock wave angle i tvifr- 7 vb:slf3s-p.t 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 v.hbab 8(i 22wbovl 3p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planh.6nuhe2i4 + 9ttdy8 a rvum2pe exactly 1.5 km above the ground flying faster than the suye8m4 6th2ah29i.r+dun v p tpeed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses do21 +h+wqbyl 1m9mcnzg wnward 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 time between p1+ 1bmghnl+ m2wy9 qzculses (in fresh water)?    s

  Approximately how many octaves are there icy9: zbq4gd zr/ouox ) .w6nj;n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphotc++q-,mrcpmc 1 c go3t9a.uwny. It consists of many plastic pipes of various lengths,+-,u3mogwcmct1c+t9r cq ap . 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 t 5l pzs7okula41zh y.6de:v :threshold of human hearing (0 dB). What yuo:z. zlde4va57tp:16kl sh 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 soungrjydw :,pkt1r y6 *kk ,5y;mwd are heard simultaneouslyd *r1kr 5,k wtym:p,yy;wj k6g?    dB

  The sound level 12.0 m from a loudspeak2 ;h( md6wwnlmer, placed in the open, is 105 dB. What is the acoustic power(2 dmwwhmln 6; output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rateiyv kdk- 6p.3gap(2c3 nmqpjm,,:cb bd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powen 2cpy3 qpmg3j.(,6cmp:,v k- ibkd abr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prot e53s7wn0v1gn kjqo)lma wk7+ective devices over their ears. Assume that the sound level of a jet airplane engine, at a dg7e0j m w snka)kov+ 71qnw5l3istance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications i4)g)rglv ) mksystems, 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 frequenc nhn c+bi.,0kz7k.ntq y 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 points with , phx0/:corwy(i jjv7 a fundamental frequency of 440 Hz and a masi(hpj:7cx0or /,v jy ws 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 oi rp8v)e. .qdcpen 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 lv pqd.)ecri 8.evel 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 nemu-,//ir.ud t, iulfsp x3x k0ar a tube that is open at one end and also 75 cm long.us,0dxkm ,-xprlu 3.tiuif/ / How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one c++4jr m+8 b3kuzlajh q pnq96lhb-5pfull 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-H4q 3zifq(tzr th3x 9(lz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds thaq9tz4 lxt3q(zh3 ( firt 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 urcz2)t ly52:iq o gr9is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when thei:z ygu2r9)o5 qc lr2t other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it o h mt7u03u7ey/jcsldc om(c bc9p;96approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assumjscuc lh9c;o09eo7mp6c(7 bmyu/ dt3 e constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by eem:0 yyolqa:tz0 2z,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 goes by on the straightaway. Hoom:yq,l:e 2ye00at zzw fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz.26viq4 oe xn-d The shorter one is 2.40 m long. How 6evinx4q- d 2olong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as i-1i nkj -k3a 7jc4aefgt 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 listj3ki1 7-akc age fn-4jens 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 0qygc 5*f0 upz)2p zhd..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 with a speed g) uz5py2 pqd* f0zh.cof $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a motszu/e8y3 )fj ;f 4mv7tc-kr e.he xq:oyo.1ibh at speed 6.5 m/s while the moth is 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 waveb zt1yevo.ji) s74e o8: e/.3yc x ur-hffmk;q detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a seriesk; 0ayf7mkk* w*n1qyi of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms *m 70an;qf1kwiy*yk k apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oncez6nnpd+c+y4f used to send signals 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 onec d6n+z +nfpy4 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 i)h6pvcb+xx+n)uf y5d 2qnl2 presence of standing waves, which can cause acoustic “dead spots” at the locationxln x5p)+b+2f qicyv ) n62dhus of the pressure nodes. Consider 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 demonstra ,obwj2k;uaa//cq3 awtion, called “singing rods,” involves a long, slender alumin2ja; , wkcq3awbo //auum 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,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a s3uta dq;0m5qfrequency of about tmdq3;a5 0q su1000 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 eywhz) .kah*) observer on the ground hears the sonic boom 1.5 wh)a*z k .ehy)min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1:d3q 6bjxey-dq v ux.n+9r x:s5 $^{\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