What is the evidence that sound travebnt 6 ,huk,nt1ls as a wave?

What is the evidence that sound is a form of enwr(zp-a b.+kf ergy?

Children sometimes play wb6v+ +i-xinglv,5ul b +vfy2 cith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cupb- ++v fivxn2,l6i u+5 cglbvy to the other.

When a sound wave passes from air into wate j5apm;c2i3q 0b -p05 tstigvpr, do you expect the frequency or wavelength to chanptc jip3 550is-m2;a qvp0tbg ge?

What evidence can you give that the speed of sound in air doesknt,f5owo8 z)k h, )e+bs)ufj not depend significantly on fre+o),oktke))n,8bf z 5s wjhfuquency?

The voice of a person who has inhaled heliumyn e hgp84ak2( sounds very high-pitched. Why?

How will the air temperature in a room a-uv/m/c s 57oog;*hrx awir(vej / 6lyffect the pitch of organ pipes?

Explain how a tube might be used as a filteraup( 40joqs (tl 7q6nerhb3vf3)w1yd to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufh)7(fuqsdrq b3 1t 4o0 an vpj6y3lw(efler.)

Why are the frets on a guit+1 ghgk* x7fuevh e8.sar (Fig. 12–30) spaced closer together as you move up the fingergh781xh. vkf*e es+g uboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear b85178zlfz nch f9-z5wo j f8lk5ivdx it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-d7wl8 z5z5nl fxk1-85jof hz 8fb vci9frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference inz3/r3g f6 ehxr space,” whereas beats can be said to 3/er 36xrzgfh be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency op0tk)iyuza75 f the speakers were lowered, would the points D and C (where destructive and constructive interferencep z5k ayt07)ui occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas ejhja6lx b m6h 07/(iwwith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient (jbalm e jhixhw67/0 6noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. E.) f5(;uygdo q9qqbkyach wave can be thought of as a supk f9yq bo5; qqygd.u)(erposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler sh2 3f3mns:/-bhr)wdtnx3hy i;/ wgjkoift if the source and observer move in the same direction, with the same velocity? Explaihnosjhw d// -kimfx)w; gt2r3n:yb33n.

If a wind is blowing, will thiag8w9 w 5vla:ys alter the frequency of the sound heard by a person at rest with res9v8a 5w lyagw:pect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moi9zq mdo0r.9x*k 6twftion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequencydm9 .kxtri 6 qz*o0w9f for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echov+ 9e :pcmac29m*z wno of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aft2+9cz:mewmpa9 on vc *er shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just beloqcc4gvd yz*vt.uly u43b,hxo9z 8 5e1w the waterline. He hears the echo of the sound reflected from the ocean floor directly vvql.y81zec y ,d5u*z3ut9bg hco4x4 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 f3okevh y4nd+ 8eh60b air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggyxvvg7fa 4q/1 bhf(2 pg day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)(1ph f4aqg/vfxg v72b. How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when stf-f,skb u wv5) cg*f;ro(lvm c l/p;e*l1kds8riking the water below is heard 3.5 s later. How high is the/v-)sl1p(w m5r*dsku vl8 bck ,fl;ce f*g o;f cliff?    m

  A person, with his ear to the ground, sees a huge stonjdvk s epx+p2l .,,hdf d87vc-e strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the oth2,e .p7hddv 8l+,dpfsv- kxjcer 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 maktkj5g0qm -bo .4d9km(m nxfiu0g5e270xma l de over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30u2 o5amen4d9(ik j0lkxtgbk.-0mm 5 xm07gqf $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ;zi3k b-qaz/mat the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of ari/txqbq9mj*61 1dq o sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultrub. ql,5x9bakjc/ vm )it3hc1kos*2 aneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add inhojmv bkbqa *2 ,csr9itl5/k . xc13)utensities, not dB’s.]    dB

  A person standing a certain distance from anq(ess8u)r 7a3trnea- 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 shusu8 t(ar-eraq 7e)s3nt down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a si0 xi5hjyea08ognal-to-noise ratio of 58 dB, whereas for a CD po0x0j h5aei8 ylayer 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 output of sound from a person speaking fcqbb1or.fh a6l/+h4dp d) (e in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered pac1+6fhbhb qfd/l (o4).dr e 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 wa/1 b* h dhj*f8lw 6j*urskc**6huyqahose 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 i4gsvzxi-3l3v: 9xee ds rated at 40 W. (a) Estimate the s3d sixe:9 evz4x 3-vglound 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 130 dB when syd y5n(rqt22placed 2.8 m in front of a loudspey2(d 5stqry2 naker 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 m z9:9l*u ;jr*z/ jrpptgi7d wdifference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels m7u*j/ rd*j;9pr 9 gtziplwz: differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will theja36rt i:oj78 mtzg9+bj 7iqv intensity increase? Increase b:t9j+6i z7j7oi3rmbatj8vgq y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacmijbv;bxgz2 2ff,f (:tq q:3uement amplitudes, but one has twice the frequency of the other. What is thebqm z3u:tfgxvfq :;2 (f,ib2j ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corrm95n+ atgh4)qwyw q dy0rui5 an9., nfesponds to a displacement amplitudew m+,.irtn quay59f 4)qag whnd 09n5y of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must ht4spw/;n l.rzl1w nb0 ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB soun0p;l/ zb t.lwr4 1snwnd level? (See Fig. 12–6.)    dB

What are the lowest and highest freqlmrb by xu c gj1a4rvov/1 r1617ufe)1uencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) 61 1 1xlrybu jvcvmo) rufe/17b gr1a4

  Your auditory system can accommodate a huge range of soun6j gwc 0tg2+bjd levels. What is the ratio of higheg6wcg j0+2tj bst 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 fundamentalp 2p584t wm9xom lrf7h frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35lom2x9fp5 8p 4thmrw7 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whau 6aw-6ogopj0.1opk 7yg 0vxu t are the fundamental and first three audible oveg 6pu 6o0y0pa1kogj- x. 7uowvrtones 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 eyf*/y1k 7/c f7r klem. v;cfz4afy t:sxpect from blowing across the top of an empty slsfyf c/y c :ft;zm/v7ea*rk .fk 471yoda bottle that 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 wi 1)n6obctodnsgl( ,3tdt8l.c th open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes ren, gltc6t tlo1d) 8(bds.onc3quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a 2miodandn:flt/ . dk:*5ov-a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it/a:nv.lfo2n5k di*ad: odmt - is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovem f c6;gclx -gz,(vvz2 middle Cvz, 6(g mxvzcf-glc2; (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 of an open organ pipe that emits middle C (262 j hop0keybjx:ey8f461u ow 95Hz) when the teu o6b5x4p k0e he9j8o1 wjyyf:mperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2w o6 f2qays;gk(g :dz.0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should trhuzz4 x7hxl:jul x/d:trh8a ) 4oq)8he hole be that must be uncoveroh4 8at:)x x/)hl:qrxhu 7u rzj48 dlzed to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ peb(pi e ((ith,ipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an o tp,h((i eebi(pen 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 pwe cmf6e)8 pel*bzhmj46m.;is open at both ends. It resonates at two successive harmonicf 6wemlp)mej8.e 6mzp* c; bh4s 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 lw;,b2m .a6n ixw2vj z$^{\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 fob.db: :fvt2h er a 2.14-m-long organ pipehef2 b.:bt d:v 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 txc0 t1te fm: rrvp8jd(.2mk(uhe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the sta(rvck8: m t( fr21j. mutd0pexnding 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 onemvh (hq4)a+q3w5 2uea3 nafo *ymnmz3 beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other styau 3wof3 n*em+zn3(5m)2mq h ahqv4aring? ±    Hz

  What is the beat frequency if midx/ fwf:l4tmm 7in;, 1na)dajldle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand t gh k obmp8ez:it*,3)X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine *h gtmpoe:k8i3z)bt, of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beh7 eqr4f)* uzlats/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 frequenc qzrfl*eh7 )u4y of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one sgcmnc .-kv17 ftring is then decreased by 2.0%. What will be f7g v.mkn cc1-the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fr skcl*rm)d4-lutes each try to play middle C (262 Hz), but one is at 5.0°C a)k4rl-csdr m* nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a ys13p; c+a*v uwlbp;zfrequency 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 frequencb1p+cuyp;wazl ; s3*v ies 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 person stands 3.00 m from one sp 7rr-mo;gdv9 ayr1k3oeaker and 3.50 m from the other d9g1 rr3;a vmo7-kroy.
(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 tlf7 , m77psfkw0lu cpv9nac7.uner hears three beats every 2.lf 7,kpm. lvwnu 0797 fapcsc70 s when 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 m1 .8vn8efz mvjst -o1j and 2.76 m in air. How many beats per second will be hearsfmtn8jo vj1v8- z.e1 d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’spous +l4vsuz/d 0fw83xn;j.kym h5q/ siren is 1550 Hz when at rest. What fo ;s8m0 uv4lkq5+sz/n fj./ pxhyuwd3requency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fren3 .udksx g74gquency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/k34x. n gugs7ds
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if +9 bm/v*0qrrf*prvmt d hi0 +fa 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies e 0mhpm 9i*rtrrb+ +fqvd*f /v0xactly 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 f4m* wt-v4zoo 44;ocf/6v njnv yhbgh4requency horn. When one is at rest and the other is moving toward the first at 15 m/s 44zh 4tocw-f4;y hbovnj6o*/gnm4v v the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 k6njt 8s iam/j)Hz and receives them returned from an object moving directly away from it at 25 m/s What is the recejstj6/ma 8 )niived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As itbqzx y) a-/fwq jqqx h.2ch/ )42-botj flies, the bat emits an ultrasonic sound wavq/)zw j .-oq4)c b 2thy2qh- bjxa/xfqe with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origina:ru5 v; ,mb invlu*su0l Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and as,5vuu vlr nuib:;*0m 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 speeds. Suz2f -swaywgc 454iih59c *v.nin0veappose 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.yhcsvgn 5i w9eifazwv2i0c4a5- *4 n at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves 8wter* x.tp0i 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 frequency 570 Hz. Whe ++f5-say wbxqn the wind velocity is 12 m/s from 5bwf - qy+as+xthe 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 moving on land if its bu/q0ul,jt u9 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 59vooq jtf 2ub,yyd/)2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes wit d/tvoyq)uobf5 y92 ,jh 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 pla31+f+a gi t97pmm:pz9aylq lanet where the speed of sound is only about maaglm+:z pl7aftpi+9 3y9q135 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. Determin:k6kcp nj57l ke the shock wave angle it produc5kck :n7pkj6les
(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 m*:m vhvxg+cpi 5.t e6$/theta$ 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 tv; ,y*ll m./wctb7 3 qkyxzcy9he 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. Se,cl/ bm.wyyct;v q*kl7 yz93xe 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 pulse 1k2* cn1j3ebwzqy 3ylpru 9v6s downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time betweenryzjekn 116q29y*wl p 3ub3vc pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibl9ndy8xw 6f7 bhe range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disply 3hytvkonmy7q *26 1uay called a sewer pipe symphony. It consists of many plastic pipes of variou 73yn oq2yty6 m*hvk1us 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 cya5+o0htwgd35 n+ wd7dg b4kplose to the threshold of human hearing (0 dB)d7t+ h5gw w+ dabdkopg0 y354n. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundgf 5 bj)zhv(e -1ko*mx and an 87-dB sound are heard simu-bjx(e* mgo5 ) 1zkfvhltaneously?    dB

  The sound level 12.0 m from a loudspeaker, pg53*6u5 )vaiu )cxtpb;tow el i mwh)1laced in the open, is 105 dB. What is t*lo ivxwuu;))mtp ch5eb3g51 )6t ia whe acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W out)9ev )ym phr4oput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in ymp o v))49erhwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oboi8 qhk/t. a6ver their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 16/h. oiaqkbt840 dB, and that the average 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 whn-d1:kjm8l p/w a.csystems, 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 frec;wr4.u kb5he quency 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 mhv;x96ex.w jewox)l eq*q 59 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit ;*5 xqwvwe)e. xlxmhj e96q9olength 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 filled3 xgqkejul9i9 xxduz ;y r2g, pc3;as5rf62a- with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the wat6,a3ipx9 9 ; 3; gxqzu5la2 ke ygj2-ucxrfdrser 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 mas5i2v5 k3lwy* p ggqs.- yv;m8bseqkj 1s 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental moi-y1j ggq5wlq;p 8bsm2e k.vkv35y* sde) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l yy;qmb2ei :v,oop ($\frac{1}{2}\lambda$) 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 two so ygqvat52l-31a;s1 axl8 l2i7ntq oyrurces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the p 3snx8ryt 2og72-va qql1l ly 5a;ta1ierson 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 m t7x )c7 )/qpk7gvr0fkbw o4ytrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches4qvb0m/7 ))ck tpwg yfrk7 xo7. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle u*)(l aheqqe4 as it approaches you is 538 Hz. After it passes le* hqa(4)queyou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spebfx ums2ok)zd3* 4 4b0 x0cfueed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound oku4b0u 0o 3s f4m2fe *xzbxd)cf 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. /p6cfa cv a iq*rzdv)8m90sd 9The shorter one is 2.40 m lo f*/z qasi)dp0 c9v9vdcr6m8ang. How long is the other?    m

Two loudspeakers are at opposite endsvc(8 (;ewen nk- fs.ds of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he isf-ndek(; wns8e v(c.s between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what b5g9e 1r 5wttfeeat 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 a tter5w9g1e5fspeed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth3kpca1gni ((z at speed 6.5 m/s while the moth is flying toward the bat at speed 5 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 1a(i pnkc3z g(moth?    kHz

  A bat emits a series of high frequencylgkz x6h; (j,k sound pulses as it approaches a moth. The pulsel(z xkg;6k ,hjs 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 from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was o qaeeu1)h*kk9u5 nv,dnce used to send signals from one Alpine village e9 daq*51n ekuv,uk)hto another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. 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 compmhee7,.1x i e +wyl1mlromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the press ,y 1eme.x7il elm1h+wure 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 demonstrationrgs;g + e(9nkj87*pcbh4iigy c mlt/ 7, called “singing rods,” involves a long, slender aluminum rod held in the hand near 94c8kg/(b*sie +7rh7;mp cgi ln jygtthe 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-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 hearing9/kg,yt dg+ary5e +rm for the human ear at a frequency of abou9g /r,++t dkyma eyg5rt 1000 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 heay hd3xr48 +akurs the sonic boom 1.5 min after the plane passes dr48k3a hxuyd+ irectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 y6x))dz9/ptr s/i kw f$^{\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