What is the evidence+)op bihfk8;x that sound travels as a wave?

What is the evidence that sob, oi3ftk03 j :kju0g;lo- psfund is a form of energy?

Children sometimes play with a homemade “telephone” by attaching6fol/ +y mn2n,svfhhwh)jf46 a string to the bottoms of two paper cups. Wh/m fsv 6nh4jly+oh)nwf 62 h,fen the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wa ht,)(r npagu7jh(yze fu779es1k ge9velength tohf,jzp9 ) 7eheg unra7kte(971 (u sgy change?

What evidence can you give that the speed of sound in air down omqfh(7hz*7lht3- 0tg2 j fes not depend significantly on frequen-hgf07wth mlh (tf3 j7*onq z2cy?

The voice of a person who has inhale/s ynjn6* 5sznuv1-k bd helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipespapfgk( 9pn7ko 6d ;(z4+ kmmd?

Explain how a tube might be used as a filter to reduce 8ui f 8wv+zg7en et)8 afij7mkzmfw0kn2-m; +the amplitude of sounds in various frequency ranges. (An example is a car+ jv ufn mwfi0wm7zm-+k8a72e)8z f;tge 8ikn muffler.)

Why are the frets on a guitar (Fig. 12–30ugtjx j p*t2.9hwk6p 34yf 5ws) spaced closer together as you move up theh4s69*jpft3 g wyuwx2.jtk5 p fingerboard toward the bridge?

A noisy truck approac/v4m6pm fee4y4x5 azzhes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section yx6z4vzf44a m/me e5p11–15 on diffraction.]

Standing waves can be said to be dugp4ntuh 39 22fcpbe 0ge to “interference in space,” whereas beats can be said to be due to “interferenc0f3p 2b ceu9pg4ng th2e in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lower (5ypp0 8gxaxqed, would the points D and C (where destructive and constructiveyg5x0a(p x8p q interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wita 2cml sbz6;p2h very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new tebmpz l2ac;26s chnology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig;0y 9kogox4 hn. 12–31. Each wave can be thought of as a superposition of two sound wav ykh4;oo9nx g0es 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 if the source and observer move in the yugm;46y *q rjsame direction, with the same velocity? Expr u qy;*gm6jy4lain.

If a wind is blowing, will this alter the frequency of the spodr(1w1pc05f xkf b ,ound heard by a perso ,k10d(ppxr1w of5cfb n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child ic2n.9bc7bv0;zo4lhcu9lqniy m3 xi 1n 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 child hear the highest frequency for qxc4cbvb72;lz31y uo0i nic .9ln9mhthe sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoutbabhcf ymc6h)9:)wu . reflected bh b a9hfmwyucb6))c:.y 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 heareln:khsh 3 0o)n8 lu f8.qkd8pk/xt(ts 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 seawater is 1560 m/s (Table 12–1) and does not vary signifhpno)38q (t u8tkn . d0/f:hxlsklk 8eicantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths is6a1 zkl7 yqh80 qtut46f)jhln 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 schoolb,sf8hgeq,eti+ bor f)(1x2 qet.*7,ydk erz of tuna on a foggy day. Without warning, an engtsh)q tbbg. *8deef2z ,krx( i oq,e +e7,rf1yine 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 of5.mj99pgor- uwnzah8a( - 1upydv,*grp ; l qe a cliff. The splash it makes when striking the water beh5 o8 9qgmap (-lu, rpj p*dnv waz-1.reu9;gylow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grounu qhw*+)nd.t nd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: nd+hq)n.* wut 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 one mile of distance by the ;9cza v+wgd7y “5-second rule” for estimating the 7+ vadg ycw9;zdistance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 16fsd)f ( kfiz0(()el s z8twfb20 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 -a1, dwhw4n-45 tpz: k trxuojis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9(t4u,wtkj, kmel9( up5 dB when fired simultaneously at a certain place, w(u(wtkk9e,lp , tju4mhat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jyq+ ubw/ph8- *nevd j-s9mb 6set 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 engi96 nbmujy-shedw-pqbs +*v/8ne? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 5 5iiy70lun um.9 cno.r8 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devic0.9ori5.ny um cu 7line? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converseqz/mjqdi03 wfy j)8 u(0/xubation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mout xq d0/wm j3 u8fey(/q0jzbiu)h. $\approx$    $ \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 area1qcyd 02 d *.uucwc1piz:yda ) 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 of (9edq,n3qh250 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 odqn9 qh(fe, 3a 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 registk g0ktaxs+6- dered 130 dB when placed 2.8 m in front of a loudspeaker on the stgkaxt- ks 06+dage.
(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: qnmrqg+)q y, dB. What is the ratio of the ampli qy+,:g qmn)qrtudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound waezch*gg98 a-w b /.mazs,ncv9ve is tripled, (a) by what factor will the intensity increase? Increas9,/9azgv-c hb*gn .aewmzc 8se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onbv v3u8ln sbt gu3*(2he has twice the frequency of the oth2s vn u(tlb ug8*h3v3ber. What is the ratio of their intensities?   

  What would be the sound r64hi6u wsp(u;f)jkh mm 4o0jlevel (in dB) of a sound wave in air that corresponds to a displacement amplitud 4 jps6;wu6jmf 0 k)h4ormhu(ie of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wha2o gqw5 9-fmtmt sound level to seem as loud as a 100-Hz tone that has a 50-dB smt9 o qm5w2fg-ound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when t tpk ./d b*1shh0gs0mohe sound *01hbomkps 0dst/h.g level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatm,pp :g w3iab/ is the ratio of highest to lowest intensit3g p,mpi: aw/by 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 o8er5v.7ch ly ne qniaa/861rhf 440 Hz. The length of the vibratiahnal6 5 ./1 887ehcvn rqiyerng 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 longpnv z.*pns*w)xuqg/8 . What are the fundamental and first three audible overtone) z8wxq* /vgun. s*npps if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowiu8k 9un 7m0. pwsup1mf* c+zosng across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a0s*npkc om781fwp +.s 9uuzm u 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 oyw ca8b0 8++ykaf: uqbpen-tube pipes spanning the range of human hear w8 fcakbu8y ab+q+y0:ing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frii,woh :v24v3ygl0 qeequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at,lw 4:g03yhq ii2 eovv a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle f 9qmh u(p 59es-4: rs8tfsqv2-yqnhlC (330 Hz us4-np5hqeryfv 9 2 (q- s:lm9hq8tsf).
(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 o /ctth:cn-cv7rgan pipe that emits middle C (262 Hz) when the temp/t7c - vtcnch:erature 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 /kz6vnrjbd7/ 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 holfu4ejf gvm1;y6km q37 e be that must be uncovem e71 k qjmgyf4u3v;f6red to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at d i sbpl+pa0ms0sp-::z,int /xon50yany other frequencies in between. (a) Show why this is l :0a+x s0mb n/s z dnt0,pposip-:i5yan 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 .or5ov *djd6ur 4 kh-bresonates at two successive harmonics of fre5 hdkbo- *vr4r.6juodquencies 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 ww+n d)6n ,0 +tmdbmar$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-z l kwtx4fm867d* ,hjjlong organ ptwk*j d l x8hmz6j,f74ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is6kfng(d d05x a 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 0gn axd(f56 kdanswer 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 ev:.6watwg+ p q5mzb z7 :ltssw,ery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string7 .5, lp+a wzb:zmsq:w6gtstw? ±    Hz

  What is the beat frequency if2kiv:wcb h ,+v middle 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.p71 3r611bl.w qoruzr4u.6u gcnjdmg5 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 occurs when they are pla6 o6.1ucrgbrgjrqw7 nmdzupl1 134.u yed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning f54zuyy+ug-w / mn7fz pork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of tzn-upyy u4+wf7m zg/5he string? Explain your reasoning.    Hz

  Two violin strings are tuned to th) 5+ 1l rwrg4ektiqj6le same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. Whattl5eri+qrkjg416w) l 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 to play mb4a1:jkh a3fw iddle C (262 Hz), but one is at 5.:k hw3ab j1af40°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freqj/1r2,o e44mxa g egmcuency of 441 Hz; when A and B are sounded together, a bemx c/1egraeg4omj2 ,4at frequency of 3 Hz is heard. When B 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 1.8tqhsu+z +p7)y/5fo23j/tmdyh in3 r o0 m apart. A person stands 3.00 m from one speaker and 3.50 m from /3 pz nhi stdo juqh7+2y3)t5+/yrofmthe 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 ar;7vb p-i +j-wkf ,vhy ,kjlm5ve supposed to be vibrating at 132 Hz, but a 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 frequency of the othjwkfjl;k-5vvvh,,+bp- m i7yer ?   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 / 9 hkt+;vcsaxand 2.76 m in air. How many beats per second 9;a tk hxcv+s/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 when vvp+ 1nqui9g ,cvpj21jaa w5) at rest. What frequency do you detect if you mova+ w1v ivc)aj5jpq vg1n2 u9p,e with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dl3ff a2u dkw4uu ivr5 13 hh7siw-)mt/etect if a fire engine whose siren emits at 155uw 2h fdmw7kisu5a- tlu4h3fi)31 v/r0 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 toward youyu,ke (3s/ j)ekrw/2k /g psb6.em sz.x )vhcv at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they clsg(/z e2k c),e. xvr/epsuh6/kyjvk3s .mwb) ose? $f'_{source\,movine}$    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. When one is 7cwr/o mc)j frd/0ulq,z9 :c tat 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 frequency the horns emit? dwjr lc/q/u97z0)rtf:,cc moAssume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and r8n3 ydor lblz.a(wl61eceives them returned from an object moving directly away from it at 25 m/s What is the receive (z86ldllo1.b an3rwyd sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As w 4hg2,evc e3u29nbsz it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the rheg4wcsv 92u3 2nbe, zeflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movxs*fg)kg8e r. .t dg o5z1ff*ying flat train car at a frequency of 75 Hz, and a second identical tuba played the same to t)geos8 xdfk5z*frggf *.1. yne while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses uqemdvuo ) (ywtk.7l7x+fp-p 2ltrasound 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 expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awayxfkpedp7wv- (2 l7yum+.)toq from the sound source?   Hz

  The Doppler effect using ultrasoni w8te 5hw+gd j o)yjx:om*/3fic 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 soun+ *abokap 6/tyd of frequency 570 Hz. When the wind velocity is 12 m/s from the ta6 y*oabpk /+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 ifeiruaac icmpu;456h.hj: v *4 its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed o*gky kxvn.y 6yyeo9k- 42wj* df sound is 310 m/s (a) What is the angle the shock wave mak29.6eydxkn-*y*voky4 w k ygjes 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 speedduih r,+:*xf2fwt1.p c ;nwdxir+0 op of sound is only about 3i+wchw2rt p +dnf duoxr:,xp;1 *fi 0.5 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 ocnkbz9j c b*fk:zbas50e.o rua0g*4a ry, k3a8ean. Determine the shock wave angle*geyzra: 38k*bo0a bfcn uzj. 5ak0 rbsa k49, 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 : *yp33iwvfd7( q 3qgwp3kjzh$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and weqfwx2c 5v1 s(/4eo z5wd is)see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal dist x w4)osq1(c 2v/5efwe5 swzdiance 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 sonczkk2(wz 2 w+zb ck0b5ar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, 5wbzcwbk2 +2k0c zkz( what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ranjmey ) tp +0,p(bd8brrge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a y oy7c /bubr38sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on bbc7 u8/yro3 yboth ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a so0 wtg. dl rpv11jv3s6ciaaz3 :und close to the threshold of human hearing (0 dB). What will be the sound levelsdjl1zt p v: ig033a w.a6r1vc of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound jn ,t6)y.fnf vand an 87-dB sound are heav fjnytfn6.,) rd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed tz -wae9y 0xe6 94bpqs zr1s8bin the open, is 105 dB. What is the acoustic power output (W) of tyw6e 0s-q8stp99 xe4a r1 zzbbhe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is m-3p opy.f:cny1 /gyb;ie.0c dru:dxrated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power r;.fmp:x yyn de1ud- cc/ypg 0io3.:boutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earwgch6 f3cd)45xf,a b js. 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 fh56d w cx g)j4afbc,3an 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, the gain,qu i,:kykwwv;f1. c l79sz90luyw g -x $\beta$ 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 violsj ql y4 88 w7(r(hjr3dqnk:yrin is tuned 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 violiia +o 6pq(zl6s 9vx fgn/,tbf5n is 32 cm long between fixed points with a fundamental frequency5pb (xv, zft96+ogna6f si/ql of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open z5u* dw14k5 k0tvb)hdlvd9hstube filled with water (Fig. 12–35). The wathth)d5z ul4 vd wkv*15 9kdsb0er 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 n17yjrnf,0:4kme a f fend and also 75 cm long. How much tenf jf4ekny:n mf a071,rsion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was xi8/3sbyv z+ yobserved to resonate 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 fs) 0vu5sr .0qrjo6r w +* ze,7nolr*akjqbzk;rom two sources. The sound is loudest at pov)6e ;q7ojku 0rorw*nk0s a+q,b.r rz*5zs jl ints 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. Thg5fou*4su+iir+f8 b.l e vz*ge conductor on the stationary train hears a 3.0-Hz beat frequez8*b+ o*grfi.uui vfle s4+g 5ncy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a st.dn )g ao9 vk+ 4m2 dshu-f(pg;vskxj(eam train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving 4og km)kh vf+-da(jg(;psxu9nv2s d.(assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeqwz*-y3ppu yeghiley73vpp 6 v)33w -ning to the difference in pitch of the engine noise between appr3*vq 3yyl hp)p w7gwz pveuiyp -3-63eoaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hzbpr84 ipr,a, r. The shorter one is 2.40 m long. How long rr,, 4ri bapp8is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stan)2 g vkkuok a bhlqjvkg2w5l01v8 )17tionary observer at 10 m/s as shown in Fig. 12–37. If the speaokglnv5w2v)kkvl7u 12)q a g0 hb 18jkkers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bea) otrbm 56tet8t frequency would you expect if 5.50-MHz ultrasound waves were di)rt b8t6te5 morected 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 whiletgsnd19f;/c m the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth? fm1c s/tng9;d    kHz

  A bat emits a series of high frequency sound pulses as it appgcmdm 6z;ac,y 5q;czg74vi o0 6ifsy5roaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected s a;fm zci6i gq v54c0d;6 cgoym57,yzby 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 sidz22 q7 q) pgf/ziozll(0ht1ignals 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 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 longh)g/il2plotizqd0 q(z 2f1z7 , 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 3) xm*4e+w t odb0gwk*rsj;kulistening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider ajr t0e*wwgsb xk)*dk m;u+ 43o living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvesxo h-xp;9.ds l 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 -px; 9dloxh.sclear, 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 at ke *vezj0*6qya frequency of about 1000 Hz is *ykqve*jz 0 6e$I_0$ = $1 \times10^{12 } W / m^2$ 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.y7 dpbek- ( wgrw00x/asj7b-zsm0b 7f0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s a7z7-/-wm0b sypsefx r(wgdb kb00j 7altitude?    $ \times10^{4 }$ m

  The wake of a speedbpmmph :p3,at:oat 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