What is the evidence that sound travels as a h3zjvg6qb v38iq7.1fgci a g8wave?

What is the evidence that sound is a form o.ia 6u(.yweko , 0y od77wkhorf energy?

Children sometimes play with am1n 2sp2 tih:jth+n-b homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one ch +1htp-m 2jit:n bn2sup, 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 y,gyod42mhd::(lg/ h.ya uc bexpect the frequency or wavelength to changy :c .(dbay,h2/ 4ogy u:hdlmge?

What evidence can you give that the speed of sound in air does not dept1-8fn(7ub 2twhrxp0)3w 5n ytviqo f end significantly on freptynx-uqb8w ro 7v2hnit1ff(t 5)3w0quency?

The voice of a person who has inhaled helium sounds veub o /bubm 9-wx)g +lmja ;rrm)0j(f7try high-pitched. Why?

How will the air temperaturycfz )t+f p61re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce t zlmi, ljxt6hw:2)i e:he amplitude of sounds in various frequency ranges. (An example is a cart 2:wjx6l:z,l ieh mi) muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movexq5 ;kuj*qc0 o; urqm 0:*oozybm:rq2 up the fingerboard toward 0 *oq;jzrc 0qk ou5 :bmo :u*2q;qrxmythe bridge?

A noisy truck approac;(l uf:g)n yts*nav ou6:xa/ ahes you from behind a building. Initially you hear it but cannot see a6a:lyufxn*:)u; / g (va ostnit. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfexpm/,bth/rax ll98j gj60h u- rence in space,” whereas beats can be said to be due to “interference in ti gu l,at-rj6p9jbh/l/xh 80mxme.” Explain.

In Fig. 12–16, if the frequen:; oi h(s,kvl1obt1n6c*zmq lcy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closeb1 t6l;:cvs1(*z monhiko ,qlr together?

Traditional methods of p o61mjxbmp/2protecting 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 a2b6xo p/mj pm1re worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave cape428;u u yifg8a4t lnn 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), a 8 pt8gulua;y2fei4n4 re the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and ogi6r .6 r(yk:pcjx* iobserver move in the same direction, with the same velocity? Exp6:i*gy (xc.rp 6 ikorjlain.

If a wind is blowing, will this alter +9d bhpl3.,ak yfuj; dyqba(fs1* 9dd:*ens mthe frequency of the sound heard by a person at rest with respect to the source? Id 3.dan(:lfs y9ad b+e1b9umkf ,y*j ;sqdhp*s the wavelength or velocity changed?

Figure 12–32 shows various positiee443 /5qsz3pay q tw:xi c9sof(qgj,ons of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At wh o:3yspqei5z4gw qex(jc4fa/9q,3st ich position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the le vqyov-6ofv6 6nh +aap8n c/2gngth of a lake by listening for the echo of her shout reflecyov /q6hc6-nogv6p2n v+8 a fated by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the su4.c/ jog(ygxjhp8 z .ide of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with cyp4gjg /z.uxjh.o (8 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20t(uzf4kp;x: 4:u a waw $^{\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 day. f3+dq876zaux teb7r zi 33atx)s f 3znWithout ata 8z6ez37iz br3x +f3tnq 37dxusf )warning, 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 cliff. The splasydm 160 shzv rzi;d86mh it makes when striking the water below6hmsy0;vz id1zr8d6m is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the g;jq h riay0p tzx-ahq h/1:8j1round, sees a huge stone strike the concrete pavement. A moment later taxzq1 8jhp;-/1 rj hhiqyta:0wo sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error ma qu7nxfzy, 97+ukv(fede over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatvy9x+uf(fz 7e 7nq,ku ure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain s4 9bkm3+atobfkf )y7level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensl:w5w75 c(rmvtj rvn+ity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whc ,c,d9aae9tyen fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hi,ct 9eady9ca,nt: Add intensities, not dB’s.]    dB

  A person standing a certain dibhjznh *4owjexky ./r 23/e5e s1b5cistance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dj*wb51ejbsy/2 ze /r c kh.4e5n oix3hB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 djkre;o .m*b4 eB, whereas for a CD player it is 95 dB. What is the ratio of mjr;4e*ob ek.intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakins 36ylxstq g.*( awas+g in normal conversation. Use Table 12–2. Ay63s gxt.+ w*aq(saslssume 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 eardrum whoo:;0 bf zmz( 8suibt82ndkx,mse area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whi4w)o/9 m:ttjebzr8 hirmv 2w;le the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would exper;h:i 9wzt8to wm)/4rejb2mv ct 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 huczxeo 8ac e b5fpyx1 sfrn.52:+8)nplaced 2.8 m in front of a loudspeapf+sb1e 8ycrx n28xaz f)55:cnh.e ou ker 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. mrdqn -6ya 1/hWhat is the ratio of the amplitudes of two sounds whose levels differq mh-n1y6 /adr by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the 8;ij8vpznwln47 k fz/ intensity increase? Increase n/lnf8i wz74k ;zpj v8by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ee-u,d9m7 hik ,wu2m damplitudes, but one has twice the frequency of theduh , 2wie-uk9em 7,md other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wa p tmv.gksomq.cft unz-lh:- l2430 )ove in air that corresponds to a displacem:cghz 0 pfmm)quo.o n 4-stlt3- .v2lkent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seema;h,-sdz7yp o as loud as a 100-Hz tone that has a 50-dB soundzopd;a y- hs7, level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can *zvy;g vtrya8g q)0x 4 9,8aqfewjgt(detect when the sound levez 8tat xv90v *8,)yre;4g(j agqf gwqyl is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounjm)imp h,uk 5io 32x-)/l*qp6ukytjzd levels. What is the ratio )l p5 ,pmqkozj6i23)hy m/-uui*x tkjof 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 frequency of 4j3epnwp48 .5;m7 (o gvzh u14jznhyhz40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensi.4 h;ph48(zovejznh1 y zm57gunjpw3on must the string be placed?    N

  An organ pipe is 112 cm lebu ui41f1on:ong. What are the fundamental and first three audible overtones if the pi1i4uun : be1ofpe 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 fres yn059zhm u 0lrs7m1bquency would you expect from blowing across the top of an empt1n5 0y buml9sm7zrsh 0y soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with dn;uuq76mf m x :tp4l./i9psp open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of u6:7ppsm9 qd. xtm4ipnf ;l/uthe 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 harm d;:g5o aowta5onic. What will be its fundamental frequency ifa;d55 : gowota 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 sk- kke i8mcx 7ll46x9j66fglmiddle C 46 fjlkx-89lg6kis ke7m l6 xc(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 (( 4,:+vyw szvxat/rus262 Hz) when theav rsyw :tz/x s4+u,(v temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 o l iakk.2qdx9sg/3x6 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece ofn d87km :i0-dzleuq+f the flute in Example 12–10 should the hole be that mus- q8 0k7n+df:de muzlit be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 lnl/n+/-baqy Hz, but not at any othera b-l/lnq/y+n frequencies in between. (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 w 0apk-mrh(+i ykf39i resonates at two successive harmonickfi yk p93am- wrih+0(s 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 sr-s0q;dd2.nsdxoup e 6o. ).nuq:as $^{\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 tuj.mr/z5 ju-zhe audible range for a 2.14-m-long organ pipe atzz -j mr.j/u5u 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal o.do3a6k 1 d5mebn 7u12nz rjtmx v(d8is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate ton57jzo r d tmu811adm kxen6v3b(. 2dhe frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trya.09/bw +8-a pdjibgs jbgg:aing to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±aiwjb9 /8-s :b d0agj ab.+gpg    Hz

  What is the beat frequency if middliwnvyib8*iz:5q * 4 zqe C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while7 f bbv2;eq)s gj r ,,qmf4iq8m;bd/ib another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whin em ;m q7 v/bb,,b8br4)2ii ffs;qqjdge of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 c3-jl cf1nkc1 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tunin131- jnfkcccl g fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to 9 b1 rgh;o9ggathe 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 are played together? [Hint: Recall ah1gg 9ob; rg9Eq. 11–13.]    Hz

  How many beats will be heard if two identical flut(vs:odzll4(:n itk q1 es each try to play middle C (262 Hz), but one is at 5.0°C and the othertn:(ql:i (1ld voz4sk at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B ha7 ilpzl( *kmy,s 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 possible frequencies of A and C? What beat frequencies are p 7yikmlpz *l,(ossible 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 mdqw90e xro7x. 4wta+i5pr 8sm from one speaker and 3.509rp. 7awm5ts4ex 8 r+iqd0xwo 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 tunerpkpjs h /b(vq.d17ce(8aks 3tt 3vw6x hears three beats every 2.0 s when they are played together. (a) If one is vibrating at qjbk 8t(e3cxkvsptp a3s hd6/71. w(v132 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 dmew*bn/ nvu* 9e+n,6d0pn3nea2rsq +l eu 6pwavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Asennneqen*3n6mw vparde p/ u9+bus +026ld* ,sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sire*q l +rwo d+6pcxb)o6rn is 1550 Hz when at rest. What frequency do you deteod)l+w *orq6r bp6c+xct 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 detea +q(qd 4inm6gmzc gle6 yg.c:1an;m: ct if a fire engine whose siren emits at ; gqiyng(m4cgdme.n+a 6cq61mz:l :a 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 a 20r1r):kw1a/bz x/h 4vwzjhkr900-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies :)/w bzh1z axrkh/wj4 vrr9 k1exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the samf64skp (n lny4e single frequency horn. When one is at rest and the other is moving to(4k64lpfy n snward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0ol ,xtv 2ge4t6 kHz and receives them returned from an object moving directly away from itx264o vte g,lt at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sp*e /tpr7d/szd eed of 5 m/s As it flies, the bat emits an ultrasoni7drdze / ts*/pc sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played +4n*; 8pfr*xk bduymnida t (;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 approacm+*pdnrfn8d4a;*t;uybi( kxhed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wav(flwfc8b:2 fpes to measure blood-flow speeds. Suppose t:f (bfcw2l 8pfhe device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ,ofq+ii0h0 5l *9zzu yp;omkb 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 *+le0ohj kro(is 12 m/s from the north, what frequency will observers hear who are locatojl*h+oek (r0ed, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 26 m p,i,wt hk6lt6kue50 $^{\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 sl6 i8ejjeb 0*jpeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo*ejbj 68jel i0tion?    $^{\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 plan,im8fi . vx ou*rsv+a1et where the speed of sound is only am.ri, uoxa*8 +si 1vvfbout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine thef;f.k-5goyyu. ybf (c shock wave angle it producf. y5 -kgcbo(yf.uy ;fes
(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 wet-5p+ iu : qxc6ny9r$/theta$ 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 flyintl)t8x aq; emah16 gz (c2yb8s9h :hpog faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Dea(l 2 hehxs)bayo8qhm p91 ;zgct:86ttermine
(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 20q2ls8* lcu.*ig3) vpp fx hc*f,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxi*up2cl 3x8l.phv*)ficfs*q g mum 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 therecnhh)t5 0z4ey in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonvlkjj3h pbke6e/z-- 9 y. It consists of many plastic pipes of various lengths, which are open h3k ze6-j/9- ke bplvjon 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 y .g wmad+9a6zof human hearing wayg6a9z md. +(0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level rr;ng+t * ga0ulkt9e3when an 82-dB sound and an 87-dB sound are heard 3 ;tlre+agtn ru0gk 9*simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op1)9crp g2lc 72j t c)xu5rvnunen, is 105 dB. What is the acoustic power output (W) 2 nl vurcgrxpj1)7c2 ut)95 cnof the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The poweiaiypx -fr0 017 1tlntr output drops by 10 dB at 15 kHz. What is the power output in watts a-nipy f0a1rlix0t7t1 t 15 kHz?    dB

  Workers around jet air83 c uo6wr4i+ y.sika4qj+ zlycraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the averacoz4iyaqi.3s l jyk+6r+8 4uwge 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 sfb79,vwk:jr uo1pa. cystems, 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 vio,.j emvl t8y)alin is 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 violin2)ud0uo5hesa qid. g7+ ac0syv/v 9jj is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per univ0dy hes/jo va0)dg92 u.qa7jiu+ 5sct 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 tube filled.+c/o),;opjz kar6z7tkwnfy:el 2 ts with water (Fig. 12–35). The water level is allowed to drop slowly. As iok t j26foa+ptn) e.w;y7, cz/s:rzklt 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 neey+1 tcjxwm ra18,1 d3aex5krar 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 fundamental mode) with the third harmonic in e5y3cm 1kea8xxrj1w ,t1dar+the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res( e*oir mlq2bw 1)l8dhonate 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 500–1000-Hz range coming from two sources.h.v p0kpdof01ds*0j);5 kta bte , ycz The sound is loudest at points equidistant oc0*seaz1 5pytp, k0v)j. 0d;k btfd hfrom 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 whistlesp2z e0f;6y q0hsa4 -o)jn6:qfsh gfyt. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spehnfps gq0zy;:6)ft2e6 jyq -h a so4f0ed of the moving train?   m/s

  The frequency of a steam train whis: p tmr3gcyn,2tle as it approaches you is 538 Hz. After it passes you,,2rgcn myp :t3 its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spel8cj5exxio-/;c j6 h:g:hm8 ov ywqy1ed 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 (frequenw ij 6e1mcghxo8l5 v qcyxy- ;o8h:j/:cy halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, e1*f+*zrdf ofsounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long 1*efo z*fdr+f. How long is the other?    m

Two loudspeakers are at opposite ends of a fm6dz 8go p ncgf034gpa:u;gzu60yn /railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he3n uz 6 pgp /4a;gfouyg68cmg:n0zf 0d 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 whax5ufau8dsbqag e*h zx(f . 0a f-,i/w1t beat frequency woug5.(uwf- 08*qzx xaifafah/eu d1b ,s ld 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 of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the mbnk3aus + w;6wuzi-3noth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the fr;zuswnuki 3w6-a3n b +equency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses 3xpid; 2 2qr)trvw vwy avq642as it approaches a moth. The pulses are a;w2xiv v3r ryq26wqdt)2vap4 pproximately 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi2ex .8g:oa82 6v9;qftid2 lwk aotgzallage 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, thao q2a:f o.8gz6l8xvti2g2w9; et dka e 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+31mj)e*1w ulb1 dlw .x:ppku n9jmmg can be compromised by the presence 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 fundamwjm 9b)1: wl meug u3l1pd p1mkjx+.n*ental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alutqesa,,g- 2kuminum rod held in the hand near the rod’s midpougqa2 ,etks,- int. 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 h5wtfn p/elu 7y6ll.4 jearing for the human ear at a frequency of about 1000 Hz is 4 n/e y7j56lfptw.lul $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hegsna :mqy :i9*ars the sonic boom 1.5 min after the plane passes direct9m :n*sq:gaiy ly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbaot+2q rcgn, r-9s 4-qyrfq1soat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h