What is the evidence maf+g)vgg / 18 +bxjlllmqe(+ that sound travels as a wave?

What is the evidence that sound is a form of enermo *r.o( 1i-5ovbnns z8 7 nhhnx,g(thgy?

Children sometimes play with a homema s7 pq,l5* bmvy6ssr8lde “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child q 7lyslv5s,*p b68smrspeaks 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 i9jp iz3 x1 pe8fo 7-tac*4mvcinto water, do you expect the frequency or wavelength to chan a*x31ojzci m9 ef-p8c4 ip7tvge?

What evidence can you give thmd8 tqo:: 3+t 9p mrbhwewh)(mat the speed of sound in air does not depend significantly on frequency+p9 omh:e3h d)q 8wrbw( mtmt:?

The voice of a person who has inhaled helium sounds very h-,wyxnv pbou c5b;x6 z,0t4x nigh-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipgw* uevz:apkjt4e0 q s2yq:62es?

Explain how a tube might be used as a filter to reduce the a4j n df/cjb.db2(1vl gmplitude of sounds in various frequency ranges. (An example is a car 2f d.c/4 bgvdj1bnl(jmuffler.)

Why are the frets on a guitar (Fig. 1*b t 82xp)zijd2–30) spaced closer together as you move up the fingerboard toward the bripdz8bj*)2x t idge?

A noisy truck approaches you from behind a buigcwd y5570 d6fcf g5 p.ohmt/k6rir+elding. Initially you hear it but cannot see it. When it emergesmd7e /5hygcwrftp5r6 k .c+io5 df0g6 and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intz,glcs+ f5k8 herference in space,” whereas beats can bez+l,fk8c5gs h said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speao0sqyz2/3vlc/ o o *ehkers were lowered, would the points D and C (where destructive and constructive interference occur) movc0 / seol3/vhzoo2qy* e farther apart or closer together?

Traditional methods of proqm 1.zd q0i.kztecting 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, a device is used which detects the noise, inverts it electronq1mz.k.z qd0iically, 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. Each wave can bir.;- ael 1dw)qf1nhze thought of as a superposadzrqn)1 h.1-wl e ;fiition 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 shift ifb(,hcl ,gq+bn the source and observer move in the same direction, with the same velocity,,bg hq cnlb+(? Explain.

If a wind is blowing, will this alter the fp6, e9a7l, (qjlmxbf rrequency of the sound heard by a person at rest with respect to the soul a fb6qm9e,(rx ,jp7lrce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mo p7uk 2d:7xdl(( 7ct3okryql ynitor is blowing a whistle in front of the child on the grouukldc (oq 7723dx7ryp tk( l:ynd. 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 len 8rk3y5smb osq0gg. tht//8ntgth of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the lengthor y3g . 5/0mbnts8 g/s8tkthq of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below 8*8kyhe bn;ay the waterline. He hears the echn88*e; bykyha o of the sound reflected from the ocean floor 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(a c p7 ig*7;o6seesos in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dao 1htu*n)3eiemz+x s (y. Without warning, an engine backfire occurs on another boat 1.0 13)o(e iezhtmn su*+xkm away (Fig. 12–33). 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 whedo, d,7nis4 pdn striking the water below is heard 3.5 s lid,7so dd,n4pater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pave4)l zwje8ah ciu5,o/xment. A moment later two sounds are heard from the impact: one travels in the air and the other in the 5x) jl8h/o4,ezi cuawconcrete, 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 errorah ;zu)7d ppcb3bh0 n:je4vo 7 made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tempevpnua7ebj hob ch 3d:70);4p zrature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity o p a5svw0ve),zf a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level oh vou hmk za8;d,ms(:b(0,yp 1asppp pa+-l(bf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whenaf+ ows:g8.yd fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint:d f+syago8w: . Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy l1o q/ s7olmkui9e0 9g fng67xjetu 7nsogq7k9/e9g1ml0fo i x6 l 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 engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is.x b*e p(3o/0ye0d-s puwtbd p said to have 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 ea ob0p(*-we dd0tpx.pb3/s yu ech device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nueputul8w 6 g.h53s5d ormal conversation. Use Table 12–2.uutgl8e 53. spw du5h6 Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose/h0w1 ,hx*r63 emdxd pr1 refw 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 rr iqvy:io/p7 b4)b;h 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspe 4 pv:brb y);/ri7qhioaker 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 regis9k dtow aufd:1fj3s+8tered 130 dB when placed 2.8 m in front of a loudspeaker on the stak:o3f1 +uj8w9a tdfdsge.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. We nc59sqxmo6pp: 6y5ihat is the ratio of thee6m: q5p6 po59nyx isc 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, (a) by what fact:socfjn s u*y*79kxx7 or will the intensity increase? Increas j97y:sf cukox*x*s n7e by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement82oy y+k)lnqoiof6q4 4d2 wq b amplitudes, but one has twice the frequency of the other. What is the ratio of their intknoy+doy24fowl)4q8i qb2 q 6ensities?   

  What would be the sound x:j*p 2..pc hix2rh mclevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hchjhpm .*xpri. : 22cxz?    dB

  A 6000-Hz tone must have what sound level to seem ;a)e3narb0zk ) :jxv uas loud as a 100-Hz tone that hasx)uk:jaaz0v3en; )rb a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tbo - 8-w4whhgshat an ear can detect when the sound level isogwb hh-84-w s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelmu mnz9achs/ ) 5.gjn-s. What is the ratio of highest t.u schjmm g-z95na/n)o lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length oo-tm(ot 15o ewf the o e-(o ot1m5twvibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundame(: m 1ljmb3npdntal and first three audible overtones b: 1nm(3pmdjlif 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 tz9m f54 pdqs.from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubeq9s m tz54.pdf?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ wiqbdt4*mzy:j*-zz bl/ 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 required? *dzl /:tqzy*bzjbm4-$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency 6 -f fmjdz)rx(of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered fj-xm()zrf 6dat a length of only 60% of its original length?   Hz

  An unfingered guitar strin6f.o*n lup(uv)e hgx 83)cm0t ia ;tdkg is 0.73 m long and is tuned to play E above middle C (330 Hz) f6pv)ugcu)0ndmoi xe.a(k 8h3tt l *;.
(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 orglvow/ yxwqh* 5 9s5ee4an pipe that emits middle C (262 Hz) when theh 5lyqe*4 w/eov59wsx temperature 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 t kg4o3dd2f0yvn)l 6c 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 hapr0,- djr8w +/ y79x kufckwkole be that must be uncovered to play D above middle C kw+dcp70 rxwkufykj-9r ,a/8 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 pi:.whpja- fvk1x-9fp6zy4 ;os5j5edj a5tzut pe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequenc pktewjftp1z.ds;56 v:j5 ax- 59uyz-haf4ojies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates an p ;sz sa(ip0ri,1oc3t two successiv,r spzc(01;pnii s 3oae harmonics 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 sp v k-ixl+ em(luyka)nt743;$^{\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 0fhh lt-vo5s3within the audible range for a 2.14-m-long organ piphfsl -ht5o03 ve at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelqd ipybqit07413a4w xy 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is thti y0d7pxi1 qq4aw34be relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust*gl* 3amn4-dzr +m 3tbdb qxb2 two strings, one of which is sounding 440 Hz. How far d4gx n* dmtlz*-br2b3+ qm3ba off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and 52ty, i ett( 73)umilc.y(vak m leob,$C^＃$ (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) operates ggtydj0ph(joa- c ; 98at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of freqj( hpga9- ;yd08c jgtouency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and r;jbz 9 8v 8wnwd3u a5rr1fu,e9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of t3r ar 9j,uf18r8e5 z;bu wndwvhe string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Th w1o2 x:ax5vda; z5cuse tension in one string is then decreased by 2.0%. What will be th dc51os2:xv5z; axuaw e 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 flutes esl - ;fzrgmbk3h )fo)-ach try to play middle C (262 Hz), bshlr3zgomfbf )k-) -; ut 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 frequency of 44 lnns90b.e/4o is;iij1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togeth0s4esn inijo;.li /b9er, 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 person stands 3.00 m from one speak 0nljkhlxd5f10/ cjt .r6po d*w7cuz0er and 3.50 m from the kpl/r0two zxdd1fcnj70.j 60*hul c5 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 ai;v1y, no 5)hh wac2ti piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the,i;h5oia) n2y1thv cw 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 2.6i0v:-wxgh eu6d2ask;r dm+-u yl27px4 m and 2.76 m in air. How many beats per-6e:u dws-7yukr2;+ lvgi2xmdxa0h p second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eo t+2f3oq(5iv2 ovsxjngine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of( +sifxtqo2 52v3ojvo 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequen v98s)j2bcj7erch nu:g xld( :cy do you detect if a fire engine whose siren emits at 1 ercl :b):n g9c(jxs827vjdhu550 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 source is moving tox)p9u+qx;g9 m8z0l, mo wf japward you at 15 m/s versus you moving toward it at 15 mpm w z0gj9 o+p;xu9x)lfq,8am/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 frequency hog/ks2ew i1o*h4 /py+ydxg m5z rn. When one is at rest and the other iyyxpho4ksmg/21i *g5e w+z /ds 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 50.cujyb(2nr h3mi -iy3fy;;/t o0 kHz and receives them returned from an object moving direcoym ;(tnir-;3cjfbiyuy/ h 32tly 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- qoz)rvthu5* As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectt)zou-v* h 5qred wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen,lk(wtk9h5 +egx: pzw ts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone whiw ptwegxz,l5:kk9 h+(le 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 bgxgla4p 53:y m m4f tjzhs5upim/e2wg)(qh7 2lood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing7 g2hqm: gjax)hm e35mz4 ygs t (/4l2ip5fpwu in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultras0ghd g -1j,htnonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fre(xcj-nbey - *gquency 570 Hz. When the wind velocity is 12 m/s (bcye *x-g-jn 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 moving on land if its speed at 2ffad+mpb / 1c7- vel+t0wwo4g 0 $^{\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 ( l( dyyrmde0 yl+e4)uwhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplly(+0 ( my)luderd4ey ane’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 c:fmga(,a8zt- mk,qx the thin atmosphere of a planet where the speed of sound is(gamt8-c fq:ak,zm ,x only about 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 the spl,ze ;v + 2pvlt5jxe+hock wave angle it produ p+tepev2vj ,ll5z;+ xces
(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,9: qlq:d)sy)opj 0 - 90vuu/pdi v fqvvinc$/theta$ 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 abw*su,.v hog yy5e z9a+ove the ground flying faster than the speed of sound. By the time yo 5avh .z+e*uwg, s9yoyu 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 pulses downward fr:cgo(rvtpn 2 ik*v5,iom the bottom of the boat, and then detects echoes. If the maximum depth for which itr :ngv k*pv(2,ci5i ot is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many om 3qkv zzc(ug-m;-q 8i9ozy p*ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists o1qc zot 4qr)r uy8 4lwy9tgo3*f many plastic pipes of various lengths, which are l ruoo w3 zyt8g* qy9c14q)rt4open 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 make /1v firm*mu7ns a sound close to the threshold of human hearing (0 dB). un m* m1ir7/fvWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultantzdbw(83zp2ebh 5wp: (mrq kr 6 sound level when an 82-dB sound and an 87-dB sound are heard simultaneouslppz rbr3kdm(z qwhw(2:b85 6ey?    dB

  The sound level 12.0 m from a loudspeaker, placed in :(0 0)*twubp)6r)i gto z ywu :uxdfvvthe open, is 105 dB. What is the acx:g:*pz ytt) fov0ww)vr (buu)id6 0uoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The poweg/3d7ump )i (py3v jf;jt+bh0f ho: ldr output drops by 10 dB at 15 kH3yf/td p uj;(opbj)dh3i0h: flm7+vgz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. fc(bc-fs 2 hq0*pz; ynAssumhns q(ffb- c;2z* py0ce that the sound level of a jet airplane engine, at a distance of 30 m, is 140 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 systems,hy .g0yt/ wxr ;y3q p5bw4:h6 wjb3mpu 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 frei3 7e yu/jjehqqj9;j2quency 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 b5h m9*-d4cbvn, 9) u7soiwm4prkjan between fixed points with a fundamental frequency of 440 Hz and a mass per unit length *jkbmwb44vo5h 7n psr9n) uc,d9m -iaof $6.1 \times10^{-4 }$ 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 filled dlo1jij,+: aoo0u g5ewith 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 do:,o+aj01ju golie 5is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of manhr5dyw 0c wrwpze(*vh+r dv9u0 b557ss 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 mode) with the third harmonic in the d9ynr50 b7 w uh pz5e50rvrc* vd(w+hwtube?    $ \times10^{ 2}$ N

A highway overpass was observed to resek3rbd:p i+/po l9ak.onate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. T3k* s l3pvp5oxhe sound is loudest at points equidistant from the two sources. To determine exactly what ths3vp lk *o35xpe frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The88 o5 zd2lmoet conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the s8 det mozl285opeed of the moving train?   m/s

  The frequency of a stcgbh8/ g-xo y8eam train whistle as it approaches you is 538 Hz. After it passehg/xobc- 8gy8s you, 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 oq qn jf2-c+ic llf 6(:5ok7bzos,pd9 speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dropn-fc lz+q72io, p9kosol6:jfb c5( dqs 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 freque+tfv ua3jzc7q/ o.wjl-3h ks )ncy of 11 Hz. The shorter one is 2.40 m lvtk)h/ qojzuj7l -a 3.+cf s3wong. How long is the other?    m

Two loudspeakers are at opposite ends of a rail4g 7*hm3)uemzno8 uqu t+-ms jk4 *uudroad car as it moves past a stationary7egu4 om) t zqumn4jkh* -umdu+u*8s3 observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is norb; n,- rqzl o +ud j ;qvf*m+/o8at2izc7flh/dmally about 0.32 m/s what beat frequency wotf8a qcvioz * b;rno7,hdud/ l +;zjf- /lm2q+uld 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 speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spee.m7xqge5mzhogi3 z ,9d 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 tq9 ,e5gzm3 zgmi.7hx ohe frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high f: c ojh(6+y(p f2tjjlfrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 msthl+: j 2pf(c6j(fo yj 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 once udl,+ uns6;* y/b1yezr zxgp:rsed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity lbd :; n /,szu61r+ygpe*zlxryoss, 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 c1yy y.u,eq7sku5fa+n ompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.a.eky nus+f175 u,yqy 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, calleydqi-rtt 1 y/lk+)x 1nd “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-cm-long rodrl1i td n- tqxyk1/)+y,
(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 v5,p o3ean0ytthe human ear at a frequency of about 1000 H aopn5t, y3v0ez 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 Mafxpi a5r0l ub29d.;x qch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the pla d l0q b.pa5fxx;ui9r2ne’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatq0syzb7 a9 5st 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