What is the evidence that sound travels a mc+2 bu8ler-b t +xm-snvf l5zr+hq74s a wave?

What is the evidence thadmw;i,ya*(d+ dx bx9ct sound is a form of energy?

Children sometimes play with a homemade “telephone”ylszopvzd 4p6 k(/i5* by attaching a string to the bottoms of two paper cups. When the string is s6p/5 p(4dy vkozils z*tretched 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 pa94xqpwlv+ mft0x .dj1 gpnp;4sses from air into water, do you expect the frequency or wavelength to cx+1jpf lxpg4vd 9 .m p4;n0twqhange?

What evidence can you give that t iaa2qqx zz8wd8l2 zg53ax0w6he speed of sound in air does not depend significantly on 36gdz5x xzw 8a0 zialq28qaw 2frequency?

The voice of a person who has inhaled helium sounds very high-pitchvpjpue saec+ z-/9 ,6ped. Why?

How will the air temperature in a room affect the ed d4u(hkf9 z2 e0jxd8pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of 2ol j29xra1 qusounds in various frequency ranges. (An exam1oa j 2r92qulxple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30)) 9m4)m plskntm 1vs*y89e twp spaced closer together as you move up the fingerboard toward thept 9mmts *pe8) s1k lw)vm49yn bridge?

A noisy truck approaches you from behind a building. Initially you hear it but cxvx )e8q0+w kwfpj0- z)n k+ztannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you j -n)+)w0zkvwfe8xtk x 0q+zp 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 spa50oa49h, .l mqrroooace,” whereas beats can bem5 rol04o ao 9oar.hq, said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou,du wdj;.9 jlbld the points D and C l u9jd;jb.,dw(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearib5-7z+ 6 b o/jx2u,jq ir aplajidz:-hng of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more nois+jj hxp6 jzai: b-b2rl 7-zo ,dui5/qae reduce the sound levels reaching the ears?

Consider the two waves sho:9.aqoj0 piyw wn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequenciipj.o90 y:w aqes farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if tjldw,u) w44sb- f3nmnhe source and observer move in the same direction, with the same velouf 4sm,dwnlb)j4 w3 n-city? Explain.

If a wind is blowing, will this alter the frequency of the smiq/v/m29 ho4;vj+ gx (.3tpgtb pyua ound heard by a perstxi ghoqbp9a;v j3 ( um/+g2y/vm4.tp on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mon49-midj1ps o el7:qr6:kdkg fitor 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 okd-:qrpjil 9fgs7:14 e6m k dfor the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofd( m 8xc1rb7nj her shout reflected by a cliff at the far end of the1(jn m78xdrcb lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the s 8 umaky0l5r/oide of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor direca k 08yrml5/uotly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthsed99y o8f1)iqo mhv6 z 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 h.jd23ger9p)47c.nh zgv zo xw.a7rs drifting just above a school of tuna on a foggy day. Without warning, an en7 ja 4e w.7og v.ngch9r3 xhsp.dz)2rzgine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splashpdb1/1f x6w7v ylmv whzzf3i7z6bt6: it makes when striking the water below is heard 3.5 s lat7wizwtfm1vblb6:7fyd p x6/ 3 vz16 hzer. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concre4 ,le) crdb/kqfyc ) q;;:(pv0qsxxnf te 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 s apart. How far away did the impact occur? See Table 12–1.xbc qde(lv)k f/q4r:qf ;nps0;yx), c$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one miy.,,w7 dhb:dmrr76ce shjan6le of distance by the “5-second rule” for estimating the distance from a lighrnh:wma67c , 6eh,rs7j.dbdy tning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s4l3 dlrtt 35fkound 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 soundwt(*iguunzdax- +9 -) q7xmxgs:5 c* a,v xsih whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level oft g6,88 bsqfvh)k +qpy 95 dB when fired simultaneously at a certain place, what qv 6,+tyq bsg)kp h88fwill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dist+ /9huwk qsr6oance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experiench9/sqrw ku +6oe if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is s9pi8f; ny gu p 8dhb-/sdc hb wq9sw3a9hg.:*qaid to have a signal-to-noise ratio of 58 dB, whereas for a CD playesh g ga9p n/f.dpwd8y- h9wq8u: *9;cbqb 3ishr it is 95 dB. What is 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 from a personlm2fkrr (s oao)gq618m(n/ oj speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovg(o2)(mar /n 6kj8l1f orqmo ser 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 b 1jmff*x (j0hgfm: ;san eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whilurqw o8 tp(dt;::q);e oe b1soe 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 a loudspeaker t(s;bueqodeo tq : 81op);r:wconnected 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 6: nod3c)xjyb when placed 2.8 m in front of a loudspeaker63)nody jxb :c on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically deteoh5,x; s yd)cx2dm fu5ct 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?fxu 2 d,xcdoh;5ym)5s [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wil)+ 3nuuy1phyzl the intensiyn3)u z+1uyp hty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace7nv qy.6o1lj.21 ov 7o )nzqs-zgatcjment amplitudes, but one has twice the frequency of the other. What is the ratio of their intensit6 vvzq7c1gl ay-oo7zt2.n. jn j)1osqies?   

  What would be the sound level (in dB) of a sound wave in air that corre 8dla ym894tai*v xr*esponds to a displacement amplitut 9vmdx4ae 8a* 8l*iryde of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to s833w ytcg c-dxe:bbr )eem as loud as a 100-Hz tone that has a yb 8:t-x3ccg db)r we350-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequenciesvk6:qr np u2,j that an ear can detect when the sound lever qk,up2j vn6:l is 30 dB? (See Fig. 12–6.)

  Your auditory system; go9u; 5hmhg (w6efo7y(l dp4auu5eh can accommodate a huge range of sound levels. What is the ratio of highest to lowest ih54oolgm;h6(f 9epu a;euh7(5yg duwntensity 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 .n*t h2fafvvnd01c t9l/3bftHz. The length of the vibrating portion is 32 cm,*3 h0d2tlft.n9 vvn 1a/fcbtf and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fdefrrh1/3uc35b1w 7c zjy eg6gcm )q5undamental and first three audible overtones if th5eg 153r6gd/f 1bwj q3 uzcrc7chmye )e 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 froco6onyv0q d)/m blowing across the top of an empty soda bottle that is 18 cm deep, if youdv/nq y)c6 o0o 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 witl7v. aj nj ph -glbvo.c q7ga+d+(/xi7h open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the le7/+ +pca- llbn.xg7(.o aiq7gjv jhdv ngths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its t*u+.ey-y 8aawb 8fmwmhird harmonic. What will be its fundamental frequency if it is fingered at a length of only 60ay8ewm um-8wa +.yfb* % of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovr6ou. xr vjj.y-,hz;zj j ,c:knr/2ace middle C (330 Hz).cc.ojjyrzk uh ,x rj,v.62anz:r/ j-;
(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 lengt faqoo2ti ;b 2)eyy+f5h of an open organ pipe that emits middle C (262 Hz) when the temperature2q )25i;foy eat+ obfy 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 20i v7o cq5frl g8hu)9x: $^{\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 hole,;pglswf o*;v be that must be uncovered to play D above;*ogwl ,v f;sp 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 p-*qkh. fpz.bm eh-7b64un ypripe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other- h bkzu-ye.pb7n.*pq6h 4rmf frequencies 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(fl ;xye * d1mrw7y; cko.2sz4xjhg*o m long is open at both ends. It resonates at two successive harmonics of frequen oxj cgw**f.y4y2d1x;elr7 s km;(ohz cies 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 y jr-7qxj 4v3x$^{\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 rang hct+h(9ypzqh3k nk+k c4qat -bp 362ypf- ;bde for a 2.14-m-long organ piph-p3at3p9kqk4 62 q+fyt+;z -n d (ckbhypbche at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ecchj c-+/b 4lis approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What/cc+l-hcb j4e 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 adju f5,s2f (3bk0cx6 jr;k lvaiekst two strings, one of which is sounding 440 Hz. How far off in frequency i0kfe5jrs6kiv, a; 3b kfxc2(ls the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andt6: ( 9aj5t) hq bwaxcke0gtu, $C^＃$ (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)bql7o ;byi*6nrs 3 cw operates 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 freque* b y3iqwso;c brnl7)6ncy 5000 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 ald ddti96:ngnz+8z 3vnd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your t 8n v3:i+9lddzd6n zgreasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensionv7i7v cp(pq0m ttv/f0xp ktzm.t;; 3g in one string is then decreased by 2.0%. What will be the beat frequency hetmqcp7vtxt (03v7; mgf.p v0kip/ zt; ard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eaclu2q 8bw4vtt;jj)xg ag -th9j)e 8w.sh try to play middle C (262 Hz), but one is at 5.0°C and thg hvxel)wttj8w s2gt8b9 .u4aqj;)-j e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hzxe6i03tuybzwn cq, 5/; when 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.x,3ei6 zcy 5wn/b q0ut 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 standsi5;o fana-x2x q/ upe7 3.00 m from one speaker and 3.50 m fr5 -7paqia 2/u;oenxf xom 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 piaidioui*,0c j-no tuner hears three beats every 2.0 s when th cuj -*iii0d,oey are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound ,i k;5vdsylvgn 616he of wavelengths 2.64 m and 2.76 m in air. How many beats per second w yg k56sv;e,1l dih6nvill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s kt7mztno7 *oc,91m byzlt)2g siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m *2lmokt)7m nzg ,o zt1y9b7ct/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What q3va6afniv7- d zep95frequency do you detect if a fire engine whose siren emits at 1550 Hz moda53ifv- 9 7pzane6qvves 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 tow dv +w1xtc4+vxy6g q0gard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the t61x4dy++ vg w0qvxgcsame? 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 ligy s 3j-y7+jsame single frequency horn. When one is at rest and the other is moving toward the first +ljgis3yj -7y at 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 kHz94 ujpcec0a. o and receives them returned from an object moving directly away from it at 25 m/s What is the pj 4oeca0.9 cureceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b 09 :okwh ;slke+blps2at emits an ultrasonic sound wave with frequency 0phb ;sk selk+w92o:l 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplecv4is yoo- kkiq1529a r experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station akv cy-o159 4sok2qiai t a speed of 10 m/s ?   Hz

  A Doppler flow meter uses u+*w8i iv 3b/q1h ij2ya1eq bczltrasound 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 fre3*zqc jviayhqi2b i/w+b1e 8 1quency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wxq. omf bzbk*dbf,si((a;; t( aves 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 2fm8a6xz 1qs35ym abn+jqzr 3 sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what 6m f3 aq2x5jzyb3n1asz+ rq8mfrequency 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*w(ee b qlpy+y.c g.,w land 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 lkxcgzx78 yn4fqza )4/ fbj(9Mach 2.3 where the speed of sound is 310 m/s (a) What is theqzlj7xn8ybxf4 g(9a/) 4fkzc angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed oi*o7s8z(y k cjf sound is only about 3ycsz jk7(*o8 i5 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 8c61typbt8a4 q 500 m/s strikes the ocean. Determine the shock wave angle iyb81 patt4q6ct 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 d tii9ph9 2*b2hu2t2dy7rdxs7evy(i$/theta$ 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 y.1(wq.u/ fiw cqxq,d1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane hasuw.qc1 fx(i wd yq/,q. 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 downwardez-srqh)oqlh t yyg1 /;41hh3 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 between pulses (in fresh watee1;g lyqh/31) z-yts4 ohqhhrr)?    s

  Approximately how many octaves are there in the human audible ilz0fvnjp9b(i*h3,vo;y b3d range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of5 rs 1fbkv(e.l 9pmf68baxwi/ many plastic pipes of vaf5k/ vfreb8. w( p1ail9 6sxmbrious 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 person makes a sound close to the thr ) wtedc63i:nwcl*h9as 1l:kaeshold of human hearing (0 dB). What willkn:3saciewd t*)ac1h :wl 9 6l be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound xn9;8hlp u0qx,httl) are heard sih;q u)h,t9lxltx08pn multaneously?    dB

  The sound level 12.0 m from a loudspeaker, place uc) muwg-eq ta: /1ehv9a.s-ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it r9eee) w-c m.taqu: g/-s1hvu aadiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Tnbs3w yda7doloz db(m yp- 05,beo47*he power output drops by 10 dB at 15 kHz. What is the power output in watts at yz5 dlb7 n3(m wodoea s,40ybpo7-d b*15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ee,av xo;;masm) 2 cu6tars. 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 b;eamc ut )sm,x;v a62oe the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thefk9s 4/ad ,b 07 0olc42 v)c*4isfoitwwbpexv 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 tuna)f p90zimjizpwyi 8zhl4q r6. w:(j2ed to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betw* vu6 xkyxyyfsb.7l8 k3no:3 peen fixed points with a fundamental fk y:v.pyn8fuks3l37 xb xy*6orequency 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 tube filled witk,3ss(n 8 gjdyh water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube asy gs n3jdk,8(bove 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 masm, ph/jeo69+b c sylp-s 2.10 g is near a tube that is open at one end+yseppm/hcj l6-bo ,9 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 the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asxrky/ar83 hs; 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 from two sourcexqe41 j*gx dt4s. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about axqjdxgte 41*4 nd 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. Th5tgmt z5y+yr + iu0-rx/qpr8ve conductor on the stationary train hears a 3.0-Hz beat frequency when the other tra +qgrvt50y-r8+ y/5mzptxr iuin approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After bfohf ct)y 5k(/n 9d*nit pas o*ffk)nd htb/cn5y9(ses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by kz5i fqnfwne;sy +8h z,:.) edlistening to the differencekef+eqh)yzi,.:8n 5zn sw;df in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce 6g2 , y)/k;atgwt brbua beat frequency of 11 Hz. The shorter one is 2.40 / )a2k;uty 6trbw,gbg m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rg 2r in/5. b(psoes4hssq : :j;lp0tebailroad car as it moves past a stationary observe.2gss/t i5 (boh ;je::0s4s nrlqbepp r 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 aog68o q;on,08d9 aru7gkb/i z;xz tdwjrta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that;io8naktzx ; 0b9dgz r87oug qdj,w6/ 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 lft r,kem6rym7gucj )/;e .b; 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 ofjm bm u.gylec6 ekrtf; /)7r,; the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series o 4nt 4cuuac+wwec l.28un3 r0wf high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms lol0awru +u uw 3c4 n28n4cecw.tng. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from vcp + g30y9ct cz-sh-;n3n zxione Alpine village to another. Since lower frequency sounds are less susceptible to ptcn9xvz--hys330+c cz i;gn 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 which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be3kka1w: t4u0.sw r4czho av.g 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 :3 c0.h4gsurk kw.a14ovwz ta 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, wmg xn(u8z4e*” involves a long, slender aluminum rod held in the hand near nzugemw4*8(xthe 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-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 thres pxln wpsu c)gi511b483rcee 8hold of hearing for the human ear at a frequency of about nw413bx ecu i lr)8pscpeg8151000 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 td:cvigm/ p+5wzuzue z7*7gg9,c7ajm he sonic boom 1.5 mi puz,dm *+j7:uzc7 ig vwm5 ggc7e/z9an after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 4s5-w x9uv0a5ja pxnt ls8x4e15 $^{\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