What is the evidence that sound 6 zbvk +-uom4etravels as a wave?

What is the evidence that soundvbjk 5dwmckf*.8 enmc) 64ru k9p 1em* is a form of energy?

Children sometimes play with auq 9 h 6no4m+dezt-8ui 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 hearzq 6m -uuneoh 9+td48id at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency ;g rslb35 8jlz53y mhzor wavelength to l s5gr5l38 zm;bzjh3ychange?

What evidence can yoh g(ay-wc* 4eje,/ dw8qju q5au give that the speed of sound in air does not depend significantw,acqgj(/qeeyhu a*-d45 w j8ly on frequency?

The voice of a person who has inhi42pleog 1taz+2b6 wggckr8 0aled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ofintfx ih-**7n18p gx*c +zpro organ pipes?

Explain how a tube might be used as a filter tnxz+ . nt7b2dyo reduce the amplitude of sounds in various frequency ranges. (An ex7+byx2 tz.dnn ample is a car muffler.)

Why are the frets on a gui5w;z h-/xp1 xv1opsiwtar (Fig. 12–30) spaced closer together as you move up the fingerboard toward th1zph;xp/sx 5w1 -wvi oe bridge?

A noisy truck approaches you from behind a buq ,m*uiupu- n0ilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is su,qn u0 ui-*pmuddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be s 9jc*x4fb3) oc bnb (pqbsi)e:aid to be due to “interference in space,” whereas beats can be said to be due to “inbbb :(qps9b *cin)ec3xo4 jf) terference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would (-yoecuxq)w 9the points D and C (where destructive and constructive interference oc(-cou x9yw)eqcur) move farther apart or closer together?

Traditional methods of protectii2xnt ai:756g-f jukgng 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 electronically, then feeds it to the headphones in addition to the ambient ntja 65i ggiu7f2k- n:xoise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two wavefph8 1juhe9oky k29 b9s shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as inu99j 8 9okfhhe2yp 1bk 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 if the source and observer m,l7 son,coyz .ove in the same direction, with the same velocity? Explasco z,l n.7yo,in.

If a wind is blowing, will th)n p+hy1q2 5i d.gyhaiis alter the frequency of the sound heard by a person at rest y2hyi h 1iqapn d)5+g.with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various posittv1 x nbeq3(cmm: o-s9om +4x693p wpjew+ xoqions of a child in motion 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 child9o(+tbmpoxx -cewjnow4v me1qq 39 xp:63m+ s hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening4 aqfr m ,2(/m)cyixkixzl8f- for the echo of her shout refz-)xm,c xkfa limq(r/fi 2y84lected by a cliff at the far end of the lake. 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 hea)b brprk j qz66+oppmx)h8d ;(rs the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawa8 )k6rjd;bpx)+ 6( zqpmhbro pter 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 a* xq q4 -ttpf0)0osei$^{\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 schoonif:n3 mb;xu f /wk98ul of tuna on a foggy day. Without warnu3mkx f9 8bwif;/ nnu:ing, 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,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splashkz18vtrz cs zwflqo5h6v;xz c1**/ y6 it makes when striking the water below i6s x frz*8q zkczwt1l5o6 c*hvz1 yv;/s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone gzyrcq ; nc.p:o,f3f89 7vyfmstrike the concrete pavement. A moment laty7g:cf9q8fvmp, .r zo 3 fcy;ner 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over o/v1uem az4pc) :t4ee5)sv tmvne mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperaturez)5vmt)cp/ :4t e4vse1muvae is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity r jqp45t:a.4w-eu .eixrs.sh of 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 of a sound whose intensity inemk:gj70b5+ o8.aom 3 khsnks $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a so4a)2 dhpv4 2rgy1jc abund level of 95 dB when fired simultaneously at a certain place, what will be1bcy4 j)pdh2vag2 4ra the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpla *;iz*afyw aukn 58-wsne 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 w sn*w5zak;f-iy *au8shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sa+f1,az20y /a nnhkbvwid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensin,yk/ab v n+f012wzhaties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of of1dwjno5l: ;r/9jx c nqpc 3k5/ r-ucsound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. l ndfqop5 x;orj : jk/5rw3-c1cncu/9$\approx$    $ \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 arb yqztm7k:.2x-mnr e s29hig.ea 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 m-s6r:qdex 8fnso .hg .ore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibel ..sq gsh nex:-ofd68rs 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 regiss1 rbr(mfu-1nud r/ b(mws n6.tered 130 dB when placed 2.8 m in front of a lodm6srru1/.b(fnrnbsu m(-1 w udspeaker 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 typiw,z n- u1r.cnmim9v:m cally detect a difference in sound level of 2.0 dB. What is the rat n: vn1 .-zu,mc9rmmiwio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triv; /qzwxxv2*vqtz* ;u f 7fe7ipled, (a) by what factor will the intensity increasv;e2 /w*i*;xvt x7 fz7qvfq uze? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twwb-*l: k2s6cy oflf*iice the frequency of the other. What is the ratio of their intensitieslf *l o-*: fbckiw62sy?   

  What would be the sound level (in dB) of a sound wave in air that correspwf,ks guhx/h2 l+. uu:onds to a disp: w ghx.k+2ulsu hf,/ulacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hav4li0-fjihfs ra 4h c j3ts-2)ne what sound level to seem as loud as a 100-Hz tone that hac th 432f4h airj s-nl0i-)fjss a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest fred/ts//m (a0 pcbhbdk 9quencies that an ear can detect when the sound levebk /sd//0pd9(bamtc h l is 30 dB? (See Fig. 12–6.)

  Your auditory system c c;d*6 jeuh*o -tx1zpwan accommodate a huge range of sound levels. What is the ratio of highesd6e*opuwtz* -xhj1 ; ct 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 fundamental frequency of 440 Hz. The length oid *8nbx,v1zw/m9x ncf the vibrating portion is 329xm,/xbd1z v*n8ncwi 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 fundamental and fian6njq;p95 dc rst three audible overtones if the pipe isapcq 6;dn95n j
(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 fromaayu 9e akv:/2 blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closeda2 ya avku9e:/ 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 o. ui3cpcsxj9-kftcq,2 vx f)d+r:v5bpen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range oc)9q ubkc+dj vt.35f:-x2p, rc ifxsvf the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hy /bwdd d1nnvq2 ct0qzrb;;u54 o9o,wz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengtn,;c9b5q d2wyn w uo /ddbv04r toz;q1h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lon0o7shby4-we h h3gl4q g and is tuned to play E above middle C (330 Hz)734e 4lybhqhs- 0wohg.
(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 e(b zume 22k,jxmul5,xk uje0,mits middle C (262 Hz) when the temperature is 2( ejel mukx,zu,jub02,mx2k5 1 $^{\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 aloqmt 48j*ugm +3.nr it 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o g gfn vdg(2:/.erqjcp zz5 ;u ;rg3l6m6w9rxbf the flute in Example 12–10 should the hole be that must be uncovered to play D above n9f :r3g mlqb(6;g;dj./rx regvwg6zpu 52cz middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at a : xbeocvi+;i/u 8hwo-ny other frequxi8ovw o-+ :iub/e ;chencies 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 botkud/uo89z/fn- 1ewidcul..b e8s )wuui 8z a.h ends. It resonates at two successive harmonics of frequencies 98w 1.o 8d8-iuen /e /u.iufkzaszw)b. uucdl275 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 go5*e2aqdn*t$^{\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 preylgdd(s( f (1vsent within the audible range for a 2.14-m-long organ pipe a(s 1ld(y(fgvd t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the qx, 7wcrbyp17outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible ry7rbwq1pc x, 7ange) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one be8(g rfxy)+ uhzv .e4cmat 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 string?gyu.8vxrc4mf (z)h e + ±    Hz

  What is the beat frequency if middle C (262 Hz) antdxk gn iobu(p7;36s 9d $C^＃$ (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 n2d5e;d6v8c0 h i+ prbn.p-djzem8*wjya *ps at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz ocj +nh8dyc8we2i 5.rdvd; a6mes bzp-pjn*0p* curs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4f:0 g7nc2l fjhm:ad 7u beats/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 frequea702uf7gl d:nh:jcf m ncy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequench5s3t(.fnpy sy, 294 Hz. The tension in one string is then decreased by 2.0%. What3.( hys 5tfspn will be 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 flutes each try 1e */yhe;s lynto play middle C (2 el e*hyns/1y;62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,0 9ndshw3(wcl0(l5 e0kfnx i( jj/o*gwysio; A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When Bwhj(; 9(issy nlxkocd 0iwe3* (ln0o5fwg /0 j and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C 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 zl9cwc*cs3/x7z h:e b from one speaker and 3.50 m from7* 3xcc9 z /ecbh:wslz 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 tuner hea (,c9e we2lpdgrs three beats every 2.0 s when they are played togetpewlgcd(9e, 2her. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How mancl hz dm9*a2(j pa86t wfh/uy s(o)r/yy beats per second will be heard? (Assume Tch) lum 9j((/2psfyh/arytz*d68 owa = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaiwz e om jt6 :s7c7ofqy-+yj+/dn fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speo jfce/sy 7:6y m7-tzw +qdj+oed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you deteli)p re0 )d.h ppd-3bgct if a fire engine whose siren emits at 1550 Hz moves at a speed p )ep.phgrbl-0did)3of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frel9ykt.j l :o j8c-m(dnyo :ex+quency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it :deoy: .n-j(o8yt c l9+kxljmat 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Wnd4jgl.8wza y (19n4sz94x +lsz rtlthen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5ny ll9 z 9dst+ ws44z8zjl1(4xtn a.rg Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soun.:e ntecb j7h (():o k2i4l zoxl*yfbvd waves at 50.0 kHz and receives them returned from an object moving directly away from 4xe2)v oky: lh(of7en* bzjcibt .: (lit 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 emits an ulck 2e:f -(bpsmry*,o5gkuy6gtrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in th:2g kuy*6pecs kfyog-br5(,me reflected wave?    $ \times10^{4}$ Hz

  In one of the origin(b*gd0dblfizjw r e+g bh:+(ghuzr(.y; c d-9al Doppler experiments, 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 while at rest in the railway 9:z. uh b+-cd(bdd( zgfi y;be (0lgr*hw+gjrstation. 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 wrd bcj6ej5tc 8uu.),xesk,s ll19 * xblood-flow speeds. Suppose the d, *we9xss.r1j )8e6jdbul, ctkc lu x5evice emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usi b*1.1 cy:x4bv+bmwt3y efhqqng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fd oxgn(u+-esqi3am60 requency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency u0 genxm-+dai6 (oqs3will 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 sfcnh n5n iqcplz8z/5-e0 nw-n7 :escrx)8e 2speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where thssb6;1p )g,jt, .1 l zylbqjky ax,-cne speed of sound is 310 m/s (a) What is the angle thxbscnkaly ),,lj ybt6 sq;z,. -1pjg1 e shock 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 th3 npatdg 7) a7znmoom;9lel7(d,gkj: 2 a 6vbke thin atmosphere of a planet where the speed of sound is only ml7tk dn)a;ggo jk,23ze lb677a ndp:oa 9v (mabout 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 ocrn0, lp /av wsfmg/(h3ean. Determine the shock wave angle/nahp(0m3 r,v fwg /ls it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 6t/4 eo7p4af5d ov vvh$/theta$ 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 exactlyf ycr +borl6q,45ad2t 1.5 km above the ground flying faster than the speed of sound. By the q4f6rdar l, ob+2cyt5time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that s,ih5s4dtu6e1t5q b yfib a1pcou 7q0)ends 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 m, what q47sd5fto1tu i6q ,1)5cubhba0ipe y is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are ther;um0z3i * pktie in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consist6d hil mnx: /j 0/knr-+jzie:as of many plastic pipes of varioimr:+aexi:l zj/n6d / -0jnhkus 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 ml c9f)x t.wsg6 from a person makes a sound close to the threshold of human hearing (0 dB). What will be the w xs)ct. l6fg9sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB s5p ysul 7d4/-+rmon nqound and an 87-dB sound are heard simdn57+p usnl romq4/-yultaneously?    dB

  The sound level 12.0d+gbr v*fk:1pfwg-h 4)bh0 aj m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqfr ggahbwv-j0kd) bf4h*1 +p: ually in all directions?    W

  A stereo amplifier is rated at 10 -ibkisd i)ca 2l06l6blwai050 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is tw ska0c)l0iil l6b6ab id2i-0he power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pcqg*ar w9*8db 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 human ear has an effective radius of 2.0 cm. What would be thr*d wqb*ac 8g9e power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the 8 wni,a +;c:g7jg;lepk jec;w 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 tu+ pj; l5o3pbfc:e7qgzm7xunz j 2k6:hned 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 lonizme* p l,a+as8jq ;cb13(xvxg between fixed points with a fundamental frequency of 440 Hz and a mass per unit lzai1ma,*8l xscpx(3 j;vbqe+ ength 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 vibratio .o5l1tik; swo2htmx-n above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when thom s2;o.ht5kl x1i-wt e distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tu,xs(*2,fzn1 x3bxrbsx oe(t hat is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonaxx(bnz21( ,s u3frb*s ot,xe xnce (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lo)et rlp 5m13gs5;;idx(whgsvop ($\frac{1}{2}\lambda$) 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 comibmj(e2r,6p v:g /zihjf4g8 vb ng from two sources. The sound is loudest aj8gp2vb /mbhg r v:j4z (e,if6t points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H9zv:yd ka8zapm:/om bm 98.te z whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz bem/taz 9a 8v9m.e 8:zmobdy:kpat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam th aikcp/d51p )8ag3 kro /*tdkrain whistle as it approaches you is 538 Hz. After it passes you, its fda35kik8/d gck ) p/aor*thp1requency is 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 listening 0a u3 xkfj7 ;2-shrz7tzu2a(rlte7pr to the difference in pitch of the engine noise between approaching and receding cars. Sr-uehra k22at xs7r0l3zptu (zf 7;j7 uppose 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.xwtnop j (dk;6 4dqqa5evsp1749b 2e1r u+tym The shorter one is 2.40 m long. Htet n4ud; e x kq6q1jv (w+o7ysp29dp451bmraow long is the other?    m

Two loudspeakers are at opposite ends -zor bj r(5a/ 3aa sl-v(vsl4uof 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 is between the speakers, at B, and (c) he hears the speakers aftu /a zjsvlorsv- l(b3a -5(a4rer they have passed him, at C?

  If the velocity of blood 7(g ;j wf,7 nubmi;lzx miu3-uflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dire-b3;mg liuu(if xz j 7;7,mnuwcted along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while ua+d)2lujg- qqls l5 )the moth is flying toward the bat at speed 5 m/s The batl jsl)5+a )qd-qlu ug2 emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulse -4e,sf.8hwytfe;cqbc uqy 9 -s as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth beq;qy9 uw,-4cfb-e hs .y8cef t detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from h vser,a j8bbee9a.x*(vs q4( one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a ( a *vq4,9beexs(avjsbr.e8h 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 by3oz ec 1k,t7f/e lnq olp4f35r the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living r 4q zlol e1/,e3 torpf53ck7nfoom 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involve*nn g1.n0ztni ; noo0is a long, slender aluminum rod held in the hand near the rod’s mito 0i1 .nz0;ignnn*ondpoint. 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 hearing for the human ear ats+ 3+,oukt9m aqe rc* s-fyw:d a frequency of about 1k9 ewu3srot++d:, f-sqm yc a*000 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:c ;f l ik9t4qe4u*axv the sonic boom 1.5 min after the plane passes directly overhead. What is tha4 vixk;cqt ul9*:f4e e plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 x j,uzuij*fc-; r4zl3$^{\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