What is the evidence that so 0mloh4*7x-v9c eaep qund travels as a wave?

What is the evidence that sound is a form otmv 52,i,t geif energy?

Children sometimes play with a homemade “telezuf51oz(+3d4v lq9z.pkgugt phone” 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 (Fi5qogg3ld 9fz4u1 +pt vz(u.k zg. 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 wavxwqyv0 4hb .rqo-a +n3f wb*ni.w05niel .f5bai0xworn*n4qw0 yh +-3bqv.nwiength to change?

What evidence can you give that the speed of sound in airmw h(d2xc:7lth -x5;h ynocf9-8wkgr does not depend significantl(285ydcmrl h c7x w-t9kxg ;wohnhf:-y on frequency?

The voice of a person who has inhaled2*mfl7pe (5spj6d qt hm 1w5qn e)wt3l helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch oor(i a7v;myj /f organ pipes?

Explain how a tube might be use6ixe.++:o adv nr d9pyd as a filter to reduce the amplitude of sounds in various frequenapv ei+dd:+96.xon yrcy ranges. (An example is a car muffler.)

Why are the frets on awur 0g4 m3*d0 quz-wzw: ecbb4 guitar (Fig. 12–30) spaced closer together as you move up the fingerboard towardubwurz z4m-3 gc*d:w0q4e0bw the bridge?

A noisy truck approaches you from beweyz3or - -.gxhind a building. Initially you hear it but cannot s3yxw-.o -r ezgee 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 11–15 on diffraction.]

Standing waves can be said to be due to “interference in e2ni:j-tg. 3m5hx amc space,” whereas beats can be said to be due to “interference in tmntxji. g5:ch23e m- aime.” Explain.

In Fig. 12–16, if the frequency of the speakers were loqp)7 hi nnks)zy325lawered, would the points D and C (where destructive and constructive interference occur) move farther apara h3 knqz572liys)np) t or closer together?

Traditional methods of protecting the hearing of people who work in+e1wn7qj + p86mg rxjh 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 hea7hx ewn6jm+rg1 jq+8 pdphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–ee2z3-f fzw ncat -a0.31. 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 component frequencies farther apatzffnze .c-2wa 0- 3eart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mw4u fl zz3*/;r rc5 (kn dxf+ouxxj70eove in the same direction, with thjw/fuo;n+lxzk3 c4z(xex ud*57fr0 re same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a peiqb9c9+g t0warson at rest with respect to the source? Is the waveq +g ac09btiw9length or velocity changed?

Figure 12–32 shows various positio7+y:s minj cvg,-z)s fey1* dcns 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 child hear the highest frequency forvdm+-ncesy *c ,gi71y)j: sf z the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lg(/:w.6me rto*oo d wlistening for the echo of her shout reflected by a cliff at :rol gweo.mdw/t 6o(* 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 o n.i/by(kqjizuy5 ksw:n )/t+ f his ship just below the waterline. He hears 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 1b isw k/ui.zj:+y (kt5y/qn)n 560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavele-dg)k8rsr.i/,6 tdiy s*zt iwngths 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 drifti -fw.p2b 0kspmng just above a school of tuna on a foggy day. Wit.pmpw0-ks2 f bhout 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 fr35aw t don*ngk7y:ig -om the top of a cliff. The splash it makes when striking the water below is h5i 3:*a-tgwnn dgyo7 keard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone st-9 llndj e2di:x)9 avdrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 d l99: )dnla-j vxied2s 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 td,y4y ml qhbk70f3oh1he “5-second rule” for estimating the distance from a lightning strike if the temperaturemy7 k 4by 13l,fqh0doh is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dl8c4 u( ,ainb cr2 qrk9+vyco2:5tviuB?    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 intensiz7 d/xege:x 2v5k zxe/ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produ6r /na d7epej2ce a sound level of 95 dB when fired simultaneously at a certain place, what will be thd n27earp 6/eje sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpe/apyour lwr/ko lj.+q/6u(8 lane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perlw+oruqy p6/u .a8l /( o/rekjson experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said toe:igqy7;,0 .daqx x iu have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What isi7i;g,ua0.exqy :dq x the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frodfhfy mufg 517e-e( 9zm a person speaking in normal conversation. Use Table 1fd(g 7 ef1m9-hfzeyu52–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area jt)qndm93k k9xhb.k2 5:yha h 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 atyvjh.u o9ud(k 1kiw.eg -oq( 2 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3 .idjvou( k.kq-uw9 (og21yeh.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB wn v8qqgcb5s*uk2n-a* :e je7ahen placed 2.8 m in front of a loudspeaker on the stage. ae8kgs :5u-v7qc*e*ajbnn2q
(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 mc;f.6,pddb x ;-w k:1 bbmt7wuo+ stldetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ ubxfdms;wop:+bw ,bmt 6 .7l1 dt-c;k by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wz2h* ovns2x ;oill the intensity increase? Increase by a f*ov 2;hs2nxzoactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has aj285 znona 2,dqbw+ dtwice the frequency of the other. What is the ratio of their intensitb 2qwaon z8j52ad+, dnies?   

  What would be the sound level (in dB) of a soundlj+ p2y upjk7+j+4hjd wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm hud4j2p+y+p7 jj l+kjat 300 Hz?    dB

  A 6000-Hz tone must hajyc* gwg7ftjpc4125* l 0az ttve what sound level to seem as loud as a 100-Hz tone that has a 5a*y*t05c w2z tjcp4 lg1 t7fjg0-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the p opz9o)bilf:i+ki9:(m dg* jsound level is 30 dB? (See Fig. 12–il:fb9)p (iomgo: * i9zk+jd p6.)

  Your auditory system can accommodate a huge range of soundjdhqyg3*gg cc9;eq /b6 7tx 8q levels. What is the ratioh7q xcbtgec/d 9 6;q*gjg 8y3q of highest 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 of bs4t i)d xh0.k*.iad ythe vibrating portion is 32 cm, and it has a mass of 0.35 g. Under whas 0b4x * di.kid.ath)yt tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fir/4pg1zk.wx:t qgxy ,sst three audible overtong/p,xkt.w:x1 qsgy 4 zes 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 mv.v7) dbh-z fexpect from blowing across the top of an emptyd .f7bm-)vvh z soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipesq+jj .c ) bllct6pqau7-+cd)e spanning the range of human hearing (20 Hz to 20 kHz), what would be the range.6e) qljl+c7 c-tud+jbca)qp of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencgbuwgdaf, q+4 6g l +l:x 29v7dss3ircy of 540 Hz as its third harmonic. What will be its fundamental frequencv9+ +glws:bua6g,if47 qs3dd clr x2gy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to o1dx fi8;mnw:98 reio play E above middle C (9efndoxr1i :;i8 w8mo330 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 tha7vm3y7 nu(0t; fduel nt emits middle C (262 Hz) when the temperature l7u3u7;en(0 dm vy ntfis 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 20+)5,ul v wozqc $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in g6rqbto b)66 zExample 12–10 should the hole be that must6r)z bogtq b66 be uncovered 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 Hz1l3t0d6et.jz qx* hwd, 440 Hz, and 616 Hz, but not at any other frequenci wz1d6t*x t.0jedhq l3es 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 r.n6qw; ly zu,.k q yv.1sf.boxesonates at two successive.,. y..qzoqsulwnv1x 6 kfy b; harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 0godmwi 9zy7 i c:;)i -rilgs*$^{\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 2.1*by nz*v/oh:qe0nk q:4-m-long organ nko0/:bey qh*q*vn:zpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal tzh-8bn.; g kv2rys1 nis approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimn g trn-k 8v.2hbyzs;1ate the frequencies (in the audible range) 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 beat every 2.0 s when trying to adjust tw /s3xtjhw/o, lo strings, one of which is soundin/tl3 hx,/w osjg 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (gw-. s zd/ kcj9ju843fudoxr 6262 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 o2nnk+fn: ld bp93 vf5pperates 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 50f 9n5+3:2nplfbdnvk p00 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork an1:f lj o lws)j8-v/u fbfn)8vhd 9 beats/s when:obfv1/jl ))8w 8s hfnjlf-uv sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tm(nfsavow*2w p4brn,f5 +oh6ension in one string is then wwa n4om+(vf*5hb n6of2,spr decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hehl6)5c qno e.yard if two identical flutes each try to play middle C (262 H6 oc eh)n.q5ylz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,qpqpgd;7w i)niw.;o)*( rw ya 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 B and C are sounded together, the bead ig)*;wwap(oqw)7 ;p iyn.qr t frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speakew2x(lt+a c f ons5ma2af61q4fr and 3.50 m froxsao wlfc 6a (q2nfm+a1425t fm 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 supposedp:n+pqw(.mlo2-ia 0szg cx, c 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, whcnp(:so p,-0x2gm zc+.liaw q at 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 g2)a, humekl 6wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2,6ukha mge)l20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1a ,kp6eaah/; * ,e/ cschb67g(kjqo hsczm;e 7550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s p,he cz;ch ,ja;6 /mace/ ks g(k6be7aq ho7*s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freque jkrf*q7akl3r2 8d0sb ncy do you detect if a fire engine whose sire7s ra8 rd0jb* 3k2qklfn emits at 1550 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 2000x a: s sca:6rta-39tut-Hz source is moving toward you at 15 m/s versus:xc at39 ar6a t:st-us you moving toward it at 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 fca7yjzpd0s2it)b3 e s4:2 otsuv6poq; ((swlrequency horn. When one is at rest and the other is moving toward the first at ptwo p es:d cqio(z s34(s2v0t72uy)j;lsab6 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kH ll f5cigw ht170njws4qnm)+z qn3p;5 z and receives them returned from an obtnwj ;qgip s h l0m4w) 75n+nlz3c5qf1ject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fliet6+yi ;slwa l2s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in t +lyls iw;t2a6he reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on 5g bd4:fj)iugd.jll*nk 82jwo9b ys1 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 approached the station at a speed of*gd. :g 1bfnu52sjdjwl j4yb)89o ilk 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow s,kisw rljt:;nijr in 93 s4e-*peeds. 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 le rt3 rljie-s9n* ,jw4n kii;s:g arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavesb8k g(x,/0 3g /yvo hdxslijx/ 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 frequencyixmzgr ly1 b+ 6-(2u/qgyulr/ 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observ b6-1g2qrix+( ulzlurm/yg y/ers 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 8bjcgpgb9e gaeo2dv5 0an 3(0edhs56 if 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 spir ll fa-- xss*(ww)u+eed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’swf( )r*+lxi sw- -sual 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 tcpo 08t)s 2dnqhin atmosphere of a planet where the speed of sound is only about 3)q2sp0n o ctd85 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 ocea gjsjh9:0y;qp wc3si 8n. Determine the shock wave angle it s 38hqp90; :jiscyjgw 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 xs60z46yaoun $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground6x 1kozj8gq(0 +rbrj 4pso0xz 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. 12–34. Determin 406(skr+01 q8xjjoprzxobzg e
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulec)pwvqr 4 8n6ses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time bq )wver6 48cnpetween pulses (in fresh water)?    s

  Approximately how many octaves are th4 ne-obuesb2+ ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display/cj n5 u1shg*s called a sewer pipe symphony. It consists of many plasti /ng *sjhcs1u5c pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a per 3crs 71ftl;egn,9ct zson makes a sound close to the threshold of human hearing (0 dB). What will be tr ,n3cectftgl;zs 719he sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound an 7kvj6sizg30jkpsx0 4d an 87-dB sound are heard simultaneously?376gxiskvzjpk40sj0    dB

  The sound level 12.0 m from a loudspeaker, placed in the opb8g6 nl,pzi.fm *1e eaen, is 105 dB. What is the acoustic power output (W) of the speaker, g *i,.m1 bn pae6fle8zassuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thaz,6 a*4syg a;teodayb:34 vae power output drops by 10 dB at 15 kHz 6 4ae; *o4asg:3datyyaza, vb. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tylb+kj29mntg /pically wear protective 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 the power intercepted by an unprotected ear at a distance of 30 m/ gt+j9bl2kn m from a jet airplane engine?    W

  In audio and communicati5/4;z.lnyrai / xa8 lv3k tnwnons systems, 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 frequenh)fj yvgx/5co6t s-t .cy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamentacouv:off:fe +l2o. q ;l frequency of 440 Hz and af+ovqfoe;:o .2 fl:c u 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 w wpju6n0efnclx9*,hgf o/2(v5oy ,uv82 wiga vertical open tube filled with water (Fig. 12–35). The water level is allo x ecv f gih/gw 5(nlfwuyo0,9 u2n8*owj6p,2vwed 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 maezrwf:n3ga sn h72v-(ss 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itf73n:wsegan2(h rv -zs fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one b o0x.zl3m -vcfull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two s*9,sg6)ln uvvzwglkdzvnc;z ,xn):3 ources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abvl,g6v*zzg)w,zudkc n xnlv 3n9:) s;out 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 btwhpi.o:f;urbsz9, m( d:h1whistles. One train is stationary. The conductor on the stationary train hears a 3.0:wuzobbh fi mp; (r1.,ts:h9d-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam traif7;-pytf.ip yn 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 (assume constant velocityf-.t ;7pfpyy i)?    m/s

  At a race track, you can estimate the speed of cars just by listu 7hzchf7mkl 9b:2(zuening 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 fasmhzh 9u ku(l7c 7zb:2ft is it going?    m/s

  Two open organ pipes, sounding together, produc:keq-x8 3kfyh;xh1c me a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oh3f x-kh 1c:m8yk ;xqether?    m

Two loudspeakers are acrghfp zr. 1kqt jl(+pz::h+*t opposite ends of a railroad car as it moves past a stationary obgfh+1jqc:pr zh: *l+ pz. (krtserver at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 48 upknk,/ut-p0lu ysm/s what beat frequency would you expect if 5.50-ktup, 0s nl/8yp4 uku-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/22 wb evx6l rbq+p5yz4s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detyq2lx526v b bez+wr4pected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Th vi+cd +t3ezg38czlz+ e pulses 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 beforzi8++t3vclg+z zd e3ce the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villag;hhx,jy jpkaiq b0 kd--a7,( ge 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 long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and whicy0 xhp-g7d-aq;ha,kijj,b ( k h overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenh;6xkt ,voj8 iing 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 standing waves in this rov;ik6 x,jho 8tom.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alum k amafy6,tlagj w3td(7/.:g vinum rod held in the hand near the rod’s midpoint. The rod is s3gat(, kmf7val:a/6.gd w y jttroked 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 humanfj fy25 3lo7tl ear at a frequency of aboult f 2jyol7f35t 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonicx2rtng6 v7 7cj.qml 48/psrvi boom 1.5 min after the plane passes directly overhead. What is the plane’s altituivmqr7lsjvcrgt2 4xn.6p 78/ de?    $ \times10^{4 }$ m

  The wake of a speedboat i,1ho0 xja-cev ;dlv-gs 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