What is the evidence that sound tb o3i2ugo2sg 6ravels as a wave?

What is the evidence that sound is a (bbmkcs46bx0:x x 4biform of energy?

Children sometimes play with a homemade “telephone” by2mi zbkk/ yc-. bfk,6 ,qfh/mb 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 heard at thh fk .,zi/b ,k-/26cfymmkbqbe 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 fu;d j6b7cb )hdrequency or wavelength tocjh bdb 67u;d) change?

What evidence can you give that the jd)+g9 nouw*vspeed of sound in air does not depend significantly onjw9*+vdn) guo frequency?

The voice of a personfy3*os 7ar -k:fcw y+a who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipescf+u9 krcov6y2+ :-)lixr vwy?

Explain how a tube might be used as a filabcln. +16g7hb+5i y*othv;ydhy zc2 ter to reduce the amplitude of sounds ic5htch. b76*o ad g+viy2lby1h;y z n+n various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you cmo ..:psq-b *qsfb,h move up the fingerboard toward qh :* spsco.-b.b fmq,the bridge?

A noisy truck approaches you fr3ko7 wf+dc nzv r0w/u9udit1 rxn09 5nom behind a building. Initially you hear it but cannot see it. When it emerges and tw01ur 9uk7x vn in/3zdrdc5n+ofw09you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfere11- kea)fp7fwo7 x pntnce in space,” whereas beats can be said to be due to “intppwe xfn 71 1o-a)tk7ferference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poi.(g zh uak.q,q2n t8gwnts D and C (where destructive and constructive interference occur) move farther apart or clu gw naqq.,z. (h82gtkoser together?

Traditional methods of protecti;rj6f6l n(s gsng the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not bl6;g n(r6fjslsock 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 can be thought of as afdqb-(nq lu9wc4.j:w -j qk2c superpositl2cwk -j9nbw . jduq4 :fq-cq(ion 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? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sourc51rfn *e1 q)lhzt, pehe and observer move in the same direction, with the saeh rt zplh51n)f,q1*eme velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pe ogxbne0x*(3q( o-ii irson at rest with respect to the source? Is the wavelength or velocity ch i3x oio*big-n0qe( (xanged?

Figure 12–32 shows various positions of a child in motion on a swing. A moni b wxz9caj388ctor z c89c w8jax3bis 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 lisex/q exh(v4i( tening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.x(ee/ 4hv(qxi0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the 4;slf wvyppwv:n (.w1/zqj s8waterline. He hears the echo of the sound refl.4wf s/yw vnwqp8z:(pv s;j1lected 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wa 1e 0m49bum9ivye,c5)vfdysu velengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy da5l s,yrta(zlj; zu b nv;3v.t:y. Without warning, an engine backfire occurs on another bb5yl,z utz;s: v rvjn t3;.(laoat 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 cliff. The s vjrto1l/mwf d6f,:,z plash it makes when striking the wa /,om:j1 zftr6dv,wfl ter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the co*jp:5;vjjm-qj6 ufv qouy m2 o; -a(ldncrete 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 apart. mp-( yo-:jmld*u;q52fqjj;u ovj av 6How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error mad gzl1f3n 6b5itfr7r:y e over one mile of distance by the “5-second rule”yb3 :56 ir1rft7 lgfnz for estimating 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 mym.u;+fj1cngm r ec 6pb)2 o3dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level(yge9:nd.f i n of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sov8p vfp5:vn0 4y8c libund level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBc0bpiv l v8vpy58n: 4f’s.]    dB

  A person standing a certain distance from an airplane with four ew8 e,oux9po7i +ze rms1/nlhi2.6zyoqually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shi.2uhoros n w,+ ilz 9mx6ez7oe p/y18ut 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 jmdggczs e,j 3,a60yt08p. qa for a CD player it is m 0sj36jzge.,atyqgc,p0a8 d 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 inka5sm9a ,,e output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a9, 5asiken am, sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area c5n o qy jci((b5ler 3g3h+4s1w0tecrhq9jc4 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 t np*x/ ig;3rilhkx9; 64ur 4r;csqzw mhe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibe rn4xc *kshilxzr ;qpg;ui/3w4r m9 6;ls 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 meter registered 130 dB when placev oq /wwa 0+xzg*zuy-9d 2.8 m in front of a loudspeaker on ta*w0o9w ux g/-qz+z yvhe 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 ,sex7jvn* 7ng level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sect nv*es77n ,gxjion 11–9.]$\approx$   

  If the amplitude of a sound wavlk1 1c )vtx.eve is tripled, (a) by what factor will the intensity increase? In v)vl1x.c t1ekcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but 0 uk ba; .ysy2a 2;(x48wj jiplb7tlewone has twice the frequency o27 put eiywb.4a ;(8k;y2asxlbj0 lwjf the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cor+c3 tc96i szel8ptc:q responds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hq+lt p 6ez398sic:c ctz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thact uek ei(+7bl1b(8sa:zm u (ut has a 50-dB sound level? (See Fig. 12–6. s7be+lzeut:m(c i(8ba 1uk u()    dB

What are the lowest ag.)) 4ne ysdywnd highest frequencies that an ear can detect when the sound level is 3y) endyg. )4ws0 dB? (See Fig. 12–6.)

  Your auditory systemd,.x8vug 9:w, u- l +b 52bjvkyzmzaxw can accommodate a huge range of sound levels. What is the ratio of hjvba 89., x5-,:z+l dwbxkvm uug2yzw ighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 l6u lzl mv,x 7uw,0aa o2j90bsHz. The length of the vibrating portion is 32 cm, and it has a masx7a swl ju29a,u 06,lmvolb 0zs of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audil2riv2x7dm/ cble overtones if the pxic 2 7ldv/m2ripe 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 acrok m d1 i8bcftmr4/pa h1/9bc--1xqvcm ro9dr1ss the top of an empty soda bottle that is 18 cm deerqmfx/9cc i1 9-4c htbb1ovk 1 d8rpd/rma1m -p, 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 pie;38yn kgd9gvi eg ;5bpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 2gk9ieveng ;db 5 8yg;30 kHz), what would be the range of the 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 q,qdf5txx:sb( 4:o bp +nqnl*fec(*e its third harmonic. What will be its fundamental frnbx*q l p:*b4fte (o+ n,c(xeq: fqds5equency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string i8,g2 7 kvbzlgcs 0.73 m long and is tuned to play E above middle C v bcg 8,l7zk2g(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 emda5.o c4nbpe, 9m6 xz7u7 nfgiits middle C (262 Hz) when the temperato5 6bigfu n9dc7a4z,mp7x.ne ure 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 atyog/zv ,aqbx0v6)xsp-h bm ); 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 Exampluy-v4y;g7te6py 1kx n;wopvs0e4 uyj 0 :m9gpe 12–10 should the hole be that must be uncovered too 4mw9vyyty4- u;:ujpkv x;61yep7espg 0g0 n 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 resoo ry2;oyflfm:j12d2 c nate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is aj :rol2y2cy1f; f2odm n 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/, i-g 9;pn2aoeay nrj is open at both ends. It resonates at two successive harmonics of fr nejn92y/ag;a,p -iro equencies 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 cnc79k.xoo. / nwbp e*$^{\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;wv rl 2i;); tqb/kt/mc0zylv a 2.14-m-long organ pipe at czriw2v)t vtkm / ;lbl;q;0 y/20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm b /88nulpzdrc9saloxm:8 v (*+3b drslong. 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 o d:bxlsr9r/l+8mzc8asvu3 n p*b(8dstanding 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 tor o;ef/e0 5yw0fch93tau z:j+pa /)fg fd;i kc adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othew a/ ft0dp z0oue;3ck 9)fegc/hfi+ af:;ryj5r string? ±    Hz

  What is the beat frequency if middle C (265iym )iw4kx9k 2 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 another (brand X) operatea; ;;p2 tedaimre9i /ef: gh0ms 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 played simultaneously, estimate the ope;ei0if;:d emp a2;9at/emh r grating frequency of brand X.    kHz

  A guitar string produces 4 beats/s 6w 0)-d jacl5.s 5.-i0avwcg aighwtn when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reas60awwhcjs l0icn ti.wg vd5-5 .a)-agoning.    Hz

  Two violin strings are tunewkx0a+; ry c+ld to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings axlw+cyr;0 ka +re played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pluuf9 2288s*k 2;uvgoyhlyqxu ay middle C (262 Hz), but one is at 5.0°C and the other at 25. 282*u8vu os2 kxuh9lfyg;yuq 0 $^{\circ} $ C?    beats/sec

  You have three tuning forksk,)cegiuf 4eig356n f, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the poss,i36ce5f )iufgg k4e nible 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 standjnd ) 8m/awtcb:5wkk24gh8nhs 3.00 m from one speaker and 3.50gb4 mkjwn8wa)hd nh 8kc52/t: 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 vibrating at 132 Hz, but a piano tuner hs96ay9xdt e4m7s)zhy/6 ml n kears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequeslh7n4x/ matskzyy m 69)69dency 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 ai13f mg *mlk-d:33zxqywqj 4fz r. How many beats per second will be heard?mx1z qd:yz-jf lk3mf3w3* g4q (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz x e g8b7 fpjo;nv.ss47when at rest. What frequency d 7bs7pvsnf e.x8j4;ogo 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 m-k6ckh:-, ataq jxp0frequency do you detect if a fire engine whose siren emits at pk-ax6- 0haj,q :kcmt 1550 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 hxf2)mdhhf 46 a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thefh)6hxf4 2mdh y 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 frequen n8a.oes) oz,n)vc1v bcy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a v1cbns v)o.,nae o)8zbeat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz r1s+ -e nnil4fand receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequenni 1n+s l-4rfecy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s:fmhp4 msnww*.8k 0mi As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?8w sk4m n.ip0:hm w*mf    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving d 1 wkv4wesub/i:(zc(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 frequuz (14vbwc ksd/eiw (:ency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe :aek fk,6r.njeds. 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 kj fr na6.:,keif blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ tpt6 3xn gzn.7 1-jniu0pq3stency $2.25 \times10^{ 6}$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 frequenqc: jy0wo;eb qa360cucy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,w qa0 by;:c 630jcqeuo 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 w ys1g0wf+-19 f lj3: x(dablogtdbo8ving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Ws6(7x d, s0+zfxtr kkthat is the angle the shock wave makes witf7 0k d xt,+s6rtzk(sxh 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 atmosphvm hhrfy-l*c0it m,)6ere of a planet where the speed of sound is only0*ry f-v lmi)hc6,thm 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 strikeyw n)ffp-bz31c /1mim*n(6ntk a 7v0)yf hdaws the ocean. Determine the shock wave angle it v)nawykn6pm*0icmt y a7 n-1f z w)fh(3fd/b1produces
(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 ftdo4;,ych- f 2;q apl8xpiba+ r- ;kz$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flycu0kijid-a)q, /qq n .th0x8cing faster than the speed of sound. By the time you hear the sonic boom, the plane has travel.nq k) -hxqc0ia ud/cj0i,qt8ed 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 i +wafs;ycy 0;lm81ke sound pulses downward from the bottomys ef;cyi8kl0w+1 a;m 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 pulses (in fresh water)?    s

  Approximately how many octaves are there in the rk gulsvr9o. m7uj9* (human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a se9eb3i1 )qbuo uwer pipe symphony. It consists of many plastic pipes of vibq31) uo beu9arious 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 thresh;) rqxlq9.y0qzju:cmt 9 z qy5old of human hearing (0 dB crjq.;)umz tlqx0z9yqy9 5:q). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundcqt(9 kf3qqr9 and an 87-dB sound are heard si (9f qtcq93kqrmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plm w2x ql-*,2-yqcug:auu1yyo aced in the open, is 105 dB. What is the acoustic power oolam,ug2yuq*-2 y yc-qu:w1 xutput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ou,3)xffb+ w4;elwincs tput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the i esl3 wbfw4)+,f ;cnxpower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear zhda,kb 6,8cg 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 fr, zg kcad,8hb6om a jet airplane engine?    W

  In audio and communications syste7kpkruv ivf10z p. w h(p9:xp vqe.u.-ms, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin isx;4;wy-uxd 9 qxpl+s6sh g 5ix tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cwp4o8y 6zjds)m long between fixed points with a fundamental frequency 8p64z josw)ydof 440 Hz and a 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 open tubemw/juax2c8pc t 5cl6 sf *e0n- filled with water/l* pe5cm 6ancjfw20c ustx8 - (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 mas )bsh+ytg5ur *2m(*wytr 1wkfs 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fund *g 1r+t2hr)5(fmuty*wysb kwamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tx0mxk+ 75x.iym; ctp to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the lh- /01dmn 8z /,:xmznkufpyt500–1000-Hz 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 that the sound level is minimal at a point 0.34 m farther18 z /txzmd0m, /npuh-kflyn: from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles+hvfcy4/y *l)pf;m hb . One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches4fy /fb*lm hvhp+;c y). What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it9ezic ft wpzn00s(.2y approaches you is 538 Hz. After it passes you, its frequency is measured afse9 wi z20.tpc 0nz(ys 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate 1xy8w3yp gh* f2thi e:the speed of cars just by 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. How fast ise w8*ixf3g yht2ph:y1 it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of nmvuu8tut :cg (8 o62mk c9p;q11 Hz. The shorter one is 2.40 m long. How longq2 tm;6ug cc:ou n89 p(8ukvmt is the other?    m

Two loudspeakers are at opposite ends ofn29obz up t -xea,5,os)rny.s a railroad car as it moves past a stationox5-p r e us)2bny.,n zst9oa,ary 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 the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what be62tcnz lz.dw /at frequency would you expect if 5.50-MHzlw2.dncz 6tz/ ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.t+i8 r1wo- nljry2 zp:h3rm 2d5 m/s while the moth is flying toward the bat a iw2pr3hrzlty + r:jm21o d-8nt speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of hfyj7ig os1l /9igh 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 bat so that the echo from one chirp returns before the n 1 g9o7lyjsi/fext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sign)i2 /r/tjml cuals 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 the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is closej clitu2// r)m to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the preseni 1vh fn7t lese+0 bo3odon6 n5;3dpj3ce 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. Calculatdtivl3bj0h6o 7n +o1;e nnoe3 s3fd 5pe the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called cf, qxms1.yeol;a o38“singing rods,” involves a long, slender aluminum rod qlefy3o.,;xac81m s o 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 azvj 6vit 7:ye4t a frequency of about 1000 Hjzyv47tv6 :eiz 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 kwwwbsjsep2(u 2+8 j4 observer on the ground hears the sonic boom 1.5 min after the plane passes directl +jb(w2jps s u24kww8ey overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is v1 4zl/lj-w botwc;g)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