What is the evidence that sounkb5v v,d*d8g-d*+whgf* mn rqd travels as a wave?

What is the evidence that sound is a::q *d7 hq qtdhfh) gjsv)kyf3 9z21vv form of energy?

Children sometimes play wiy66 x yja.4 hd9g5lwwuth 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 clea 4 uj wd6hw56ax.g9lyyrly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, 2si z 3mvu,4bcdo you expect the frequency or waveleng szc bmvi23,u4th to change?

What evidence can you give that the speed of sound in air d1nns p +ic-9ktyym.m6 oes not depend significantly on fnymck+.6n9 py imts -1requency?

The voice of a person who has inhaled helium sounds very high-picx0 5y9vc l(1rkuahy+tched. Why?

How will the air temperature in a room affect the pitch of organ -o6 fu)p 8yp;*mro-js1jgaxkpipes?

Explain how a tube might be used as a filter to reduce the amplir kh,.u1q 1fo-wa/z wotude of sounds in various frequency ranges. (An example i-u1ohwq r./oa z,1fwks a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yo(5sr j5xog) 9kzkrlgzpz88zu 2i; ea8u move up the fingerboard toward t2gxr8jlpua (55kz)8zi 9gzs8;oze kr he bridge?

A noisy truck approaches you from behind a building. Initially you hea((wt 7xh xpzmye-4)n pr it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noispth7)m( wpx- zex4( nye. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” w4bs c (u+m*8zkd r*5edjnai8ph.gm -nhereas beats can cd*h +.s nr*im (-pge4jb n8z8umd5ak be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the;t(:cm 3w)g jx9b6 e5cztyi8ys d ke1v speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fart58ttvxk gicmz3 c w)d6 sy19e(:bj;e yher apart or closer together?

Traditional methods of protecting the hearing of people who work7,v: s1 uv+ye.e c zs/svew3gw in areas with very high noise levels have consyu7 1/3+ss ece wve.v:,wvs zgisted 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 noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves showmqnjhaba6(;+1t3h vhvrp8(dvin9 + y5itwi,n in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two comp; ,i3 t(rdpv1(hyavnwt58+han9 vh+ ij bqi6 monent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the souri pn/b :pld83yce and observer move in the same direction, with the same velocity? Expldpy3:i/8 pbln ain.

If a wind is blowing, will this alter the frequency of the sound heard ba;x vc:m/qd07po uav .y a person at rest witmc;7ux vq/ap .va: o0dh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swjt g3y-qxq)di5 j y/k7ing. A monitor is blowing a whistle in front of the ch)y5jtyq37i qgd-/kxj ild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout h.;axv 5jz)o lupl, dvfqq(: *reflected by a cliff at the far end of the lake. She hears the echo 2.l lqdf*x;upv(j.h)5av zoq: , 0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bel, ypwbp9wn uk7 irc+)(;ay: os:f;k qvow the waterline. He hears the echo of the sound reflected ;w i,7yp:uv:w ( 9bynrafkqc;+kpso)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 wavelj n)llt odnb.1(dk,y knzgq7; .y5 )zvengths 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 abovub o ou;776(7wpeycn ae a school of tuna on a foggy day. Witho7a;w6oeoy7 7bu(ncu put warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when str+p) u8obtwm*kn .gf, iiking the water below is heard 3.5 s later. How high is th8 t).i umfwo,* pn+gbke cliff?    m

  A person, with his ear to5uc +xn:jxw9d 2nho4h 8htdx 0 the ground, sees a huge stone strike the concrete pavement. A moment later t wx590n c nxoh+: t8xud4hjdh2wo 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 -8wvp2 vn glkwilg9: -one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is-wi kn-lvw8lg29p gv: (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a qj8 t0,xsly c98)wcs, e(nxynsound 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 vj(xz.7ne5 ho fi).a,da ixs+of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lr 8hb 7qx7dmq)5umh-+om7dh gevel of 95 dB when fired simultaneously at a certain placeum+75d8h7 xgord-q m7 hmbh)q , what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a 6p6 .r ,fu z d:me(r9qw8rn9)taffdwocertain distance from an airplane with four equally noisy jet engines is experiencing a sound levf ropfme6n.,dw6( qrw azfdr9) 9tu:8el 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 said to have a signal-to-noise rat(n3 *f6 6yxcxgoo lal4io of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the3o(c4nllo x6 gyaf6* x background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv kk)/ 8cghso)versation. Use Table 12–2h8v) c)sk ok/g. 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 ;,p4bnw qb i.yan eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 25.b ;xe yc6m zz5yol56 j7ei,zb0 W, while the more modest amplifier B is rated at 40 W. (a) Estimate tm y56zb6xyl, ezi7c. bje zo;5he sound 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 dfkq,euy+5n)jsm uh o,*7 sg01a0n ysmeter registered 130 dB when placed 2.8 m in front of a loudsu+a g 1use,)y5s7fhmk0n nj0yo ,*sdqpeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in so6 7 k zq*mlasqr:3uzp(und level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose(*lmps 36r :zuqk7q az levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triplzi8 kzl3irs8 r* dcn+/ed, (a) by what factor will the intensitynzlicrk8ds/r *i 8+ z3 increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqom: pm;0goxm+ual displacement amplitudes, but one has twice the frequency of the other. Whaoopm0mm ;g+ x:t is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspu4yxerp:* :og+ zi7xtonds to a displacement amplitu: o xpryg:4x7u ztei*+de of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H rhnabq v b+2nzzq8 c/:zn059zz tone that has a 50-dB sound leve/zqzv2n:5nz8hza0c9 rbq bn +l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect whe o 67aaqxb7r8y 2qhgil/r, h7dn the sounr ba/2h78 7ryq,d q6ha7xio gld level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatpc4* s/vh arugbbo,;m p*.u9k is the ratio of highest to lowest intensity at a. 4p,*b co;mps /ru ugh*kv9b
(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 4/ t mk7glp)k4nftn :u2 cyiwb.pd08 3l40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the sp wb8n )t4klm2kyu3l:i/ tfc.7npg0dtring be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threesjyrh -2tar 44+wjp6e audible overtones if the pi2 j4wt ps ya-+6jhrr4epe 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 fr/mb87bzb9 - *ptvl+tz7 u80 lck env+ktcm+riom blowing across the top of an empty soda b cvtnv 8 7k z 8p+z+ut9+kl/mbbb0t l-*mrice7ottle 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 with open-tube47 yrw8+qcaql(k a5pucq* zi2 pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiredaq8+(ric4 y p zq5ku2w*lc7aq? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 5 6osr nbz/ex;+40 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of osbo x/e;z r+n6nly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m longvq 9nty :f6-1hb:nyxn74a 8voz z :jit and is tuned to play E above middle C (331-yx 8v tjn:zzntabqo:h96 yf 4nvi:70 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 aul adi +/+dq4C (262 Hz) when t++ qa4 /idludahe 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 at4 h4 gtiij5u-kjf4zi* ,gh e(eu1:gf a 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 1-t x q hthi4b5-ym11nr2–10 should the hole be that must be uncovered 5 x-4yrqn1itbt -1 mhhto 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 pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, buto5ovl25tjmy ef ,28c5 lpp-mf not at any other frequ-5otpp2mlm e5f2jl, voyfc5 8encies 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 at two 1sygil dftkp/9 1ul) t,s9( wisuccessive hartg19 l(ks, 1 l/w tdyspfii)u9monics 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 9(bn,true jf ji/i4(l.18 jid;grbkb$^{\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 prt.)uwcbt l 8l,esent within the audible range for a 2.14-m-long organ pipe ,tb.u w)l8ltc at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cmtgr/yn5jd 0l-m *hhmzchb/.(c0q4cy long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the informa qcmm 0nycjb/t .y 5hlzcr0*d4hg/h- (tion 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 wh ,t7vc7lg (3i)nwbx3x -nkzyden trying to adjust two strings, one of which is sounding 440 Hz. How far of kv ndxxw7ygciln3b ( 7,z3t)-f in frequency is the other string? ±    Hz

  What is the beat frequency if boqtk3n 3zo-83 0qf sdmiddle 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, whils 0*vxndj/ wuh(s)g y-e another (brand X) operates at an unknownsvy)* dg hw0-/x nj(su frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produ jktle6odv(76rb65rmp zr- ,sces 4 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 vibrationa ,-kre(rjl mv675ord6t b6pszl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned -tnk1d rw twp3/wjs9. to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played tog tr1tk 3n/-9ws j.pwdwether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fluteskcx:h pp99 lemy234c9qrs a)dx e l:xx3/uxx) each try to play middle C (262 Hz), but one is at 5.0°Ck4xxc29a c:yxeqx 9:hu lp3x/l )p9sm)3d rex and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fnp0/y-bryaow1 a i7-q ork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat fre qn7 /-r1 0-pwayyiaboquency 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 2k)zbor) h /pf6et ck7person stands 3.00 m from one speaker and 3.50 m from t7 o)62ez/b kt)rpfkchhe 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 suppos,v tf-rj r2:ojed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If of or,v2j-jrt: ne 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 1kmt*rhqh h,+ 1rv ,qh81i+esy8qjgn m in air. How many beats per s1g ivh+qnh +th*r,q8,1ky 1rhqsmj8 eecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wr 4 /s)hplnrgm9u2tdy 1(cbg8 y (gzn)hen at rest. What frequency do you detect if you move with a speed of 30 9u(/)t)gry1pcg h(n48zyrlgdsm2 n b m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What ftk w.c( 1odh*8 1b6e: p wzker3lbf5m ;ns,kclrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of tclf1k;h(35w*n .c rk8,6o pwedes:1 bmbl zk 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency id9 8fhx(un7 atf a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequ 7f nda9ht8x(uencies 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 sajziz: w*r (.na4eb;h z alv3mfg3u,p-me single frequency horn. When 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 5.5 Hz. What is the freqm.zv3uef zgp*w n,:z4i h;3 ablrj-a(uency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves wrv pb5+fj 7l7-c ndu)x6 yi9cf.0iip at 50.0 kHz and receives them returned from an object moving directly away f +id- rl6i50 7p) byij9cup7vn cxf.fwrom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 592u-x s0 k7ukc maq2fa m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wh2a9xmck0uf qu s k-a27at frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, d9lj9anwf0;rm.hjm- -+boq g-jkhi0)sppl9a 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 station. What beat frequency was heard if the train car approachedj -gj-b f dlh-.p9s wnq +i0;r9lhm o)p09kjam the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrlvk ,pi dl6(wt1c/)msasound waves to measure blood-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 ms v l6d/li(w,kc1t)p expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofp bhfc5 8k,ho*aym+j4 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 emitso 8rx 3/y0b9.aww wsdp sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear dowx8bs9/. wp rw3y 0awho 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 i/) m7x/eng/wtnlche + s,qvj nk.f6.kts speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 iom)pnbajgb):, (+a5l6oa op where the speed of sound is 310 m/s (a) What is the angle the shonap l6(abij): pm o5bo,o+) gack wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sound ist47iaj ks9eg5+7f; yow aeo0vho g,e2 only4f2he ; is0okj7+g 5y97o, aowt eeavg 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. icv-+u j/- t;jusly*g0kp u:u Determine the shock wave angle it p+ jg-vt*:u uulyip-j0u s /;kcroduces
(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 g.gv/lr( d mj.$/theta$ 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 aboyq zz(-5wlulj 896 e/zjd -mwdve the 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. See Fig.-e- 98ju/ zjdlw5ld(qwz ym6 z 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 ae ;mrg,ff w*f.8ul4yn sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it imnrwgf8* ;y4e,u.f fl s designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arev2w 48 ttpdnu/ 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 consww+ c0)p(l;n, vnchbtists of many plastic pipes of various lengths, which are n+cl 0bw()tvn pch, w;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 2g7w(6f,klc4m*k qjt-nv b uta person makes a sound close to the threshold of human hearing (0 dB). Whawc24gk ubq6(jv, m-nk 7lt t*ft will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dBrk6i5ol a3zxc;+1cnh sound are heard simultaxnk co 5h6+3;c1zliarneously?    dB

  The sound level 12.0 m from a loudspeaker, placwhzr9il8;af e 2.9t- midc/qc ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming8mc/. 2w 9hed; iqftza9-rcil it radiates equally in all directions?    W

  A stereo amplifier is rato nr egrr05;8ded at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 1n eg5ro0rd r8;5 kHz?    dB

  Workers around jet aircraft typically we/iy xv/y)5nmm pun5p+ar protective devices over their ears. Assume that the +p/xyvm5 /u)npn m5i ysound 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 systemk/ cb9gl azo++*0qh gus, 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 freque(ry1i ,p i cr :zd3up*(p+l6vtfwz4pgncy 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 longlofe19da)8 wccq x7p 2 between fixed points with a fundamental frequency of 440 Hz and a mass per unitq)2w9ofc8la cd1ep x7 length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set lwh88g1e zpyus6.k( linto vibration above a vertical open tube filled with water (Fig. 12–35). The ( uez sw8y 61g8h.klplwater 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 is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one end m *(9 orhr9rxad2qi,i w n0nn4-)fnow and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with a)9( d9hoqnnm,ir4 n xo 0nwirw2f*-rthe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatej *y( otlnm5h( 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 t )k/ zgzaxu98uhe 500–1000-Hz range coming from two sources. The sound is loudes /gzkz)u8x9a ut at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductodt drhmzzf6-1u5:y +aa 2e1oor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. 6aohdz:+ty 2aefom 1d5-ur1 z What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 559,i: r*km6 tjywtzzb38 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (as6* k5z:9 t yizt,mjbrwsume constant velocity)?    m/s

  At a race track, you can estimate t +.4x8i9 jvsik ho 6ts9hvi9fphe 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 drops by a full octave (frequency halved) as it goes by on the straightaway. How fast iv+9s6 s8hk xjti4oh pv9.ii9 fs it going?    m/s

  Two open organ pipes, sounding together, prneb 4hi4w6bv0oduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the 460vbei bnw 4hother?    m

Two loudspeakers are at oppt,oz2/ a e)e ;sjt.rrzosite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If t/e;)tr,rtjzzas . e2 ohe 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 th0i c b,.ri-g(2xgjx cge aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speicx ggr b.-c2gj 0i(,xed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward t - 5 shg-ejq6b-(ncv1hkuru5u he bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequr k5cu-e1s q hnu(v6hb-j-u5g ency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a serieswk)ipkw me25- of high frequency sound pulses as it approaches a moth. The pu)-kwm ie2pk5wlses 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 once use.;bd7b2 ywivez)(q hkd to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When plawbz.)2 bevd;i 7hyk(qyed 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 sterer6znw dl)st eoh2l x(3aml-3 +o listening can be compromised 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 2.8 m high. Calculate the fundamental frequencies for the stanml6e3z2 xr h(l3d- t+soalwn)ding waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvesb;sk-+ck og.w 8(mjgr a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod (o-bm g8 w;.g ksrj+kcis 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 theqn8. adn7y+ ip human ear at a frequency of about 1000 .iyan8 p+n7dq 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 the sonic boom,j g3:o,wvvjc 1.5 min after the plane passes directly ovec: j, w,go3vjvrhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ijp l b5v8j)n dr6ougxoaf e,w2:y354k s 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