What is the evidence thad0xkdt*zzdl*k7 rk k e.-0j*t t sound travels as a wave?

What is the evidence that sound is a fo7ptkah6s jl,) zf u bzm(**py0rm of energy?

Children sometimes play wih:lxlma )aa b8fj- 99qmud8w:th a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one c8:w9 umq9fbla) h 8xlaj mad:-up, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the/y++ 1shmff wz frequency or wavelength to c/z1ff+ smy +hwhange?

What evidence can you giv 1n. fb/ zy izcz4wufv,)f)3vge that the speed of sound in air does not depend significa.n)fgwfv3cu /zyf,4v)ibz1 zntly on frequency?

The voice of a person who has inhaled helodtx0qb6t /3 vium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orga+y3gr.h1 b.-rap bu:k1phl opn pipes?

Explain how a tube might be used as a filter to reduce tj1j ylwi)ffi97-u:hthe amplitude of sounds in varioui)il1tyw- 7jhu: jff 9s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tr:l r a/r/x oe:umm6;8fx.ljiogether as you move up the fingerboard toward the bridgemu6mlx/:;i. r8fao j:rl x /re?

A noisy truck approaches you from behind a building. x06w9wn5; ubpejm)b b 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. Explain. [Hint: See Section 11–15 on d ;bmb wnewx509u6 b)jpiffraction.]

Standing waves can be said to be dueu6t,.l q* sxgn) .ckyc to “interference in space,” whereas beats can be said to be du tnlk,)x.q c6c* yg.sue to “interference in time.” Explain.

In Fig. 12–16, if the /)e2xg ;*aisx)wm wb xfrequency of the speakers were lowered, would the points D and C (where destructive and constructive in/i ;x wsgxeba2m *w))xterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopli;vuy3iicx u 6q+,kzupp* j:/5lfy/c e 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 yi:*6,/qcy u +vczfi ; kipupj/x5 3ulelectronically, 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 thougwp/jx*kgs wr52z j:2sbk *l 2h+j)oezht of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? ):x* 5 epj kw2zljob + z/js2k2wshg*rExplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thenmahsg-/ xue :3j(c /vzg4sf+ same direction, with the same velocity? Expl(mh f n-cg:4szs 3aj/u+veg /xain.

If a wind is blowingj 5vtn1ec.udas7,2o l, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengvdtc15juo7 2e,n las.th or velocity changed?

Figure 12–32 shows various positions of a child in motion on)qqtr3xlh4 ui.-)qdn a swing. A monitor is blowing a whistle in front of the child on txq ludh.i)nq r4)-q3the 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 bfoy8m h4t8 ph k.ut(35cxty 0dy listening for the echo of her shout reflected by a cliff at the far end of the lake. uyf4. o8 8p0mx yhc(3thtk5 dtShe 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 watebzbtd jl/,nyyo 9e 64(rline. 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 seawnt9/eb ,dl yoy(jzb64 ater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen (eu 3k mihliubuvcvrh1p-1d8*1sl r+i6 3)slgths 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 fvb5;l4yic vh9 oggy day. Without warning, an engine backfire occurs on another boavc; b 4i95vylht 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 orij088z-ya qi f a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliffari0-8 8 qiyjz?    m

  A person, with his ear to the ground, sees a huge stone strike the conc;z g3d aa3 +,7pg0ykn(lnn pgkrete pavement. A moment later two sounds are heard fromkn ;0p 3zyl(aadpn,7n 3kgg +g 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 made over one mile of di z b*6 gz-zo;e:jwib.om:p ts/stance by the “5-second rule” for estimating the distance from a lightning strike if the -iz;* . zt6 osbb:ejgwoz/mp: temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev)5stlyfo 9zbp olm)*q6;pt)wel 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 6rjkzs 0dlvg;k (.6 0 fczbcd1of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sinyiu5q,g/3qd/o hz;vmultaneously at a certain place, what will be the sound level ifo/dn qqhv ,/3;i5gzu y only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from 6joxd.o sk )3man airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the ca)so 3 .oxd6kjmptain 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 5piy n6-rng)cof 58 dB, whereas for a CD player y grcn5pn )i-6it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person i7m3.6 ;v7ld d,4gbzg c h j8w0ocbblqspeaking in normal conversacb gb qiwm;d,d .0v c7blljoh 8376zg4tion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eard+;j a kr:q eey:o)9fkirum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B irt0 sd 9 ty0 yg(y3lnp)uyej;b *51qeas rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each a()ds 5ajqepyy0 ;bettu3 ln1g*9 y0ry mp.$I_{250}$ =    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 nd bj:t9 .5dqg1mmc mh*:,nbw when placed 2.8 m in front of a loudspeaker on gnhnc*w9b:, 1jt qmb.5mm: d dthe 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 diffqp r50nb- )rvmerence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11nrv -)bmp0r5 q–9.]$\approx$   

  If the amplitude of a sound wa7 oiwz,(qorb cfrrz /yf(58x. tz6lx4 ve is tripled, (a) by what factor will the intensity increase? Increase by a fax y(r rw zb8 ftcf7(oo,5zr4zqx./l 6ictor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicw)bl,7e;g ifv ssyz.0 vt 7re.e the frequency of the other. What is the ratio of their intensiti7 g.slb wfry t0vi7.);vzese,es?   

  What would be the sound level (in dB) of a souq:o;: (uy9x-u6joi oidj za; +d-ozo a)5m hognd wave in air that corresponds to a displacement amplitude of vibratino5gi(:);d:d +h oyooqa x-ziu azuoj;96o-jm g air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud 1 ( ;9foatzq1 ocp,q0u h;fuzeas a 100-Hz tone that has a 50z1; 0p(zu t;9uohqfec1 ao,fq -dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thlul;39 -fa1bz ntrs6k e sound level is 30 dB? (See Fig. 12–srl6l9 ban1-k uf;3tz6.)

  Your auditory system can accommodate a huge range of sound lev4s0z c8trcypl-d8,r lels. What is the rat8t8rcrs 0l, dpz4ylc-io of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin han6/o0ltkxqh)sy ,s 4es a fundamental frequency of 440 Hz. The length of the vibratint k,60ln /syhq4x)soeg portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aud 8 7eztav2k9roy .t*rlible ovy.2av l tr7r9ekt* oz8ertones if 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 frequency would yzewsi +5cxj(9 x;)gh vou expect from blowing across the top of an empty soda bottle that is 18i zjxw9 e(cg+;5)sxhv 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 open-tube p6j ye /ccl51 0vpsoqf-ipes spanning the range of human hearing (20 Hz to 20 kHz),0cfyc o561q v /ejl-sp 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 its third harmoniceidt c96v68/m : p* uqq ht4j;lo.rrir. What will be its fundamental frequency if it :rpqqc6riu8e i/l. 4tmjrhv6;d9ot *is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.)x61hwj*um ,i)eokyn73 m long and is tuned to play E above middle C (330 Hhki,) njx6ywu e)*1mo z).
(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 68f 0bvm j8 klu)vrje-j:ww0oft 6+ udopen organ pipe that emits middle C (262 Hz) when tv)-m :jd u6f v8j6 wj0f+ ubrow0tkel8he 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 ()i2b 4qok:euoy x* xxat 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 Exag c mtynf*-m euq)2-6qmple 12–10 should the hole be that must be uncovered to pmeqf tyuq-)6 * c2m-gnlay 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 Hz, but nofecm 5*gn-()83cjeyos k;htu + z2afwt at any other frequencies in between. (a) Show why this is an ous-e*3a;wj2n (ymhez c fcg+of 5tk )8pen or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1:ij2 1wx gusqh+ m );oysf2xn/.80 m long is open at both ends. It resonates at two successive harmonic2/1w g;x)+syqo:nus jfh2m ixs 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 t6u i/ipsn7 3g$^{\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 s;2 whhds6h ,dqf8 o3jfor a 2.14-m-long organ pipe at 20sh8hqw ;6s,jd3o2 hf d $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is :6rtlce2gxkf2 y n i,1approximately 2.5 cm long. It is open to the outside and is cfei:ngx2rk l 62t1c, ylosed 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 : 3: ;gsvl/vzrwc mm-gs when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the gml:svz vg:/wr3c-; m other string? ±    Hz

  What is the beat frequenpx:)df2 l 4j4ds0,rowewhcu ;cy 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. ,1 :qpze u2mik ,0;5hv/bit keqj6vks5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate th;q6qej vv/:t1,iis5 kep khmbzuk20, e operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounde tehq/ )+3rh6aow3 bh wj.au+ psl6o7ed with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency wer hw/s)opj36oa6+.hl7uh+ 3qt bae of the string? Explain your reasoning.    Hz

  Two violin strings a /kbeclb(2wc 8p*vn6w re tuned to the same frequency, 294 Hz. The tension in one string is then decreased 6b*pw (c v/ec n8b2lwkby 2.0%. What will be the 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 f m0ee .d*0zlaklutes each try to play middle C (262 Hz), but one is e. k00 ldeza*mat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, +9b aumqir2+a ih0k3x B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat 9+kmau a2br+i x0q 3hifrequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80--csj0xa+sn hj)h;y: v 9fgsj m apart. A person stands 3.00 m from one speaker and 3.50 m from the othervjssh-cnj hy)0aj+ sg -9 ;:xf.
(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 vv)cee5ewo6 l 43cu p5kibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be o5 cee5)u p46vkwe3cl 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 soundn 7johh7dlqi:r 0u 0f vw,,q0x of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 :0hlq,,7h ow7u inq00v jfxdr $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire en 7 nm3wpgu,h yoe ah;k3nt7s3.gine’s siren is 1550 Hz when at rest. What7ko 7pn,a;esgtm h3uw .h33yn frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency q /ytzpfw(uw g 1((wlh95 o)rgdo you detect if a fire engine whose siren emits at 1550 Hz moves ahwrw51(9g lyto/pg (wf)q(z u t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toq,kyyo-9 i mr:5fyg +yward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly th yyyy: fk95-moigq+ ,re 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 hc8,:qvezq;d gorn. When one is at rest and the ,c edgz;8q :vqother 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 s;j x uqm9p,6awznon, 1,ac/fvound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received9cqv o;,npnmza,,6xjw fua 1/ sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies,le3+zq ,:gc0 6ed0 oi ijqduz3 the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear iz e+udocz liiegqq3 d6: 3j0,0n the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played oqda8 st)i ,m-6ctry .nn 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 trt6c). -,i amn t8dsyqhe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Su3nr*/i tzc6q),te k6bp ma/yuppose the device emits sout )rz6qp3ey *c 6m,tu/ bi/anknd 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 of frequency -wj0xl z qmbvac4oji -*z/-t:$2.25 \times10^{ 6}$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 emit;r 3i 6s *jsjxsr2pph/s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, wh6j*jpri xs/ ;rps2sh3at frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object 8y . 70grwn.vkeg.rohmoving 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 3sbi u5myh 1a/t 9)q2c8z i/pno10 m/s (a) What is the angle the shock wave makes with the directioobqi/ mn8h)2tcsy1/ap9z5 u i n 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 1pcyov2.(np2sg 2 xq:cwm3nf of sound is onlymn cq1vxpf.sg w c pny232(2:o 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. Determine the shock wave angmgb3v, w6hlm2bbscq *j 3 .me*le imhg23lm 63e bvbmw j*,q.cs* bt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle z)le3xkyx;ilnpd8 vuuz1bez4) ) n 75$/theta$ 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 grounde 2x c9.9eiwfhn.v.oml7, a vbn sep89 flying 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. See8 9slbmf v2.9p7cxhie9ae n.o,w env. Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses/oth j-lr2rdbq 0/t*r downward from the bottom of the boat, and then detects echoes. If the maximum 2j* 0ht-lrqodt b/r /rdepth 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 hcul4z +kbf;+ yn cy-;e0 i;gjzuman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ewy7f jqw1 2dxqb7*vx zy56c,aa/fs*many plastic pipes of various lengths, which are of,ys6 djzqw wc25xav f*e ba* y1q/77xpen 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 theh t,fqs4wukju/xb/2h clo4* 4 threshold of human hearing (0 dB). What will be the so,/j4lh 2ubtux* sqk4cf/o4 wh und level of 1000 such mosquitoes?    dB

  What is the resultant sound levezqssc;p 66rv*l when an 82-dB sound and an 87-dB sound are heard simultaneous6; cv6qpzs*rsly?    dB

  The sound level 12.0 m from a loudspeaker, placed /jr- lpw ic3;d uzdg/;in the open, is 105 dB. What is the acoustjwgli;dc; z3-u/p/ r dic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dwf b ,8bdr,8rtrops by 10 dB at 15 kHz. What is the power outpr b,8 8btdwrf,ut in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pb7p4z fge*0 crrotective 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 a0p rze g*fcb74n 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 communicakod,7n ; bn5*fto; zhntions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency .em 3r6no8/kcdwqjf+.oq0d6 j + 4,ilezostl1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fund i l 9mqdhlz.hw4cyew86 u8)c0amental frequency of 440 Hz and a mass 0w6ch q)l8 wi lue.dh48cmy z9per 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 tubeueml w6mb( qezq 1lc)2 y(fd-,q5j5co filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to re eqc(bcj(f e) ly6md5qz,ou5 2q1mw-l sonate 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 v mgai+b.v+f3near a tube that is open at one end and also 75 cm long. How much tension should be in the s .m+avi v+bg3ftring 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 fql:fgm b,+5p keak dun7g24eb8y1( iloop ($\frac{1}{2}\lambda$) 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 fromlto+e z1mepw/; p .jp7 two sources. The sound pl7.1pwte pj /zme+ o;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 farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor +eywljjwu y,6 5ulnc7u . k2m9tw .nx,on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traxunw ,.ye+,lk t769c .w2mju5jwu lynin?   m/s

  The frequency of a steam train whistle bg*gl3u4* d ad1qw3 ndas it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (ass1wnudl3dgb a*4 gq*3 dume constant velocity)?    m/s

  At a race track, you can esti6yxo b(tgw lvn737h(s ,,xp qjmate 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 o 7yq(3 x6hlj wp,(,bnsvgt7xgoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, +f0gtz)7st+4cgu ) tyfr m0a oproduce a beat frequency of 11 Hz. The shorter one is 2.400ruat7yff4g)c0 og+ z+ms t t) m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroaby/t k4sa 50 ghshn/:ad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound 4yhastn/0 ah /k:bgs5frequencies 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 beatnpo2m7r9 s h0m frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from thh p2rn m079some 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 whi(6lzkwduhldqn6a b -tf8 /y9 4le the moth is flying toward the bat at speed 5 m/s The bat emits aua6 nbt f h d(lkwqy-l48dz/96 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 high frequency sound pulses as it appr 6d:3k qqs9g-tr twr,soaches 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 ,k6dqt 3g9sqsr:wrt-so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to ab;e8 y2p mos1us,, 8: 5ftqsiq-vcxr send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is sy-v st;ebqs8 8xf ,ou,5i rmqac12:presonating. 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 99aaijih xttepd) 3tnv6:y 76listening can be compromised by the presence of standing waves, which can cause acousti)t66d3 e n: vyt9jx h7ipatia9c “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv5ms ak// afg b24xhmk6olves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing soukh ms42m5 f/aka b/6xgnd. 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 heari+tcp/ menw8h7el: (fqng for the human ear at a frequency of about 1w qfe(/8l: t+ c7emphn000 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 obse8/ 2w(aorea-h -n9 clu+epjy wia *u6wrver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. W8-+ueoia c/h6 - (w9p 2auwlywj ear*nhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iwcxnt;v+xm*j 3nag v;wpuj3+k-ab** s 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