What is the evidence that sound travels;h 2q7ykg ae64s 9 d-6fio5chrr7hvam as a wave?

What is the evidence thauvy as46x * xvj 8x:jl8mkgl33t sound is a form of energy?

Children sometimes play with a iux,vm;1c v1kn pj3 pjq8w7 q0homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a np,cv781 p3uqqxm0 ;i1jjkwvchild speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into/ngt: du p-9ko water, do you expect the frequency or wavelength to nu/ o9dpkg- :tchange?

What evidence can you give thatg lnw e nd ;2.b6f,gd;1f/6ll0fxb dwt the speed of sound in air does not depend significantly on frbn2 ne;; dgw d0dx6t/lgf bfl 16,f.lwequency?

The voice of a person who has inhaled helium soukc x7w 8 )+wfyfv zp8h0-o9sugnds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?2s* .v7mup8 i50ze(fbcb yndu

Explain how a tube might be used as a filteri 6ogr1ros-.;s-x gef to reduce the amplitude of sounds i; gsf-xors6-ri o1e.gn various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov 0-7n;5ubt g3,saku n 3qrjqko8c/qebe up the fingerboard toward the bridg qcq;/3rngu87jbs 3teo0k nu-q5 a,bke?

A noisy truck approaches you from behind a building. Initially you hear it butdm,o*s0 3j3bf: qmpve cannot see it. When it emerges o3qb0*sj:3mdv mfp ,e 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 saidag:ffr8m1l3uu1b(y * 6j4wdsb0jvj l to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explar 1fjmg(l vy:0f 43 6busbwja8l*udj1 in.

In Fig. 12–16, if the frequency of /n r765jnqpyo the speakers were lowered, would the points D and C (where destructive and constructive interfe rn7ojpn65 y/qrence occur) move farther apart or closer together?

Traditional methods ofc3xv j2h/ w0 1lnmhhytqnh7*5 protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, v2tc*l hnwmyhj5h1q0 nx/37h a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 1rb;n)vx/7e oxpw0d j ,2–31. 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 waves, (a) or (b), are t epo0nw/vr;jxxb) 7 ,dhe two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mo0fi1iyh1d5 aifl/)a nw q,n/xve in the same direction, with the same velocityfi1ynq a/w h/adi xn1if5,l) 0? Explain.

If a wind is blowing, will this alter the frequenc:0gy t -o0y.x52scbcb5bcmio y of the sound heard by a person at rest with respect to the xmo0-: 0 cco5.tibybs5 2cbygsource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motiomgw.j),9n szt n on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position twj ,ngsmz.9), 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 peh6u -gll2uj/dy /o7lake 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 after shouting. Ese/6dyulg7j-/plo 2hu timate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.:uu u5 trp6k8f He hears the echo of the sound reflected from the ocean floor u58upkrfu 6:t directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at ptu4l:hb3,2wi tu3r w 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 ad wbr0/ilf- 7.goh:wy foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the bacdy:0/ri hwo .wlg-bf7 kfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the 8innwykq6d+nw (-y2dtop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high ki6nnq2n-y w8(dwd +y is the cliff?    m

  A person, with his ear to the ground, sees a huge ha)hvlc3n+d2xvx),qzs / zu zkx(rs1 t ).ub+stone strike the concrete pavement. A moment later two sounds arxa1uczz hrs ,3)))d+ 2.hlqvszun/v tbx(+ kxe heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile:68 jtei l z9j4hqxm,b of distance by the “5-second rule” for estimating the distance from a lightning strike m:hix6, ltq8b 49jzje if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev8xt ux1fid/y zdph58)7 ,a)9wj wli tiel of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wh *ct,8rq.v f,q, hfrdsose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce1)7h7llvol r)mh.o bn1;c pcy a sound level of 95 dB when fired simultaneously at a certain place, what will be the souo77lchrh o.lp1vn by)ml;c) 1nd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane witf 6a7d;4s)) q. xwji+*oy flpcsxj5rhh four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thi as+j rjl;x5ci6psh o7qd ff.)y*)4wxs 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 lp*c4b np6i q+ln2 tnhs5h(d5of 58 dB, whereas for a CD playh+n*bd nlsh5ct6 p(ni4pl25 qer it 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 a-s 6in+ l ./f2tt/jm2oyeq wjoutput of sound from a person speaking in normal conversatio.nj m2fq6j/ -t/ tos+w2al iyen. 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 earoeb 9u7g g)b3rdrum 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 Wtv3/xvsftr0*5: fdbj , while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poivt03xvdr5 tfs /f:j* bnt 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when place ap,)wq2j-.vuj u6wlxd 2.8 m in front of a 6wuuv -jw lj.pqx2 a,)loudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect apc 0hw72 d,emgoa 9)bq difference in sound level of 2.0 dB. What is the ratio of h,27gewobq)m 9c a0pdthe amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,,jh u41rgxo1 u:zu:bo (a) by what factor will the intensity iuoxu jho:b41g :z1r,uncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have euj 6g;nx4 h1lnd f6ye5qual displacement amplitudes, but one has twice the frequency o dx g4y1;n65hl6 jneuff the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a soundt3bhv s8jw v210 jhj8f wave in air that corresponds to a displacement amplitude of ts j jhw f031bvvj288hvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud aswp.y/tm-ns5 -ml xwf5 a 100-Hz tone that has a 50-dB sound leve .pt5mfwm l n--/w5ysxl? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ejle 4y h- + l4fwy184rw+xufztar can detect when the soundl4u 4ef+h+lwft- xjyzy41w8 r level is 30 dB? (See Fig. 12–6.)

  Your auditory system can zjm/xxs 3c1 .naccommodate a huge range of sound levels. What is the ratio of highest to lowest inten/ xzn 3cms1j.xsity 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. Th)dq8iq; koihu -x 8;oze length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mu qq8o8io h-)i;d;ukzxst the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first ths(ph 1l *xljom9a zgao31i4w)ree audible overtones if the pipeo)a13p9zl1 moij( sx4a wghl* 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 the top o5)zb vksqyjbh1 yv 6,1f an empty soda bottle thazv , ybj 1hyqv)5bs61kt is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe o* bhi*6.ge(rqm x sby-rgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of t y ix*b mbe*s-.6gh(qrhe 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 harmonic. 4bseb6m73at4 r clg7l What will be its fundamental frequency if it is fingered g7 bl3ae 76mlbr4tc 4sat a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to .6gtmc4i vd 8nplay E above middle C (330 Hz) .mi6dcn4gv8 t.
(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) whfw*kvy8u4jjv :5*f8 m y1fbx sen the t845j1bs8vjff*f yv:* w kyux memperature 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 7bme4du,a 49.ada l6+bc me wdat 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 Example 12–10 should the hole be tha(g(ypnb q8/7s gfta9et must be uncovered to play D above middle C at 294 7bt(9(gpf8sa ye/gnq 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 not at cm qc*6r0sqx/ any other freqq0q *r 6cs/mxcuencies 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 resonati(*fbuoj 4g m 4epxl1 m5it+-jes at two successive harmonicji gf ei5+p xt4(m14olm-*b ujs 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 d43; k9one5k:xoo cm x$^{\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 with su 9-kij l x*p*gur k*zf;50yspa2:wvin the audible range for a 2.14-m-long organ piyua5irpg ;*s*kl9 j s2up-v w0fzk:x*pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the k ay76.z1df,q wjw. ueoutside and is closed 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 gray eq 7f,6u.kjw.za1 wdph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one k jna8,roac4 6beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequna,jocr84 6a kency is the other string? ±    Hz

  What is the beat frequency if middle C+h,jne zrtoxa 5ly o7l jo lr3*/3*a8f (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 2 0;r ng3*lcrx jm;qh18s mlnkanother (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 the ok0nq;x r12n*jml 8 hcsrmg; 3lperating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3509rc nip h rqy.p;(t4c;-Hz tuning fork and 9 beats/s when sounded with a 35(qhc.cr p rp9;nti4 y;5-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tunen vy+x 10 *iekcmcrie(q41 n7fd to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two str 04yrii+nxck neq*mc(1 71evfings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard iy+s4; 9bf e htp k,tavljg/.f:f two identical flutes each try to play middle C (2:.94 thab j;/fsge,tl+py vfk62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frvjwz g8i --ldvx74pv+equency 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 v+l zv p84gdv-iw xj-7are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and :k+8r bsyh2q u5j oq(p3.50 m from thejb8q:pqhu(sr+ 2 5 yok 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 ;p8h79* bowlkv+lntv be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s l7pt hb+; nklw*o9vv 8when 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 2.6u1v dzy j0i(kapql4 b+)od y.74 m and 2.76 m in air. How many beats per second will be heard? (A i.+qddjvuyl)k4ypo 7z0a 1(bssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 H6 /hpf.e4pap,m phnw2 z when at rest. What frequency do you detect if you move with a speed of 30 m pw2hfphp ep6/nma,.4/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frej/:ctc5/w0y andaootbh s5oa6i / .(tquency do you detect if a fire engine whose siren emits at 1550b5d(w/ooctyc0 hasot:ij.n /a a /6t5 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sou 8fviyj()uub: rce is moving toward you at 15 m/s verb :uv(fi) j8uysus you moving toward 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 wi8ltgedmq;l6/nu0/ /l edc: ow9b3vdu th the same single frequency horn. When one is at rest and the other is moving towalt/d0ul;e:3meund ocb8 wd q 9v g6//lrd the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.s 6r0y/ sik*iu0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the 0*6r sukisy/ireceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, ts-vii6gzb+u qcv1 +-the bat emits an ultrasonic tvs+c6b+ iz1 iu --gvqsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on c+xpq har),2aa moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while axp)ac+rhq2a , t rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe*nz2/mm4kt nn.ccon) (wgj 3f eds. Suppose the device emits sound at 3.5 MHz, and the speemt4on 3gzc.c* k n2/)fm jnnw(d 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 o wng7,tk atf1wv4mqo9o : 4w1zf frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind veu5;56 oq*5d fl;vo6u ixy wkwyy -.cyulocity is 12 myk ;c u*w66uf ydyq5wovo5l.iuy-; x5/s from the north, what 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 movigbu pc fdy ur(*-)+w1png 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 th mgqn z 9iihgk3zu*q,; l+)0yle speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction qzz0)* lgmh+9 3,ulq;iki gnyof the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soundlrdc c96e3y3h;ya-26abi ysm 0+frnn is only about 35 3yyb2 c nhrily69r3-6dcf e ;asan0m+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 76) xsjwej6h cwave anglej7e )6wchs jx6 it 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 wml p cs*e xpprd4 b258h./3(ki8 zguu$/theta$ 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 ground4 p68z:a(qe-fu.3be 7zfxj ree1mq vj flying faster than the speed om(eb4f8euzq: q6zx-p er.fv1jj 3ae7f sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulsb yssiz)x) h6ag, wi+/a0ek,e es downward from the bottom of the boat, and then detects echoes. If the maximum depth for wh+ewke ,6zix0sa)as ,gh i )b/yich 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 2; dcq (u: 1cnll f99cudvwt- -1zszfcin the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called b nt7p)zt (jy(sq /ydqt9rk5dj5 )l* ba sewer pipe symphony. It consists of many plastj( lztynbr)pj (s5 yd*t5bq) dt /q97kic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of wnrj,3oso 9 mvx 4t0c0human hearing (0 dB). What will be the sound levestmoo 4c90 3nrvw0j x,l of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound 8qd ;5c c7.fn7q jpqyjand an 87-dB sound are heard sj.5j; q dyf77cn8cq qpimultaneously?    dB

  The sound level 12.0 m from a loudsp*jqb ) icf8+aveaker, placed in the open, is 105 dB. What is t)bf8qai cvj* +he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outpuipfz/;7 --stn3 wng,zb x +elst at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15-wnxz/z+ 3 ,;sb pilef7nst-g kHz?    dB

  Workers around jet a1uznov.fo(* e47 fhlaircraft 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 avu7 lhfav4oeo. (znf1*erage human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,h1)z yk8/*u7ku) o u;ftbtkxlcr bkw f p2,g;, 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 bgnw8*q9k o7 4zi/r1sn,plvt tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundaji yt(tw2t q9.t-m. l:+fsvprmental frequency of js.ilm. fv : 9pqt t(+-2ytwrt440 Hz and 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 vertical i ls9o4kt:e(kgb;3re1iu-bq 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 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 b g:9i;ke kqi (l1bo43srt-ueis the frequency of the tuning fork?   Hz

  A 75-cm-long guitar vz(8 )dj 4je1 aivac.xstring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How m jcv(ai av8e1z4)dx. juch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed toadr hxyryf: h7e**8(b 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 t4 q, 5ulzl fiusm4 )c7pq)r:oin the 500–1000-Hz range coming from two sources. The sound:s4q 5uz)r qi f7c)ul ,tp4mol 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 stati goss(jog/z.nmz )e3 (h:*bfg onary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachzsj(/ sg.*zf eoh)3b nmg(g:oes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isq +n;qo 8dbw:u 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vbq:;dw unq 8+oelocity)?    m/s

  At a race track, you can es2h4w8 i8or.vu wpci; mtimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the s m.;whv8ouw4i8ip2 rcound of a certain 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, produjf*pmxp f o8+-ce a beat frequency of 11 Hz. The shorter one is 2.40 m lo-+pfxpf* 8omjng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p81b9tdr dpuz+y xtl lh/- 5t8vast 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) x drl8zt5tpy 81uh/9l v+-btd he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0x hn 6g4dp(0fmr,k0tr.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wagkpx6rf0(m t,0hr4d n ves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is f *xma khh1:k90d gp3nblying toward the bat at speed 5 m/s The bat emits 9kpb d*nm:g31khxa 0ha 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. T:si b qu/fdq5ybg7f00wza9 z+he pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth 975/zf:b0y qai ud0fw+qbgz sbe 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 (;p/ dwdlea g:; m3cyzsend 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 resonating. The mosc/ ;y:pwz3emg;( lad dt 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 be compromise8ousl v-la3bzx,b.y.ot g6)ljd w* .rd by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the prego.3vtl 6 wjx..u lbb)ra*s o dzy-l,8ssure 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,” involves a long, s,v l 7;wihb;bplender 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 i7blb; wh,p;v 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 at a frequencn)g:j; xylru 9u,q m02x.q dayy of about 100 yxr2g)y,jxu: q0; udq9n.lma 0 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 on the ground hea 4:5x*ayg ejywrs the sonic boom 1.5 min after the plane passes directly o4wx 5*jyagey :verhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat- j7)be a 5ko5+ljptjm is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h