What is the evidence that sound travels assped(l7f; 8s u a wave?

What is the evidence that sound i li75btzncj zgls;zj;7te6a.z*/7 kos a form of energy?

Children sometimes play with a homemade “telephone” bya qp7+fz ,l3lb attaching a string to the bottoms of two paper cups. When t p7qlf3abl,z+he string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave paag )t d7myqde +4v2ih(sses from air into water, do you expect the frequency or wavelength to d yhd7eiv(4m g 2+q)atchange?

What evidence can you give that the speed of souu--h*rmbnjmae 0 5 ew-nd in air does not depend signifir-mwh e0na- umje-b5*cantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. 8ufl-0yp+tlcWhy?

How will the air temperature inb -6 (sg9rao.uav,l*co88tscp zra- x a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to redi8pemk.eky k2 ..8o hdfkl; r6uce the amplitude of sounds in v. y k6leof8;.ihk.k pd 2ek8mrarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced5;2hppe5a fayp a 9dmxbv61;j closer together as you move up the fingerboard topep6d1 fxa59 p; j;a5 avbhmy2ward the bridge?

A noisy truck approaches you from zl0 .r rbu :ump(,l2zlbehind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explml0rz.uu2(lzrp :l b,ain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats c:v,n:l1ujim pan be said to be :mpn lj1u, i:vdue to “interference in time.” Explain.

In Fig. 12–16, if th mdlwg g q;n7v8r8 ey,/:vu3uae frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer togethevugqr8md7,8:ul /nea ywg ;v3r?

Traditional methods of protecting the h6dg 4;v92 l+4grw cftl7 jdheeearing 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 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 ;7+64rcfdeelwlhgg j4vd2 9 t reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a g a -sbkoc; 8e9)9qjjmsuperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In 8sbj;eq9-ckam9j og)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 thelq ui*zq)gjek 1:ch.8 same direction, with the same ve18q*gjq l. )hiuk:c zelocity? Explain.

If a wind is blowing, will thisb3ubeps9-* wv2tz /e o alter the frequency of the sound heard by a person9be usoz ew*p-2v b3/t at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows varioy0hk mm 0a(9mous positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highemma h9k( 00yomst frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of ng+z svd; h :a(hv4m/ra lake by listening for the echo of her shout reflected by a cliff at the far end of the lakemgz +/n vah4:dh ;srv(. She hears the echo 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 waterlin( sv) 47m)m *)b6i ales wl;xu)brg7jnryv-zse. 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 im z* e7i) ya bg)ss4vr( ul-7r6v;)b) jlwsmnxs 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atx7m(zho,t *6,onloq a 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 nr-ws0 v/*jas- gi k pml(yed0c3r,5x on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backf305/(sg*m0-n-scjdyv walkrpxr e,i ire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tr+sw):jey .j fop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hj. +e) rf:yswjigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pave+r p-3kgepnl (ment. A moment later two sounds are heard from the impact: onn-k (3grlpp +ee 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 made over one mile of dvj:; k*,depuul3n ;e5s.kl uy istance by the “5-second rule” for estimating the distance from a lightning strike ifudnl,u5.;kje: k3upy ; l* sev the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the p9f c/pc v*v+gpain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensit /t 7/gt9vrdcly is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leve((hzsniz*nmx ozg0tgn3) 1 b 6l of 95 dB when fired simultaneously at a certain place, what will be 6n3g z(0z *1z ghx b()timsnonthe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane (d a5 0ndox(0qs,keawwith four equally noisy jet engines is expo(0 k,an s0wx(a qde5deriencing a sound level bordering on pain, 120 dB. 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 dB,p,wc,,3 )+0w ld-e /xhk-ix cxxhxxsd whereas for a CD player it is 95 dB. What is the ratio of intensitiesxex/h,pwc,-,xds0 x)c+k 3l ixxhd-w of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powg caewo gk /2rrk33:zjl(k1rpz :r:k8er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere 3: r(a :kjr 1:rgwgzkerpz2/kkc3 l8ocentered 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 fe ;e1; icokfq;(t vq:whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250sqq0kwc59 gksvx-d+au81xc. i 1wjs7 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 3.59wq+jsq0s du 7ki.gack c1w-5v sxx 18 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 placed 2.8:i1m2 wd4gpfy m in front of a lo124wpmyifg :dudspeaker 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 leveckg45.gkn f-q l of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diq.4g kf5c -gnkffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave xh/a )h6aggr r5lb: v p0yhk6syuq/wugd8 4-3 is tripled, (a) by what factor will the intensity increase? Incr4wxhgu0- sk8bpar ghv6 5q3hg /ual:y/d ) r6yease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one h: fgyf7v qjcqny4 8;6zas twice the frequency of the other. What is the ynzqfc64 8jvq7 ;f:gyratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondska lbrb.u*p :4 to a displacement amplit* 4apub:r.bkl ude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must ha+a;mf 7g4ciuq ve what sound level to seem as loud as a 100-Hz tone that hai;m +u4fgqca7s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wv *n./k/qdrcu );omtij p9 4imu )eb1nhen the sound level is 30 dB? (See Fii ;irc) j mbmn u)etp14o*.n/vqkd/u9g. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the +lk:ut +h4my -1 fsfyjratio of hig-+fs 1uflhk y :t4mj+yhest 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 fundament(opkpuk;8 s4s al frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mustk 8ok u;sps(p4 the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three asz4+ r5otq+ w1fc1uu r fwd*j,e:y;to udible overtones iff ro;ezts++d:t5 y o* 1wuuw14,fqrcj the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant freqo:zzh)vaa6sn 6 (c9txd67 xkwuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed itcwzn(9:a hd6z)xx6 7v ktao6 s 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 open-tube pipes spanning thee-, zg omp/ao oy+0o mc/rjc(( range of human hearing (20 Hz to 20 kHz),roe ojoag p(yc+/ mo/mz,0(-c 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 ha*vh*+q) ncozq92neil 1 dnj f7s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fing+o1nnf2iz*7 hqdql n*e9 jcv)ered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long syvk(0t+ amgt01 cr)i2m7vkj and is tuned to play E above middle C it+mcjv1)strv 70kkm ag 20(y (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 q 0poe;x; 7d*0qv1ybc g2lfuhpipe that emits middle C (262 Hz) when the tempq ;b0udg e21o*7hvl0q cyxpf;erature 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 y-a4z4f; je7quk9lwj$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12jl.;,vybj ns1–10 should the hole be that must be uncovered to play D above middle C vyj,n .lj;1sbat 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 aqz/a 8l6s0 lt/qq nb.hjm h*+can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any othjl/. zabn mh6*l8s +qhqtq0 /aer 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 resonates at bx+vrh80).qgzq kug:2q+g o btwo successive harmon+.bx8:guvr+bqzo) 20qqkg g hics 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 max k*wo.h,18yxfyf - $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lbr9 qals,l 1vwn0k a8 ;90brmgong organ pipen b0 lrkab99v g;maswr0 1q8,l at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelye-o(j ;9b6dn hrr)xo w 2.5 cm long. It is open to the outside and is close(6nojrrb o)dw;x -e9hd at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship 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 two strinvq j,7l k74fxx0xu sy.gs, one of which is sounding 440 Hz. How far off in frlyvk 4uxjx 7 fx,7.s0qequency is the other string? ±    Hz

  What is the beat frequcl6e)le; +ae rzje+(*fb yby5ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anoxt xur 8vkg)m 13l78bwther (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequvkm 3b8gu wtr1x7l)x8ency 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 a 350-Hz tuning forke:j: ijm1)v6 w (yzoza and 9 beats/s when sounded with a 355-Hz tuning fork. What is oayj6ij1 w):vz ( e:zmthe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to txbm p.y 7plzml / 4pvzw3 4od.z8auv+0ev5jd1he same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be t .uv8vld/3zvpob0 am5 p7p w1.ed4 +j yzm4zxlhe 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 flutes each try to pl +2jts rjlo2ile 3rz)5ay middle C (262 Hz), butj)let+li z2 3jsrro5 2 one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzlj(r/l8- h vss;bbo k2; 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. W8sso2blk( ;rbhl v-/ jhat 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 7(xu9v0 oqci 3 : 9/:lkvvf8v lxyzjqhspeaker and 3.50 m from the otheru9lz09x:f7k lhqyo v8/:x v3v(vc ijq.
(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 he qi2; dv) ofq2xcjvtr61+rmh: ars three beats every 2.0 s when they are played together. (ihoq jqvt m)r+f; rd2 x1c2:v6a) 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 and 2.76 m in air. How man6 e)af4 *; cyyq,cdasjy beats per second will cs y,)qed;4faa6yjc*be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firetpufo jc/o25oa z.mg-c 7u. 4a engine’s siren is 1550 Hz when at rest. What frequency u.pmua7 c otoozjac 54. 2gf-/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 stillpvy 5(sygf.l f h:+ixjnn u3((-vdy0e . What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spe(y+ve( fy 0 xi.h 3spgnyv:-n5ul(jdfed 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 movpeiv/ 8dl1y h0ing toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freq/ 1p i8dvyh0eluencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is ap8n p2: 1 xnn/k)yrnqrt rest and the ) rqnny :ppkn1n2/8xrother is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0d(6ro 9qk t*gw kHz and receives them returned from an object moving dire6(9o*tdr gkw qctly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flfbo t-**mld3 x au3dg/4amo+lies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does th+tamad3x do*/g4u3fmb *l- loe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Do4uz4 xunlt 7zhnzzujj42(+)e ppler experiments, 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 wase 2t+u)nj4 u nl(zzz4j7h4uxz heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasove; 8tc45 hwr sczb;y)und waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to b ;r8 c;cbw4h5t) vszyee 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 wavej/2;tg(zhln h.- l jzvs 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 i rt 0pmh 0i3oqts*d3q9s 12 m/s from the north, what frequency will observers hear who areo0m9 irpq 3*hdst tq03 located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving oj.8(ii frg2uff -hu; ln 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 n aw zs/d:e ha)n:,e5wMach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes witse/:)ha , edzwa5 :nnwh the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound isvya 94d:bg(xdy zmou:q)9 ku3 onlxu zod4dybugyk): va9(9m: 3qy 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 strikes the ocean.3aec/ .04tdtwc jgvb7 Determine the shock wave angle it prodc w4t.t/0 3b7deavcgjuces
(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 :) j)ivnmqj tv.7ao c3;zq)jaxon)j9 $/theta$ 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 g+xwg0j ) p7jiju.ng)yround flying faster than the speed of .j +i )0wnxgjjgy)pu7 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 tha*xpepeloa.-aa; a l(4 ;m:ur*xn ;yci t sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum dlaeup;x*.er (oiy;lx a :*acm4n-a;pepth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ranwsyci+ .l,( qfge? $\approx$    octaves (Round to the nearest integer)

  A science museum has aubgsh9nze-7y le7 50l display called a sewer pipe symphony. It consists of many plastic pin gl e7yh-z l5s9ueb07pes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to thev/d0c;6mu7ah10 a rvbq x ym9l threshold of human he 1/ 6x7aay0;brv9q ml0uv cmhdaring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant:w73m-fu0ozgv :va w/h ik)hb sound level when an 82-dB sound and an 87-dB sound are hea3vw:zwhm)a v/u fh:-koi70gb rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the c*sc*f ua)y -rahj26iopen, is 105 dB. What is the acoustic power output (W) fc6-hur y)ia*sjac 2* of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output athxl0htu l:a6 kct6(x) 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power0: 6hclh)xa 6txt(ukl output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective 16ijj:rlb qxs9fpme q 47-xw9devices 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 inwsfmqj 9eb p49r7q6j ixl-x:1tercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain /jx1lmpc,ma6, $\beta$ 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 violin7:lucwc 3xq:ndi7uy + 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 viojf3. ahes wy*,b10*mfgq or.4-lr schlin is 32 cm long between fixed points with a fundamental frequency of 440 Hz a hfge*c a3yhlfs.mq*4r , soj0br1-w.nd 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 vg:ftfvu *8m3 eue9v .* a+e iyefnqw13ertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube abovivyu m*39 e3t8e1.q ufgavwef n:f*e+e the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at uurkm8tj+pg r,5,sp )qi00 ow one end and al)gpo0 u +jptrwk5m,s8q,r0iuso 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 the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop ,n 6 zer45+b vyrybhe0($\frac{1}{2}\lambda$) 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 feittq bk*yu (;yh6o,mm (rb5, rom 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 farokt (me5br,hyi ,(mtyb q*;u6ther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stat 7v0 )oil;gujbionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the o j7iol;bv)0guther train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538) q h5aegp.dr2 Hz. After it passes you, its frequency is measured as 486 Hz. How fah)qdg 5er.2 past was the train moving (assume constant velocity)?    m/s

  At a race track, you can eswa dl.70uwvi ,oapc9nvp-pr/ q8n* w2timate 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 drop2 9 8*7.w/ lpopn-nrca duvipwq,0v was by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding v04 mdsc82;q- wc5 7icvyt oft0k(ervtogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lo7v4d tw5q8-20tc 0ivmceysrk; v(o fcng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as ijt/sq-8ejkol.3b k) r .ir ,aot moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (j.-is rb.a8 3j,)o k qkertlo/c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is w*9s qout w:p:normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed a:ot*qwwups9: long 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 moth is flying toward the b p,bjb13zwv*yat at speed 5 m/s The b,z1bvyjw p 3*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 oqg c0q,5*.kw5mvfvthigh frequency sound pulses as it approaches a moth. The pu 0f*,.kqgvoqmc55v t wlses 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 next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send shq 2bwgoeg;qv(ejy2o ah 2ada1ll6;6: t4. phignals 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 oe(g2;hjg6b htq a 2 6p;aoyev4 wl.d:a1ho2ql f 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 presencec6as:mo f7v ut1b,e /d of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m l vc:1t/mesobda76, ufong, 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 demonstration, called “singing rods,” involves a long, slender ai3sz ek8w4ggcx:oe2o1-2vkaluminum rod held in the hand near the e1ev2 gioco4kzwk8:xg -32a srod’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 heara/l*hayzg90d ing for the human ear at a frequency of aboul gz9aayh/0 d*t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An oosloo9m:: p1sbserver on the ground hears the sonic boom 1.5 min after the ppo:l91oo ss m:lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat(pp 9v tal0zs :ptsg d.3l7,qa 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