What is the evidenceb;3y ; qr* uvjd2irdd( that sound travels as a wave?

What is the evidence that sound is a form okumpa:ggm al)t7054 6h hn2bmf energy?

Children sometimes play with a homemade “telephone” by a cmh9in*8 y ead5tf5 w+blw9b1ttaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the s91ewi tnbb5y9*85lwc a m+fhdound 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 2rfo8 m/n7npt from air into water, do you expect the frequency or wavelength2 tnm/8orp7nf to change?

What evidence can you give that the speed of sound in air does not depg * wbu/k,3hk9 scsz+aend significantlyas zwb+u/9*k kh3,gs c on frequency?

The voice of a person who has inhaled helik3jpk(54f.nnq h +.zs /zdhhlum sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of oey) s l8+/jixe o3f4ygrgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundu, 5,. osdzls5rnx+ k/irl5 wos in various f5sl5wo,nir.z/ ur l,+ x5 kosdrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Figylzp8x*jncypw o6 0v4(j 61zfriq 2h3 . 12–30) spaced closer together as you move up the fingerboard toward the (cz1n 60y ixyp*6zjv q ohf3wj4rpl28bridge?

A noisy truck approaches yo;h se-7xkr.zno 5pt;+jbfnb ,u from behind a building. Initially you hear it but cannot seeks o;t,pb7z rn5+f;exb h- j.n 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 diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be 0 df2dzn b4sxgdo0 rlie5*9p)ats can be said ton2 dgdo*b rpd4)0ezi s0lx f95 be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were loehjlpxkbnvjv/ / 9x;i+ *m2+s mqy)i7 wered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer 7iv hxyxjm qv+2bpk/+n; l s )j*e9im/together?

Traditional methods of protecting the hearing aqp4psnh0 .h1 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 ambientp1s0 h.an4hqp noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sujq o))npdbhkym:-+c4v,,fa z perposition 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 faqayonh,: ),pf4 m) -bc k+vdzjrther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if eg8qy6 rvrx8qc ,v 1u.the source and observer move in the same direction, with the samevy1.q6c rq,x8uvgr8e velocity? Explain.

If a wind is blowing, will this altewl1- kk8r /.ub1+ nc(knce tq+bonim:r the frequency of the sound heard by a person at rest with respect to the source? Is th/n1nqknwb:cob+ur.8e mkk(+c-lt i1 e wavelength or velocity changed?

Figure 12–32 shows various positilt3 xj2c as(l7ons 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 highest frequency for the sound of the whix( cjt372sallstle? Explain your reasoning.

  A hiker determines the length of ;oqj xkj,v3z3. jiw ps+ lj6cl4;/udk-4sebfa lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aft l; j4j ve/3pw ss uz+i f3c6-qlb,oxj4kj;.kder shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.d lzp*2c(,ss4guh dg*pr6r w0.a srp- 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 s*a0su rs 6ph4*rzsl( wp d2g.-,cgdpr peed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng+p7h ykwcsvi6xw0f .uo tw; ab6e*18i ths 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 orv lwtwu., b7nmj38n4f tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses wl.7w n,3mnt8jv4 rbubefore 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 splash it make:qw3xuj.9h2 *tm r bs e1u7mejs when striking the2wx *u.9r emsj3h:j 1m7 tqebu water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, 2z+mi6ucqsy4sees a huge stone strike the concrete pavement. A moment later two sounds are heard from th4qyz+ui2cs 6me 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 ei 57y,g qccid:0dtc-v rror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatureqc:07dcy d- iic,g vt5 is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound w)z198( 2greqhtav2 y ttuh8w at the pain 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 le ;vkovf f)s5)rvel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when f9 s2 osr)oux6pired simultaneously at a certain place, what will be the sound l9)r6u posx2so evel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a +ii3, 9pybprw .wdy6/mb5 p orcertain distance from an 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 captain shut downr,bi/ p b mpdy6wyw9pr 53+.io all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nois9 )ipd and3)z8c,ywi le ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background i8p)l3ai9cdd ,zy nw)noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fro9s-n2m h+wkk(xp bw 7wm a person speaking in normal conversation. Use Table 12–2. Assk9n(h7w ksp+mw2-wb x ume 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 pz2*hms1:wp4c s z,vq eardrum 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 amplifierj.p2b,p kfe lv+td.,i B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3,j2pp+ d el ,bitv..fk.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 placess *ad:x0. zmvvwly9g1*bc0me z 7,emd 2.8 m in front of a loudspeaker on the:z 0es,xz1v 7 bd s. ygw9ve*malmmc0* 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 2.0hx3jbm4hss ept)-rp /q9 1 7bi+gw/mu dB. What is the ratio of the amplitudes of two sounds whose levels di7reu)4m// hbp bg 93 w+-ijqsh1tspmx ffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whandi jl.61u 7m3zmas)e t factor will the intensity increase? Increamze ija) 7 316.nlsudmse by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplik hyi,zd,(y 7 1bnoa+rtudes, but one has twice the frequency+1bk,, noi(7r dyahy z of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wavgxc7 (z/ q:wdme in air that corresponds to a displacement amplitude of vibrating air molecules of 0.gx cd/wqz(:m713 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lere;m2h -g6t(z*h nkxvvel to seem as loud as a 100-Hz tone that has a 50-dB*( ktgh xe 2-6rmhv;nz sound level? (See Fig. 12–6.)    dB

What are the lowest and hig;w0tuwnq giyyj up131j) g6n 9hest frequencies that an ear can detect when the sound level9 pgg10y3njq6 tu) iw1w;ynju is 30 dB? (See Fig. 12–6.)

  Your auditory system can acc) bqbd m8lz /)ljczw9+ommodate a huge range of sound levels. What is the raticd 8mb)w)jbzlqlz+9 /o of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of tj2ii85q qiult4h *sc6he vibrating portion is 32 c6u qqc5i*l2is jh84 itm, 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 fun,.*)ozly6u tip 1h atrdamental and first three audible overtones1i attpzho 6l). yr,u* 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 you expect p5 ff;ajsmt 8:7pzz kr. h9q8tfrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a c7s.89jzf pz8;h a:qpt5r tmfklosed 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 pip2bc vq(nqjr +ym6 i)- k62umztes spanning the range of human hearing (20 Hz to )r6(b 22j q-knt6ivq c mmz+yu20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar stringr0;pmcy jg) 7r1wx nu, has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengw7px,rcmgn)0yju ;r 1th of only 60% of its original length?   Hz

  An unfingered guitar stringua6 4kzcf5bi 4 is 0.73 m long and is tuned to play E above middle C (330 bu4akcz4 fi6 5Hz).
(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 (262 Hz) wml. cx.y*)o*w+iyxcn hen the tempera.*mx .wy) +oilxn*cycture 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 2a ozk45u *dp/epvrae-d8 +ec ;0 $^{\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 12–1z i;h75svx bl, 3t-.byodb*qz 0 should the hole be that must be uncovered l-q,y3zdt vbb*b7.x izso;5h 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 2e4 s 5ja9s ra/p7qculaw;zw:164 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open os 7;5/:4sucawq1wa erzjp la9 r 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 bo i/pm8 k1(cpguz;j vc.th ends. It resonates at two successive harmonics of fmvkc zc (ju./p1p;8igrequencies 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 e,c 0.vbqp:ji-kc ho ($^{\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 2.14-4oa-vyilk h+a8 kyf/hi ;p/ e-m-long organ yp-a;ky 4h- 8aivo/ eilkh+/fpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ib u+fatz h8 cg-hv1w+6s approximately 2.5 cm long. It is open to the outside and is closed atw1ubc8+f+g hhz- va6t 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 toztj lv0f -2if2 ng cib: 1m)k8n;5hjcrying to adjust two strings, one of which is sounjf n-o1zt0icf klg25i8 h2: ;vcbjm)nding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freque p;q0bw5l ds/;fxf ,qm uz:-f /)debrcncy 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 anotn 8)v i1o1tdikher (brand X) operates at an unknown frequency. If neither whistle can be )8v n1odi1 tikheard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produwn gi sunh 091d;xgo)p,ts- (nlwfb :xmoy;4 (ces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frf(g;o:)0no4w sub 1x(;i whmps-nntyxl9gd ,equency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam-w*i v+.) yvwo6pk akie frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frevpvo.w*kw )i+ 6iay-kquency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac: i0ld1l:ek pth try to play middle C (262 Hz), but one is at 5.0°C and the other ateltd:p0i1l k: 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B bekj2m0 i+8j8 hdu+v 8ajk 3tohas 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 possible when A and C are sounded toge2d 808oh3+uj ik8 j+mk tvbeajther?$f_A$ =    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 m7u3-vf ff2o2tmt nq8 u:m7jzf 75 dxjb from one speaker and 3.50 m from th bz7ujfnxm7fvt8f37 d:u 5f 22jqomt-e 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 tn tr *jp(4/arut;7lqc uner hears three beats every 2.0 s when they are plaqrc u l*7(;/a rtn4jptyed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 .6xtn,nj(iqm .l* r:3w s:zb hc0wpq zm in air. How many beats per second will be heard? (Assume T =ziwpt b.3*z(w: 0chj nlq:nx ,r 6q.sm 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency sqcy +vlhi(qzs5*n- 8b n)bm5of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of ib5s(sb-85qych* nlvq +nmz )30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sinuzt i)m *f9-suv 22yzren emits at 1550 Hu-2miz2nu9 fsy*) zvtz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency d0hy/ 6tb* (szwfxte h8x:ht9if a 2000-Hz source is moving toward you at 15 m/s versus you moving x(h z*6fsd9tthe8x b y/h:w 0ttoward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single bf93d5m cb1jnfrequency horn. When one is at rest and the other is moving toward b93d mf1cj b5nthe 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 50.0 kHz and receiw3gn,ssyks x3sp(83) )f auopves them returned from an object moving directly away from it at 2p3nu wky)s8sgfp(3a3sx o),s 5 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a ;.e3fc(j7xa wa3tho+cya + gzwall at a speed of 5 m/s As it flies, the bat emits an ultrasooc zfy3;ag3+7h+a.eax(tcw j nic 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 ;d93lna.d5;gce j n qswas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station a3djq;agnndl5 .9;c est a speed of 10 m/s ?   Hz

  A Doppler flow meter;/r* vuv8)(yxqmr01 7usex+ aa uepiu uses ultrasound waves to measure blood-flow speeds. Suppose the device esp8e /)r i1y uvx;xamu 7uq(0v+ea *urmits 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 usir83sm9c u w7rqng ultrasonic waves 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 emitszm ,)racy de/7z1t7y o sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are)1cytd/r oa7 ymz7z,e 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 m* 02tgatu ipv5oving 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 the2 9u) l l5e8dwk4qm2xpe.ttgc speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ofw29dlm4 5 tx)2kltqu.8ecgp e 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 planxuf t3*fj0(fnwcdzuo 1u6/a0g d5zu3 et where the speed of sound is only about 35*wutzac(j3gzo u15u6/ 0x 3n0 ffdu df 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 strikess7rkyzbxa u37*a 49 6txr*rvyv7dq .w the ocean. Determine the shock wave angle itxr3xz7vkvt b6y .7u swa qad4*yr97*r 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 p8 hg7;d.eoqv$/theta$ 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 eq0/e/*hcct zpoho (a 7xactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizozoa c 7ec0 qp/(*oth/hntal 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 sonnnug i5bbtm9;3vr 6 9zjco1i/ ar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum9 vr5zcn i3iombb9 6/nug j1t; depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible -6qxae+wxhya cd 5j:( range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. Itmzr- jcc4h oi b2:*-mk consists of many plastic pipes of various lengths,bczhk-i - mcmo *j24:r 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 ahxan9t ha h;*lnv -0j: person makes a sound close to the threshold of human hearing (0 dB). Wj; tlh-a90nxah*nv h:hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound leve ty*+bt-/ qme x0)f5iy4klq vtl when an 82-dB sound and an 87-dB sound are heard simultaneousltm)y0 ivl t4bfyt * q+5k/qex-y?    dB

  The sound level 12.0 m from a loudspeaker, placed eov mk+dzhj+gq;, 0+zin the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal+gekqd++m;,oj0vz zh ly in all directions?    W

  A stereo amplifier is rated at 150 W output ae*bxsb),puyixf8s co 680i,st 1000 Hz. The power output drops by 10 dB at 15)yp,ou6fi *csbs8xi,e0 bxs 8 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraf5ct c7a4b i 8hzzlg*t9t 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 average huma tlctc 79z4*5zagh i8bn 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 communication k,bw z0zxx )(7khstb9s 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 idk)2zcb:v -j3se8 jzmv+)v cto a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fua.i:v 1c(,z k ubndac8ndamental frequency of 440 Hz andc,ak(8: ub.zi1n vcad 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 verticalu 9+;zn o jr)(xo340bofcnjlg 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 a;ju nogox03j+c)( nr 94obzflbove 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 2y fya. /t um2/jl5cmuis open at one end and also 75 cm long. How much tension sh5l /.mt2 2uf cymjyua/ould 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 todk (iv,b,j ix,ud (vz* resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz rav2vode j mdndnhn:5 h z4;u5 l41*j6grnge coming from two sources. The sound is loudest at points eq4dgodn hu1nn455l :jvrd;26e * vzhmjuidistant 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 traibwby;q;u mda35x.;b gn is stationary. The conductor on the stationa wb;;q byxm3g.5b uda;ry train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle .l o.pvj66m,9h rllqzc nh. 6ias it approaches you is 538 Hz. After it passes ylzoh rj p mv669.c.l n.lih6,qou, 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 speed n2f*gx ;uvgx(of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certa;(xg 2x*vfn ugin car drops 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 together, produce3h:*xim 9on3mwwqja7b 8xib ; a beat frequency of 11 Hz. The shorter one isiw ;8*jnox 9w xm 73h:bqimba3 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car 6u+rx 2sz.ygl lzz2m; 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) he listens from the pz 6l +r.s;2gzyzxu 2mlosition 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 l9ce zr.o,al, 4: jymbkyw1* xe0wt9vm/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the wykz.1c eel*499mwb, xy,:roaj l vt0flow 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 my m-ymyxkuk ;idu,;i,,+ o,xk/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave ofk,,x iuyk i+ ;xykm;dmo-,yu, 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 sounagi7 a5k*xeoo 6cx t 5iq(9g0bd pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each ise6(ia*x9xb g qo0aioc575g k t 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 sig2i z,b1 e* 1uulyx8kq m:rhwe.nals 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. W lym2k erwq*.8,: hbi uexuz11hat is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised qad:la g4(f ih 5d1;wcby 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, aa4wd (;ail:d5 fqgch1 nd 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 “sing. byeab t2az;9ing rods,” involves 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,9ty ;2aeb.b za the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear/k* 2 +y l0rmi5yazoil at a frequency of about 1000 l2 r+*y5 0lkima/zyoiHz 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 ouf+pg:n+ -gdvbserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is then++f:vg-upg d plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1,)rcj6 )f cjxv *mv k4se/0tur3d o5ec5 $^{\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