What is the evidence t9neria.ttd7 - c hf:/+iik9,v9r wv ckhat sound travels as a wave?

What is the evidence that sound iql* c ci52hc-(;m2zukcp*l8 qcwe0 ies a form of energy?

Children sometimes play with lz( hk76;urp(p c yx:va homemade “telephone” by attaching a string 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.7l(;p 6ypvuc kxh( r:z 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you ex -yohiw gcsk*5a):4ptpect the frequency or wavelengtcshy:tp -*wakg o 54i)h to change?

What evidence can you gqj2ea- )djg d.ive that the speed of sound in air does not depend significqd e.gd) ja2-jantly on frequency?

The voice of a person who has inhaled helium sounds verjf/obhgx0 ;o+,;gcn y lf39 pyy high-pitched. Why?

How will the air temperaturuhb ./qz b 0xaj-a)4one in a room affect the pitch of organ pipes?

Explain how a tube might9wo4k+e x5tjj be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An exa+xoj5wk 49te jmple is a car muffler.)

Why are the frets on a guitar (Fig. 18raj.fj mg5xggx8259li:4/oh wtfs o 44 ndpg2–30) spaced closer together as you move up the fingerboard towardo d2/4fx8:g.l5 jgjx s5h4onf9 rwm48api tgg the bridge?

A noisy truck approaches you from behibpt(i8u 1qro- q*zg 8knd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15o -tiubqkp (qz1 88g*r on diffraction.]

Standing waves can be said to be due to “interfe 3 l dksv/8kef,u;e/nsrence in space,” whereas beats can be said to be du8v/u /3,des;kknse f le to “interference in time.” Explain.

In Fig. 12–16, if the frequencytwbqjg h3ws mhm- )36; of the speakers were lowered, would the points D and C (where destructive and constructive interference ocsm gw;b3 )w m6hhj3q-tcur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopleo*xb gsc uc ;d7y+ ( ,n)c;/9znbcodtm who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new tco gn)s;y c/ ucm+*b,7 (ndb9c xdoz;technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Ext 2xv* bwgnto* +y.h7ach 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 the two compo2b x*no7x+wgy.t v t*hnent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the ( ;sp:m, r5(nxjqld xysame direction, with the (qn:pj,m;y5sx rl (dxsame velocity? Explain.

If a wind is blowing, will this alter the frequ +cru msq 2x4fvl-rxen,g+g51ency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity cha5+lqrucsgr4 x feg1,n2 mvx-+nged?

Figure 12–32 shows varip5(9gqzw6zka;ko.4t s sffp6ous positions of a child in motion on a swing. A monitor is blowing a whistle in front of thefpzzw.6k9f46 k(5s ;pgas toq child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakvwc.hlq 4hwph*g6uz+9*1 hsk rw6 ki+e by listening for the echo of her shout reflected by a cliff at the far end of the lakg6qcs9wr l+w4 zw pu+h h*h6k.v1hk*i e. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears/tynnvs0 p-6 4oi s*ka the echo of the sound reflected from the ocean floor directly below 2.5 s later. How dee-ts 0n ako/pvi ny*6s4p 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 20 vzp4mp4uyq1vx8 6wm9 $^{\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 o0ol-j r-x b3.oogp3jaf 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 is heard (a) by the fish b3.-3ojxl r0o-o gajp,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clf0nqq-m/g)6 a0a sdh wiff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliqwhm0a 0)-gnfaqs 6 d/ff?    m

  A person, with his ear to the ground, sees a huge stone strike wt ;pp/oecw--the concrete pavement. A moment later two sounds are 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 oc; pw tpw-oec/-cur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ov8*dn j /og8wpz n0u;b+2td kjter one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a /kn*tt8j wud+208zjn dgpo;b) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1jv ti5o2dm 0*q20 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 .t.mbiiaz;/ : v7uvrg whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prodipocm(52 y+iphw b *cw(/) neluce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,wel(yocb(n 5pm* )2i /icp h+w not dB’s.]    dB

  A person standing a b/c xae w1ot 8cd2;2wq6p:,b qnm- indcertain 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 down all but one engi2/8t, cdqdpw qabn;me:1 62x oi-nwcbne? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hs u hkq*pgbpmna.78pk)6f* bvnfd v (8ht9:7qave a signal-to-noise 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 noise for each de d7v f87)bfah q g.puqsp8( tm* p:9nv6nkkhb*vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal r*o ycm6ef37e b-m 2c, (yzecmconversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spheb-7 fce ,ry6c2mcezm3(mo*e y re 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 whonap6n 6kuf 65ose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B irojte9 h p70(ts rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker(rtp7je9 0toh 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 reyb zb ,xvzdd6 z7*a9k8gistered 130 dB when placed 2.8 m in front of a loudspeakez7, da* xvz89z bdk6byr on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound leve 8q4xi*gvu sv)+ 3anz0ar5qsdl of 2.0 dB. What is the ratio of the amplitudes of tw g*nvs5 i)qax r+q034v sdu8azo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound m-jz es:f3 )jgl 8m0vmwave is tripled, (a) by what factor will the intensity increase? Increz3:)f lg mejvmsm8j -0ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has6hkpz7 qe+-oc twice the frequency of the other. What is the ratio of tkc-6zep+7o qh heir intensities?   

  What would be the sound level (in dB) of a sound wave in aiduewbl.s +m h ee9 h)n3aqzx*x7.qt;.r that corresponds to a displacement amplitude of vibrating air mol39.*mz sd.enux; la.we the+x qq) b7hecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1gis )-an*ba6p00-Hz tone that has a 50-dB sound level? (See Fig.)g-6sia* bapn 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the so(y(bb-rmb.qtoz g :n.und level is 30 dB :bgt(y z o(m-n.rbb.q? (See Fig. 12–6.)

  Your auditory system can adk hswvpcau4 /7; y31tccommodate a huge range of sound levels. What is the ratio of highest to lowest intensityudyvwsat4c1; /h 7pk 3 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 fundamend*- ,tk0u juf5az(jjltal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.la,j* jk5tujfduz -0( Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aubz1yiv-e/1 g 5 ouoof*u 9wc-ndible oizcogof 9no-e- vwb/y 5 u11u*vertones 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 the fqi r2e5zqbl 3bxit0tz1+8v-- snh s9 top of an empty soda bottle tbz3tq -0s-z9l tq+1v5fisi ebrxn2h 8hat 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 organ with open-tube pipes.s770/xuzw2 lbys;+rkgbqf c spanning the range of human hearing (20 Hz0lwsy7 fs /b.2u;r7x+kgqc bz 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 freq 1c9mxzd6: zjzvkq 74wuency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a ld9z4cv6kx z:7 1mqw jzength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tufan f 27 wnwe7-:r*dvcned to play E above middle C (3we-cvnr:2fd* fn7 w 7a30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 H bnzd n9;nz-b 0/tfdz4z) when the tempern0zbzd;t/fn b49dz- n ature 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 atj:zlv nx6:pgx4 a.k97 tf1xz7 ff:uak 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 ther3n a*a60/uc wgi c41vlccdv h7g,dz/ hole be that must be uncovered to play D above middle C at 294 H*dgc6h7ar3vdi vcz,c/0 an w41cl g/ uz?    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, b secthsl1meogj8 3- d*6:g6ao 2)d5vdha7regut not at any other frequencies in between. (a) Show why this is an open or a closed pip6s76h1h g-dgja)loce3:e 8 s 5vgtmd r*2oedae. ----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 two sut8h hjae5r ;0mq4wmn-wx: f2pccessive harmonics of frequencies 275 Hqph:j;x nmwrt4 -eahw5 80f2mz 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 k1n v*3vrl 5tzn cm-u8$^{\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 trs.wr iwiq-c+0z19b ehe audible range for a 2.14-m-long organ pipe r rs+c0e .zwib w9q1i-at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm/xqlpow* /-pmqh;ui3re wz*3bn;3yu long. It is open to the outside 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*wun-ruw; o;q/ l3ep3b3xpm qz *y/ hi to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,)mr1;w i7fgtvw 1,hch rfdb(1f gi*k3 one of which is soundkdc1w1*ifh( b wmg) fih317v,tr rf;ging 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2i d rb+(arn46z62 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 (brand X) 7)jc dytu; cx,operates at an unknown frequen;cjd ct ,)7uxycy. 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 operating frequency of brand X.    kHz

  A guitar string prodz8oaa r 6cv31dxtsy://y 3joea,o:jm- 1 ir ebuces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats//r oa/ma,3:3jov1yza oersbed-yi8j x:c 6t 1s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the 6a*ly,y e /vcfsame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togea 6/lcvfe*, yyther? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identi1ed (0+aopsiagdb9+y b:hw. c cal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the otheriy(g+ ed0bbaa .+ ho9 c1:dpws at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. pzw x.gbn/,0;rws znn 7+ t,qsFork 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 togqng+ , / z;ts7xprwn0,nz.sbwether, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A :;jp8nxm6y3b ib dkk 2person stands 3.00 m from one speaker and 3.m k;2ixkjy 3 p:bb68nd50 m from the 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 tunptxdj .bz)xf 2vn:el 97gym.:er hears three beats every 2.0 s wb 92dytng:. mx:7vpf .jz)xlehen 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 wavay w 1:sg.1 ;ytu4lyuvelengths 2.64 m and 2.76 m in air. How many beats per sy ;a:l s14.yywug1vu tecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550ivnps 3 n(1b+z Hz when at rest. What frequency do you detect if you move with a s bs(z3n+vpi1npeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wh g7jpxgj q.;.)8ybkmihter/ 7at frequency do you detect if a fire engine whose siren emits at 1550 Hz m7rt.h ;.yegb m jxjq/7ig )pk8oves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20; gpcwp p+riw*y 9k4y*00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15pw ypk49p*y+ i*cr w;g 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 frequencds2(p 3dy5c:gdyf cgzln r;59y horn. When one is at fgd ;szlg3 :(c25d5pcynyr d 9rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50oa6thze, wmgh)t/ 4(fi*( v i,lam-bt.0 kHz and receives them returned from an hte/ lw*6,mb tiomvtgz( )ifa,(-a4 hobject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat vp 7zyzv392vfemits an ultrasonic sound wave with frequency 30.0 kHz. Whvz p7zvyfv329at frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tr2 *kqyva n-6ihm+ :5xxpyw (duba was played on a moving flat train (:dm2 k*rihyanwv5xpx6-qy +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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow a,wlya2all *t 508myy1qn cs*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 th2an1q* 8m t*s0cayll awy l,5ye expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency wbkf)a jt1 9,g $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is xoq trz0;+xr *7s5vmn 12 m/s from the north, what frequency will observers hear wh ntzx05xos m*q ;+7rrvo 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 object5alr:z dbb n(afw(qz4 sk*(4i moving 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 whered x9y2hkoqxa c:0/2m s the speed of sound is 310 m/s (a) What is the angle the shoas mhx9d0cxyq: 2/2 kock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed oi d+ 5u+oa xrrjvfb26j+lir3;a u4ai +f sound is only abo2 +f6duu;+j+ax r +ia r3ar5iolj4vibut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine tm a *:qmf3hbk8he shock wave angle it producehmqa mk*b8 f3:s
(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 fu x c :.utg0c*f2rr-p+sp4dh $/theta$ 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 ground frfx i(v+nvifly./ b ;m1 1v(tclying 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. Seem ( nr1vfv;tfxc /vi1(+i. bly 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 l qdr:2)( fdou0ggvnt8jv2 ;ssonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 u v s f l(g2rdo2)t;8j0ndvgq:m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how ma*7l2y xgf3zisdpqdh ;4j5r y( .: luagny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p c ego;f74lukve oxdjz8i:(fc6s3 z79ipe symphony. It consists of many plastic pipes of v784 jox cs d cezo:v6fk( lu397ef;gziarious 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 cf75(ksak4w hi. w 0q7,d4) v tiyfvrqflose to the threshold of human hearihid4.i0wkvfrv7) wf(q7q at 4,fy sk5ng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level 2pf4u ghcv lj)bt8/y 4when an 82-dB sound and an 87-dB sound are heard simultaneousltf4hup8cb4lj y) g 2v/y?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. W+pl u64i bhqp4hat is the ah 6bu+i4l4qpp coustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ogpc d/9a64i6b zne tl2utput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the 6g ld nae9/4ip cz26tbpower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear plezy tz5,r1p6n3ic+j rotective 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 huma6tc,i5jl rzn 31 e+pzyn 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 yw:ilef9x/6 mdx8i*pn *ck :isystems, 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 tuqzp ou 7qgv5s+hw/v,gpn/pu pr-)7m( ned 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 hvzo 0 az*1;ohbetween fixed points with a fundamental frequency of 440 Hz and a mass per 1 h*a voozh0;zunit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fill-1mj9vkzh1qq ed 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. Wh9kzqq1vjmh-1 at is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a.9b(mxeus1ntz47+2t 3(*clb l tp zfwobm u:u tube that is open at one endtbf uw*mc2 tu zl+ lue.z9:xm(s13b n7 (4btpo and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f : h2b cufjy11nf003ab4q,wijbbl6cmull 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 500–100. nqot f.-1oi0v 9( nzhrglf:k0-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther fr-rknff:h.inzvgo( . 9 oql1 t0om one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor of,qo0dzr9- y)b ak f)s z2wc)qn the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the z2rdf0,-yqaf bo) w )cszqk)9 speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you isg- w 5d0bahmbm e12eq) 538 Hz. After it passes you, its frequency i q-we5bmag0 d2e1h)mb s measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeningg ya. i,u8m8w5kiil. q to the difference in pitch of the ema5w iq lk, .i8.iyu8gngine 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 fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Theb+bgua8ycn n4do;701oh( c oi hc1u 0bcan i7g4doobo8yn+(;shorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposifjzgok0; ; (dxte ends of a railroad car as it moves past a stationary observer at 10 m/s o dgj(0x;kz;f 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 have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3.vn ub;q *aa7-l k2;:x axxdit2 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with b.v*7-axiltxudk :a ;2aq;xna speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth 9jiv rzt3l nmn.3w4yes9v ;6 qat speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a m; jnnwsi64vzlrt39 ve.q 93 ysound 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 apid(i k5av*k uii 8.1.djmol g*proaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that i ik*g1 .l.(d8m5ujik *o vidathe echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine v/6ce ym 0ob/c0g3 okm42 fuyvjillage to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were o2o6ccj/my v 0 /ufmeygbk403used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency 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 by the presencew vim5l7rh1w 0 jlz4rz8*o3zy of standinlzm*zj78 r0o1wvlz5wy3ih 4rg 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, 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, cap*8k my jyb0o9lled “singing 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, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-o8 jm0 *yyb9pkcm-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 oj+i,gvat k6e)f hearing for the human ear at a frequency of about 100)tj+6a kev ,ig0 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 hears 9s qg7nvmg,a q 6).ksothe sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altit a7q,sgokm)qs vgn69 .ude?    $ \times10^{4 }$ m

  The wake of a speedboat is 18/z z o pv3/z8ryuo3nk5 $^{\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