What is the evidence that sound travels 7mq3mygi,k1fx1dw. 9e1 bncxmd8w3t as a wave?

What is the evidence that sound is a form of . lo7:4iwfpxvq7j4e y(2 xqox energy?

Children sometimes play with a homemade “telephonec9fn0pt74xfjs lb+9 q” 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 clearly how the sound bfj nq0 9+p74lfs xc9twave travels from one cup to the other.

When a sound wave passes from air into water, do yova4owqo nk xf(1 w vu1/3clj(0u expect the frequency or wavelength to c/( f1vwo04vo1k( ua njqlxc3w hange?

What evidence can you give that the speed of sound in air doec2rw3eugzgp k7- h/1plq yf 0)s not depend significantly on frequency?f7gp l0yp1-/k32 hgwcqruz e)

The voice of a person who has inhaled helium sounds very high-pitch 3vrrx4d:d+ h*mi:ozked. Why?

How will the air temperature in a ro2d p qcw(is8e-om affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducmt(11v1oqg5h5 x fu o;c:zfmme the amplitude of sounds in various frequency ranges. (An example:f1 m 1;ohvgzmo(f1 cu tq5m5x is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as2ru xkyd:/qxdrldc4/- kt : 7-8srpfz you move up the fingerboard toward the bri7qzr tdckf /2sd- ud: r4xyl/:kp8 r-xdge?

A noisy truck approaches you from behind a building. Initially you hear it 3bsc1i+p;g8 ik 1 jqeubut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency ni+ujkc; 1e bsq3gp8 i1oise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be8 ei imil)es;8 due to “interference in space,” whereas beats can be said to be due to “interfereismee)i8 8i;l nce in time.” Explain.

In Fig. 12–16, if the frequency of tci n vke9(g53h3;b1a(jl oc fihe speakers were lowered, would the points D and C (where destructive and constructive interfoa h3c( jv3i5g fk(bcni9el1; erence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people o06ny ) +02u0ydu ralqr4paej who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not b0q64e)u2lydr0j oap+ n ur0ya lock 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. 12–31. Each wave can be thought fpet-fbr y; (u1 kz.(mof as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (r-fyfb1z .e(p tm;uk (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer e(q xf)(3wtd.3ktsebi.b 2fimove in the same direction, with the same velocitye)b3(t ftd2 qsbi.x.i3ew f(k? Explain.

If a wind is blowing, wkj 5 g3r0kes*cill this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chang5 *0ekjsc rg3ked?

Figure 12–32 shows various positions of a child in motion on a swing. A hfk u h u:8/6mb sosup65bypv0k6t .bq5eo 2e3monitor 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 the sound of th2puh8 b oo /k5ktuh b6e vfbpsuq3me5:6y6s0.e whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the.xz-0.v e f xn 8ofn0 rc,;nky/lr8h,ffkpu:o echo of her shout reflected by a cliff at the far end of the lake. She hears the o:/, rx8-xh v, klyfn0;fko f.r czpen0uf 8n.echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hi 0.*xiifdy xai4bdl0d d).(nos 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 x ()bd*axfd l .n4diii.o00ydseawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ven8x* mt ,i-vin 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 sch*qxtumhl9l7s2s u(e)ool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before thlu9l7x)( 2 eq hmsuts*e 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 whenisy1 yt0 +m;xr striking the water below is heard 3.5 s later. How high is the cliff? y xtm+1iy0r;s    m

  A person, with his ear to the ground, see0)w qz.ouj0q y akrm )3*zbi o;qp6wc.s a huge stone strike the concrete pavementjokiwy); z w. ua 6m0rqzb.p) 0oqcq3*. 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 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percen 9xg5gt8 45ksmh/j7hjy bk 6cdt error made over one mile of distance by the “5-second rule” formc x5h4 k6bj9gs7gj 8dy5 /hkt estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity5lmhvhmy ;- )hsti+.v of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a :u7d.ox o,na 7wo +abosound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a souyy8p j yt*u2(rnd level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only oneyy8(t* ru 2yjp is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nois aqb:eqtqmi;xv(2b+3 y jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s ;xbe3( am i:vqq2+tbq.]    dB

  A cassette player is said to have a signal-to-noisblyooh2rfq8; ,p 8 pp74dncl0e ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal ao hplprq8f p2yn0ob d4c8;7,lnd the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persovgrfxq6 tq0zqy 8p)(. euq f( 2sr*9azn speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly2x(qq)u g* v6(f r.8tqr zz9f0sq paye 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 stri5jjwwxfh+t : eqy:4m xa ::(gvkes an 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 ae5u -mlx*6r-w4 m7ao3fpxe m(d hzn;ct 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect 7 edlcxw n6u5m; z (m*peam4h-ox-rf3at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m ino 8 us+ddg ;0co mf(7gvowgt5* front of a loug*c domgs w( go0tu7+ o8f5dv;dspeaker 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 typicallym i+-i-x 6o5, yjdyygf detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectio +d6yii- j xoy5-gmy,fn 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wil77y ukvst;)en l the intensi7 ;ke)u ysnv7tty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thih h76noeg)b 4wcl-ph l7f q0a+(ydf:e frequency of the other. What is t hl7yc-w4b70hi:f+hq ge dp6nof)a(l he ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in 8h 7ggumq /+,hs.mrhjair that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3008g+qr h u7, hh.mjg/ms Hz?    dB

  A 6000-Hz tone must hfmr.kj;fi- im2q6o x97)2am ; xpvzydave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.d2pvjm;mkfiy q9x. r- f i6oxm)27z; a)    dB

What are the lowest and highest frequencies that an ear can detect when the souig ba7w)avxn;gz /p;p1z b/p;nd g;;w/p a;x/vg z pi1pb7anbz) level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of9tqh 7 3lvvh),yug6 i2gl n,lx sound levels. What is the ratio of highest to lowest intensi vhu,3n2y h)6tvg x9ilg,7qllty at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin htl 43 /4ku nlejbqrpe53qr-s(as a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must thlk n4jubsp 3q -e5(eqr4t/lr3e string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiblqvm5uu:i(p6f7pr a2p e ovuumq6vp2ap f5:rip (7ertones 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 blogpr xgxbj;h hwa17c4;o;: w ixk7 5/wzwing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clos4;k/h1 xogx;a; cjxwzwihwb5r :7g 7ped 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-tuob rh;ho5 5, diezp.py;sd* +5zjtq w:myc .y0be pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range odsj*tw;z. 5ycq b i;h.,z:o yh0em5d 5opr py+f the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequ181g t*gerefi ency of 540 Hz as its third harmonic. What will be its fundamental frequency g8tei *er1g1f if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long a-( ubsru+mg;t nd is tuned to play E above middle C (330sr;bmu(gt- u + 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 C (2n ,l.r*mhn /01e:i/e qvield k62 Hz) when the temp qik/:ee1* dl,nlvn0i m.ehr/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 f owqbr 5r//cgxc/;8 dat 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 holf -e c9z 9f qdo ,2dei/e/xv73eerpm.ze be that m 3.99ezdefq cie7/2,vmx prd- f zee/oust 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 26e t l pz89rlnd6rt6q.w:g4z0w lii469umjd z;4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wr9 44i.wdt 9zplr6qtli0dzuwjlg :68;6 e nzmhy 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.ntdne.+,wcb 1r9:h -k iw(lsm It resonates at two successive ha(emrwnncst19,l bd kh-wi +.:rmonics 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 )opdzs 4pn4a+k,s*n: etuh- yz cod0)$^{\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 r4;s xpb.x-3r(efx 4d/hly n/msz;ev a 2.14-m-long organ pipe atefxb vp sysrx-xnh3;4(/me r4 l.dz;/ 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatv9(6f20u*dx ryd) k42uyaxc6wmt wdn ely 2.5 cm long. It is open to the outside and is closed at the other end yfmv)y2utddd*u2xxa0k9r 4 6w (cn6wby 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 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 two strings:8j)tasj)s v n, one of which is sounding 440 Hz. How far off in frequency is the other stri8 tj vass):)jnng? ±    Hz

  What is the beat frequency if middle3l 6z1t 2wziq wvh8:hy 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, while another (brand X) opvfsyax- l0 (39+epusqe1e)s yerates 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 played simultaneously, estimate the operating frequency ofes1vx 3ly9sy (0 eea pq)uf-s+ brand X.    kHz

  A guitar string produces 4 beats/s when sounded wcgw:zdjd6 h.,ith a 350-Hz tuning fork and 9 beats/ jddh,w cg.:z6s when 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. Th2br8 xkz8oc,+b0wjs bh)h76lid.mbv e tension in one string is then decreased by 2.0%. What cl)dbb 0 jsi 78b+vmh.w82 r kohz,xb6will 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 n1bpj gm:pr 1rm)9z7htry to play middle C (262 Hz), but one is at 5.0°C and theg z91pj h)m1mb :rnpr7 other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; when /aaq ixh:/xt;sap):m A and B are sounded together, a beat 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 posx q:h; /x m/sptaaa):isible 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 stan: gw,idk;t05c5a o2f9o8 dwvexrxuw, ds 3.00 m from one speaker and 3.50 m f8 o,wd2w;i x5etv ro0gdw,a: 9uk5x cfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pi rjw.j;*xi+tt +6apmtano 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 6 j;wtrji+a+mtp. x*tthe other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in aigm0u0 mlsrk2ng 0jm/vay a8;oa;y-5 nr. How many beats per second will be heard? (Assum0 ag m0o8s5amn gj y2vkluyr;/0ma;- ne T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’sr fk fk/.ycdhck*5) - kq)dvj8 siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 h )/)kk* k85ckj.ffcyq-v r ddm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you dp f:p7jcz75pk etect if a fire engine whose siren emits at 1pz cfj:577p kp550 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 tohszyy f4bflj+ njj +7 z6ura03j 6o(:eward you at 15 m/s versus you moving toward it at f+( 6jbhr6oysjznf: 3zle07uj4+a jy15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. ah)gogd(6fxm n0 i2b:When one is at rest and the other is moving toward the first at 15 2 x:hm0bgd a()fong6im/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 sou cat(a-n. q mf 2kjn,tbvy,*s9nd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/9 nb tsa,c*f(q2,jk-n.ytma vs What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat xuxu.;jgbj61 t 3 i)dmemits an ultrasonic sound wave with frmu; .d)b g6uij3t 1jxxequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wx.bxdli7 g; :has played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same ton gxx7:bldi; .he 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 us8 jusa 815j-rfkky-n23 junw ses ultrasound 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 away from thj-8skjj3 uknf- 1ry58una 2wse sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ,+tppwxr pt :*k w ddygbs(b/822bv (rency $2.25 \times10^{ 6}$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 sostjr**;xy. v8)rogn vi yyy 7*und of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, y*xvni *tv. o;gj*syy rr 8y)7
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its )wip10+s tm2cpw bz5zs2 azo8 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 t:h +yww fhll)r 8tu)(mhe speed of sound is 310 m/s (a) What is the angle the shock wave make)m hh:l+)tr8u (yw fwls 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 isz7mq -q9wocmf .+y7w s only about 35 m/s mw+.fq7cwzm s 9yq7- o
(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 850ixaq:94h s) sglt/ t7h0 m/s strikes the ocean. Determine the shock wave angle q9h4:/h gt )tx aissl7it 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 ny7+ )div.lai $/theta$ 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 vi)d.t ojz/k7 :i iyes9 )b*;qhey7hf2zuwq8the ground flying faster than tiy 8ti)q7 2:*z7zk h y.vi)sf;ubdqj/ ow9e hehe 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. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses r7, tc8ol duf,ikz86xz-fm)my7j jm :downward from the bottom of the boat, and then detejyo6 i, 78 m m-,j 8ffku7zmtx)zldc:rcts echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octavep ozeac ,0pkycy5 a3f*w4h+n;1gl4gxs are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer g-bf8wg8 5pu v4ftx*h pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ent f5w*-ug8g8f vbx 4hpds.
(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 pe4//wiz,gki s ,iy4/ksy m6ngfrson makes a sound close to the threshold of human hearing (0 dB). What will be the sound lefns/s /z/m g,k4,iyw4i 6kiygvel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dsvg v58vfe,ay0-f + xfB sound and an 87-dB sound are heardf0 v eyvas,58fg+-xfv simultaneously?    dB

  The sound level 12.0 m from a ,f ocj.ft5iz /loudspeaker, placed in the open, is 105 dB. What is thzf., f5ticjo/ e acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 14fos:p .i 2ozt ji420xi gesc550 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watozeg2.cf 2st s jxi ii0op54:4ts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their5kv4g 9z tl;sd ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and ;klg9 vzt54sd 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 communicationdioiq0sw3i069qa)f(z2 swn ps 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 frequeno2 r a (ly.;rjwne3vr:0eu fz1cy 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 i-,e1 l8b3t4l-rkz lacsdm7s fixed points with a fundamental frequency of 440 Hz and a malzbl4rema ,dl3-ics8-t71 s kss 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 tube filled with 9m*xh(hdm oty2zr qk7 o en)yr9u:,1iwater (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork whenh)yzu*q r1x9yr omn 2eodi,kt(7: 9mh 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 h 46w,sd3b5ruar6w pg is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the45p 3a66duhrw, brgws tube?    $ \times10^{ 2}$ N

A highway overpass was observed to rev+j6)wdvp v1 o na-jb*sonate 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 tom9.zfc.k ww5j ne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determickj m z.fww.59ne 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-iut 4-l 7 /4p+02 uqw7okcwhwm*jm0q)fb fitzHz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mf fcqu)t -wb7z i+2w04o0i uh7j m tw/qp*l4mkoving train?   m/s

  The frequency of a steam traintu8attz 7.n*gzg51si 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 velocity) . g1tzs7tn*u5izg8ta ?    m/s

  At a race track, you can esvy3 jcbk62w1 ftimate the 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 by3vbfw2 6cjyk 1 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 g1zqu67o 5m pafrequency of 11 Hz. The shorter one is 2.40 m long7o pqmu51ga6z. How long is the other?    m

Two loudspeakers are at opposit:+j -urvxp*tp.cuxp*o /9a zoe ends of a railroad car as it moves past a stationary x zo* :-pr 9ca.+pju/uopv*t xobserver 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 flo1lnrv9 ahwx3r9ro pcp 3/)r6 zw in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasv9a3z61wrl3rr 9/nrpo) xh c pound 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 bb1t46ei /b jzm/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected bb/z 1itje6b4by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high f)q hgkmq*+ yd+requency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detg)q + +m*yhkqdected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send ;:4v q7vdeha* x fngk/vcqf)-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 ag;/v -ck)fnevxqh7vd: 4q*f played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenin:8fe be6 ivss-mdq-d9et8 /edg 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.qeb:d v-m-e6 d8e/s9ts ei d8f 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 r y9* bydsp8; isddb/8rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-8b;bd8yr/s* d9yispd 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 a frequency of ab yhi:. xx:*hgpxg:.ip* xh: yhout 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 sonic bsrr 2(nihrs.:q d)nfbb+;/ bmoom 1.5 min after the plane passes directly ovsi df:hmrnsnbr;/)+qbb 2 r(.erhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa vmob0p2 goq )c z:u86sxaj wd3i+:,ui.6lzgat 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