What is the evidence that s:dv/ uw: rsbdv4+k lr2ound travels as a wave?

What is the evidence that 5 nt )q;w1cz ys*4ovshsound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a st :285jrfq 8toh. (n0fa j1-bbkrgbpwdring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound ot8r.8j5fw2k: ab dpfb1g 0r njb- q(hwave travels from one cup to the other.

When a sound wave passes from air into water, do 87e:ynqh qe0v you expect the frequency or wavelength to change?nq:v8 h7 y0eeq

What evidence can you give that trxzv. )7-msfjhe speed of sound in air does not depend significanjr) xzf7v.-m stly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whyiwqo ve.3de f4gg312c ?

How will the air temperature in a room affect thoh p4-a 3cb.oke pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude(b(5p )d bmfqh of sounds in various qdbpm f()5b h(frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spac52t7j b8ix lee.:mibqed closer together as you move up the fingerjql t72x5 b: .be8mieiboard toward the bridge?

A noisy truck approaches you from behindx8ritg,, sjz, a building. Initially you hear it but cannot see it. When it emerges and you do see it, 8zxti,gj sr,, 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 sai6)96j5ygauq* n6mbyw s r0qrjd to be due to “interference in space,” whereas beats can be said to be due toy5nuq)06 qgj y6a wr*mj6sr 9b “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were l8(mw*i/ewj hll .tft -etn-c*owered, would the points D and C (where destructive and cln/.fmcj8*-e-t tiltwh( ew* onstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the henwyz3js +0*j haring 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 noi03 +yjzs*nwjh se. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown inh+w1kztn40g,t ne)yk -c 8j:thwxa)m Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the nj,k n14wth:zkcxat0+wmy h))-ge8twaves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsw(t63 ryghtq ((a8kt.s t (hgeerver move in the same direction, with the same veloh(h8t.s k (((y6 tgwa eq3trgtcity? Explain.

If a wind is blowing, will this alter t7 tug e8yl z,x9l.lwey:/8ikh he frequency of the sound heard by a person at rest witk8 llwt:9 ,ey uix8zl/ 7ehgy.h respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito+ n r;:cme9odsr is blowing a whistle in front of the child on the ground. At which position, A throughsrnm: d ;c9e+o E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines t4t3r(e jk ,rpeiaw,4khe length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. pjtr ree i,k3,(4a4kwShe 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 waterline.osofel 6apu:k2, o6m;f3v8 p q 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 sp 66;fal 2f:3 ooo8emukqpp,s veed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at d(psn tp9tba4a q7i7*q(m -rz20 $^{\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 /dqaegk76e6g+kiawu 4g67rg aaq;6z 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 before the backfire ge ia 7agq766g/d+kr;g qe4w akauz66 is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from th2e,npci7 a fl3hhu+3u e top of a cliff. The splash it makes when striking the water below is heard 3.5 s ,2+3nae3ui l7fuhcp h later. How high is the cliff?    m

  A person, with his ear to ta*-im,3in zlr3 jtk ytu5p1w7 he ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and theun 5*pi,33ym 7rj1k tzwilt-a 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 distancrub363gm m/ bie by the “5-second rule” for estimating the distance from a lightning strike if the mbi6m/rgu3b 3temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the psnm-a(sj )/z,kjqnxm2pt 7aj,rc 8 1s1li3oa ain 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 sy( bxf 7 57uczfmo)by( po8edj;d0 y zn:h0jx6ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneo,3 b ockoa4oc3usly at a certain 4c,aobok c 33oplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a u7y qagp /p,)scertain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What ap) u,7gqy/ spsound 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 j4zemd sg .7x;dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and th.;7zs4 mjgxd ee background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person f/qgt7 npp g. wfvui,c+46ur6ert 4k /speaking in normal conversation. Use v,4g 7 p+rin6rgu/uk6 f4/ tf e.cpqwtTable 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 eardrum whosq+ ta3jw z1(fhe 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, wh2h cq3zo l1.aoile the more modest amplifier B is rathaq.o zc213 loed 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 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 ggv4.q.fd0ck30 k 8h o (ctvbo130 dB when placed 2.8 m in front of a loudspeaker .gq0ctog fv3 8o(v dk. cb4k0hon the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.aevwz 6r12fq; t,1y wn What is the ratio of the amplitudes of two sounds whose levey6,1 q2;twvawr1zfe nls differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fd b m9bf+ vyhgi,7,kp;bppl+3 actor will the intensity increase?7 gk+p9il,,d mvb 3ybph b;fp+ Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displac)ne.g f wb 6i)a5etao-d1shv *ement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensian6o f1abtsw)hdgv e)-. *e i5ties?   

  What would be the sound level (in dB) of a soundvb3 :83tmh dsz wave in air that corresponds to a displacement amplitude of vibrating a 3 msdbv8th3:zir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w:m*vdtlmqrcb)o, m( *hat sound level to seem as loud as a 100-Hz tone that has a t r:m*,lmo) *(mcqbdv50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can r(qvh/la)p()ji:an bdetect when the sound level is 30 dB? (See Fig. 12–6.l(aa hj): /pbq)rv(ni )

  Your auditory system can accommodate a huge ranj:,-hz 7mcphp ge of sound levels. What is the ratippjc:m- z7h ,ho 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 fundamentavio1 dr9,g3r4qs ya ty(v.ng1l frequency of 440 Hz. The length of the vibrating portion is 32qy ,.gn1(1s9 avto r34 vryidg 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 ux5t(ro xge,7fundamental and first three audible overton( ,orguex7xt 5es 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 from blowing across thwl (6uesk :/y y9qqao8:jxu. oe top of an empty soda bottle that is 18 cm deep, if yoswa8 oyo:lex96juyq :(/.qu k u 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 omek6v6nx7x8a zs:arw 4m+ 5 zgrgan with open-tube pipes spanning the range of human hearing (20 Hz 66xrz+7enkaz: sv5 a4wx mmg8 to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmo0 q6o:i7col f8v( zbt-oqdg.f4v sv )vnic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orvffq ) ot7gl .z04 o8o v(db-v:csiqv6iginal length?   Hz

  An unfingered guitar string is 0.73 mc qot) 7din3:z long and is tuned to play E above middle C cqo)zn:d3it7 (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 o ysv3ilgfg,)c 19cn m7f an open organ pipe that emits middle C (262 Hz) when the te73 sv1, cglgn9)ycifmmperature 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 a/ tf06 ol -l:ibuo9sbfr*6d5 v2ypioht 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 Exam5 4vkuv+ ip /qh0asps2ple 12–10 should the hole be that must be uncovered to play Dv024+/ vuis khps5qpa 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 t2rhk(t hxz5d b*3zb0 resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any oth(bd*khbh x3rtz5z0t2er 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 twoed8+h.h ov yhkq)(k j4 successive harmonics of frequencies 275 Hz anh ov.j )k+kh48 hqy(edd 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 huy uf i4s9ap) ;*xu2d$^{\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:o1 uialq t00m2:l+ xaxpv m6c.14-m-long organ pipe at a:vl0mmux:6 01cli2t op+aq x20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a e,gob;1 fz:ylpproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range),f:bez1lg y ;o 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 tryingz b b6pqsq4 j70swna80 to adjust two strings, one of which is soundi40 j7aqw06s8 bnqbzs png 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C ( sgs5necc55 +joe 68lp262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brmsm,t 1wh2 pj x/c9qd-and 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 simultanetpmj/wxh, sc2d1m- 9 qously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 bv lkkdug i r(op8gr/088j m,yu 5vh.)teats/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 frequency of the strinrvkymhvp08g8.i d k5t jur)/ o8gl,(ug? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The i47,emnf)l/- m *8cruqhp cwhtension in one string is then decreased by 2.0h mrnhfl 8 /7ic qm)w4u*,-epc%. 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 hearhvvnka(a)9dh9j;q g-o 1 b an,d if two identical flutes each try to play middle C (26go-hba,)dnjq n9a ;1 a(vvkh 92 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninrfu*8sty9 2vea)q 2 kpg forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What byte)8 u9qrp2k2 savf* eat 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 stanb:ix9) zhu g;7wul5uyds 3.00 m from one speaker and 3.50 m from t)iu: b9gz;wx7 yu5l huhe 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 a3 n d0jir.l9 um98spxl piano tuner hears three beats every 2.0 s whenluldnm.xp 9rsj 309i8 they are played 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 m in air. How many beats e0f) ;u9zhd2pqx:y*bglvbu3 per second uqf2 :hgbblu*e)y0 vxz3;p d9 will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency oe rkmng sel;/ 4zw9, 22x*ju+2nzdr wjf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a /zwz ed,ulgnnmx+r w 2*9j2 ;4jsk2erspeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detec-1z2kv. bx 0 j5ap mka19aolcht if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 mz1a l-xahkapcj0k m.v9o521 b/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz slc 7:(*pzl ovy v9fzdg;fq84qource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are thez(p87:9v qql glffco4 *z;v dy 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 frequenmlww-el1 wr / j5ve/3tcy horn. When one is at rest and the other is moving toward the first at 15 m/s the drivrvlje5m31 w/ww el-/t er 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 ayp(b (20emcg6cios8ind receives them returned from an object moving directly away from it at 25 m/s What is the receiesyci60 8 im2op gcb((ved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat e68dd7es xipelq .e,, 6hns a(nmits an ultrasonic sound i,q pe,6sn 8dhene7xa .lds(6wave 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 wasx xb7 8emr:vp ;.omo3l 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 at a speed of3p 7xv :xmo;r8 oebml. 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to meas aey2yaiek2n 39g,xg)3rh0xnure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly a32hgkaniy 0rxyn)e3ag9,ex 2way from the sound source?   Hz

  The Doppler effect usi fgo qo vs)-s.tqv7g 4;2cnr)xng 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 emits sound of fr;e05pjp f4lzz equency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca e5j0pzz4l;fpted, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its*hyif)2du1hd1:oth e 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 th1+zv1/ htgnp4 g;w(m4g drib ce speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion? wpdg/ ;b4 rg1hmvi+gc4(t1z n   $^{\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(m g dssz+mslevc+(/cd07bu q+ )no1f a planet where the speed of sound is only about 35 m/s /mn70( ssf+qg z +d(uv)bl1c+dmso ec
(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/ uixzl1bd0kd lw: .w94s strikes the ocean. Determine the shock wave angle it pro:zuxl 9wdb4.01 lwdikduces
(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 a8c1v3v 5i taxta zt6v3v6e(ki2 *mlj$/theta$ 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 dpg7mvl 1tduuu9o 8 ai,d: opl/0 rt3wr cq08-exactly 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 horizontal distance of 2.0 km. See Fig8:v 09dcl uuq3-w uiap/ to7r,1dd0orm8 tl gp. 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 pulsrpn4 isl v)a j3s27w7bes downward from the bottom of the boatw ) 3lvbns pj72a7ri4s, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangemgnww8x 3 dg1d613oj bt7ev 4k? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists budiyhgz .l(qpzv6. /qe4, 3a of many plastic pipes of various lengths, which are open on both end iqy/ u3a .v4.(eh,p6z qzdgbls.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of hu9;)r9y)(ahlylhk jqt man hearing (0 dB). What will be thea; h9(ryl)jklh q)9y t sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound0j1 q.y7 sdr2xcud8xt and an 87-dB sound are heard simultaneou7.t2q80c dxxyr sj1dusly?    dB

  The sound level 12.0 m from a loudspeakerr+ksm/+grc 3 z, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally i r+g/ m+z3sckrn all directions?    W

  A stereo amplifier is ra*.9o mbp5qmlfil/ 8ujted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 lbufo* 5 /qpmim9 j.l8kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall92zds;d m uan.y 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 human e2 zd;.ms9anu dar has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems64a*z8whwf mq, 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 freque;k t+og -.vkodncy 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 lonshxa:j9p yd;cf19c l 1g between fixed points with a fundamental frequency of 440 Hz and a mass per unit length 9ccyhds1faj9 : lx1;pof $6.1 \times10^{-4 }$ 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 in.qeyolwa5.x g(o77s/ kvn + bri58dh zto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air+vknq yz5dir(.go ./7ab5lewxsh7 8o in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one ennif.po 8dk,u- ,h/mvod and also 75 cm long. How much tens,8o,-kdmnu p/oi f.vh ion 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 resonle. h osfdnjy(g.i lg *,v0b8o1 9yos,ate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from)vo)l+e2lorgf 4m t u; two sources. The sound is loudest at points equidistant frofr2tue o;) ov+)4 glmlm 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. 9f9bg+*v ityb The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving i ygv 9tb*f9b+train?   m/s

  The frequency of a steam train whistle as it approachpb:ifl0:*mg 5cxq+uqq m/mc ; es you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume con; m i*mq5/f0m:qu b:+pqxcgc lstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to6w , qwjp0e5a*.q ixb c,ec agez0.hncf 87(vr the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How qe awc75 q6*wc (hx,re0z,8njivf .cp .bea0gfast is it going?    m/s

  Two open organ pipes, sounding togeth4iu qnj1.orcjk7 2r x(er, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.c kr4( rxijj1oqu72n . How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mo8g2* l9azvj syves 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 (c) he hears the speakers after they*ays 9 2vjg8zl have passed him, at C?

  If the velocity of blo cf wqlu*lj k425(*1olt3u fxgod flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasou*u g4 (*jwoqkfc 3xt1ll5l2fund waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/5 70lvz-c nqfpx )x*fos while the moth is flying toward the bat at speed )f*oxclnzf 5qp v-70x5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Thn--x nchnp pw 2l2anq16roi:6e pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo fromrxh-ipo n n 6ap n:lc2-2n16wq one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was ,0,yzwczs+2asxc ,urxh 5: teonce used to 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 suchh,xce ux5w r2csta y:+z0 sz,, a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can bq j)aeo0k9kz,frv:xs 7pr+ 7ue compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Csvxk+) paorzfj:k e7 r q,907uonsider 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,” involves a long, sl(i m7ref y s/jadq/gn5m:q v+i9dk+ r1y66 culender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, tgd nimsq:uk+1 i 97lf /c +5 /y66qrmydvr(jaehe 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 i-e a0j0 ckjd)8l 3lbxjny2.2z*ybja hearing for the human ear at a frequency of about 1il cdje)0 *abkynjj xj8b2.y-za30l 2000 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 observer ono4zv xk 3yui64 the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alti3uk44io vzx6ytude?    $ \times10^{4 }$ m

  The wake of a speedboat ish(z9mhd b14 ox 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