What is the evidence that sound travels as a wq h/wml 7 fm((t3+t.m o8egoxxave?

What is the evidence that sound is a form oft ssh/0-u;doeytv rlpi)l7 p7 ag-k+ x7r)t;o energy?

Children sometimes play with a hdvkd vjea-.1j +cw6y6m s/i6momemade “telephone” by attaching a string to the bottoms of two paper cups. When the string idkjvi6s6/myd+ c6vj1.ew ma-s stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do yol*e( jxggtyxr,)-y0eu expect the frequency or wave0y* tyg(xelje,x) -rglength to change?

What evidence can you gq nvwniamx0 92.w:o1cx4apu) ive that the speed of sound in air does not depend significaa)02nw .9 vwcxxqm:uai1p no4 ntly on frequency?

The voice of a person who has inhaled helium soundgvolir 2pto(zn;uu:;5 wz;x9 s very high-pitched. Why?

How will the air temperature int jc.8m5ql.hc cv-a3 g a room affect the pitch of organ pipes?

Explain how a tube might be used as a fil vh-7hnkj 63uhter to reduce the amplitude of sounds in variouhh-nk6uv7 j3hs frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer f p-r+/hljez: together as you move up the fingerboard tow:jfhp/-erz + lard the bridge?

A noisy truck approaches y (t,lrw2b 1f ivs))xwg*wnb)t ou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on dibtn1rvww fl w)x)2t i(g* ),sbffraction.]

Standing waves can be9 rea o3im/29ro 6 eqbwq5aa3d said to be due to “interference in space,” whereas beats can be said to be due to “interference in a6owb3 a/eqqra d9 5ei39mr2otime.” Explain.

In Fig. 12–16, if thp1 5do1j de-fiqxb0)ce frequency of the speakers were lowered, would the points D and C (whereci5fbj1poe0 d d1xq -) destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i /u fodr ;;ew/l +:kclegqn5f+n 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 n/5 +g/ fl;c+fwu:el rdoq e;kin addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves/iflqt y; ,ca+j w /n9jxu4a+q shown 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 frequencies fartu+jy;/,l/ atwj 4 iqcx9f+qa nher apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the mgyjeesb:*g. ku. i/ 4-lhfuil,j+3u same direction, with the same velocy.m3lujj *buu ile. k :-e,fis+ g/4hgity? Explain.

If a wind is blowing, will thg;hlps2pa5 6 pt+quw /is alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or veloctl2p; +qsphp a/5gwu 6ity changed?

Figure 12–32 shows various positions of a child in motion on a swing.qgnund-e20 d1 A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child1u-0 d gennq2d hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lak7eczkyjm .lsx 4mk 8g/;kt;6unq) rh-e by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afterl;gk86u km )zc; n-ms trj/7ye4q. kxh shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the mux79szoa 33f 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 m3a39 xozf us7is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengupvfc373he o-w8s e r)ths 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 isw9 nukm/i i1.0k6ayfdik,:uh drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 :/m ,ukfnkw1ii da kuh96 .yi0km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking :d0 m vo-g7zqp0koiw, the water below is heard 3.5 s later. How -7m ik0 q0od:vz,gpo whigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pao 43elrw 95i8sd shr4kvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they aw5s 4l34od8kie9 h rsrre 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by th2ec3 o6) ,sfn9w sxqywe “5-second rule” for estimating the distance from a lightninwe 2sof )wxs q3nc,6y9g strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thv ;ursva,6; tpcp od: o3k9p+j/n8ng je 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 levewf 3v jm d n5/c8qshbg1pq:4)wl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d*wbeg. zon ,(8rapg 4wB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intp(*4r bgo,z wweg.8a nensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four sq y6cu;c 29ll 6avn9oequally noisy jet engines is olly 6ccqua26 s9v n;9experiencing 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.]    dB

  A cassette player is said to have a signal-to-noise rat31jdt i(ac(rr6-n + nalflt+hio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitil3a (+rct a-rfln6h1 indtj(+es 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 person spk s;d 6 xxhr(pxhg/-.k1j us-ceaking in normal conversatsu6./h(-pxxrj ck1-s ;xkd ghion. Use Table 12–2. 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 earx*kvs7pz 0y,3hxjv4 e drum 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 i7eah6*c 9apeo s rated at 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.ope6a7hae* 9c5 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 in front offseckxwja/+4 y:70 rsav6g h8 a loudwe8 cs/4v0rha :axksy67j fg+speaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whaml,y3e0 pz0-vhvz0m n t is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9 30lv zn,eym0v 0zpmh-.]$\approx$   

  If the amplitude of ;,sxjx+ i-gd la sound wave is tripled, (a) by what factor will the intensity increase? Increase by a faixjd+,; l gx-sctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, buac vey(s; ;if :z3d.ott one has twice the frequency of the other. W(dotcs i;ye:a3;zv f.hat is the ratio of their intensities?   

  What would be the sound level (in dB) of a2wv:,q )v4 ilf 7czdtk sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 2k:c qtdzw74f), livv300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz ti0nd9nl7 4qb3s wl)caone that has a 50-dB sound level? (See Fig. 1 0q 39nwsb n7ca)4lild2–6.)    dB

What are the lowest and highest fregivga 21y+b 8tquencies that an ear can detect when the sound level is 30 dB? (See Fig. 121bgi8yta2v g+ –6.)

  Your auditory system can accommodate a hu rg6cw2m0mta5-s -xxf; ,cl tyge range of sound levels. What is the ratio of h ;m y-c6 wftsxcm,2t0 g-r5axlighest 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 44hk u1u4rrf; / nzlys6 x7s;v8m0 Hz. The length of the vibrating portion is 32 cm, and it hz snyu7/m64sl r8u 1;hvfxkr;as 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 fundamental and first three audibw3bray) c1ul 0ff3sc2le o yc faur3w b320c)lf1svertones 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 bl c ihs*dc )a+ yjjozn+ 555uz-lqrn11rowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? oz 1ij5dz-y rscnur+* cqj1nl5+)ah 5    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 pipes spanning the ranjxg 2.6p*yvyt8a/a lfq 38s lzge of human hearing (20 Hz to 20 kHz), what would be the range of the lengthsl8xyy ql*/z pvgt28fj3s .aa6 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 third harmonic. Whq(xkr hc f5ejflj 49+7at will be its fundamental frequency if it is fingered at a length of only 60% of its originxfhefrj lj(c9 qk75 4+al length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middleuih0:jjdq)(8i) -wks 0p.d)nwac hp p C (330c :)s.wndp8k0d0wq)jp(p -ja ui hhi) 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 emidgx9w z)lv0dy. x07xvts middle C (262 Hz) when 07dl0w.v) gyz dx9vxx the temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at dcfy0 gkdv (yv/ar*.z-:qt-o q f6x;w axri8;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 sj fg6 x;xnlb oiy: 331ht4/smchould the hole be that must be uncovered to play Dx4 1gc6h3i b3j/xos;yt nmf:l above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 6sp+)b4fy*0-xz 7/cahb w bvyu0,sjar16 Hz, but not at any other frequenbfsz0y-c7ur pwb , 4 js+xah0)y/avb* cies 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 pv s6q*aza(mabw*; 2kopen at both ends. It resonates at two successive harmonics of f *kav2a;(b*m azqs 6wprequencies 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 feavn1nn64w .e-v4 gj$^{\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 wi j,xn6e:b yhuzv -0nr)thin the audible range for a 2.14-m-long organ pipe at xvnu0-j,z6n)bhr y e:20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It isv v /:gj94 q2ojng*)yeak3xztadq .+i open to the outside and is closed at the other end by the eardrum. Estimate q3x/qjtvg*njo.9 d:a ayzkg i)ve+24 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 b3 jju.llo b4lc2x1r s3eat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz 4r2ujsl.3l cxj31 lbo. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) a(ibc2;o x:k4k3r vm wdnd $C^＃$ (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 Xp8h pj /6f(zyu1kfs j au)18* oohg.xn) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operati1pu8ou/g z say8.h j k 1*jfo()px6fnhng frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soot:x9vb/az 0 eunded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning t0zxo9/e:vab 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 tension in oejtv.lwh +-4mm 4+ s eriqh9a7ne string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1 s j7+ehet4.virh lm4+w qam-93.]    Hz

  How many beats will be heard if two identical flutes4hztfd)z,8 r s)u ldn)0s 7npm each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 t lmz8fd)h407u), dn pnss zr)$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of /v1 ex/c sz-vg441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heardgz1-e/ s/x cvv. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one sm aa14h7tm dp :wci9jl-*n 6dwpeaker and 3.50 mai 7 41n6wldmwm:*dpj9hc at - from 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 vibrat( ee zg9e4so*ling at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what musslge9zeo 4e(* t be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m ih ,8qy;.oj91xnoc9ojre ;nlo n air. How many beats per second will be o h1 oj 8oej;qc.9,nl xnyor;9heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren inz8w 9 4l/r8e(vr(dgp)l dqnngmo93o s 1550 Hz when at rest. What frequency do you detect if you move with a speeqg(gr 4d9n83p9wno / roz 8vldl( me)nd of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yo 1w . d(himb9-ipou2h/ysrql )u detect if a fire engine whose siren emits aoph1-is yrbhuq)i9 . ( wmd/l2t 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifs8 itkhh0 (4xct in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are t(48 thsihxkc0 he 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 singlu+6a8 qovr qj5e frequency horn. When one is at rest 8 +v5raou6qjq and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz 2zg pof0 p;zu 92jr5voand receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency?5 f9u p22 vjpzgzr0o;o    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 dnuy- :k4iuv .m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 ku4:knyi.du -v Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on gbg* hqo,3vfxjv7 5;j- hq3om a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the qbh;mgj ,f7qj-vh3 xg*o35vo 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measujs .d4g6lwj)j-lw g1nre blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1d -lg1s l6j)g.nwj 4jw540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fuh mtmy w10x29x)o5vxrequency $2.25 \times10^{ 6}$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 frequency 570kfe.t,n l /,me Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hekfetm.nel, , /ar 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 movin57r *g4 xwsr(8g a(aindauuz ue2d8r3g on 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 an3ns8o,xm i uh :7(znrt Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the sh3rns,n zoh 7m8ux: (inock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sok yp g.s6bra) zi-3 v8i01asfdund is onla-fvps 3d) 1b i680r.siazgyk y about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500yvyh0 x9ny/3d8t l 0bq m/s strikes the ocean. Determine the shock wave angle ityvt8nyqh9lx3 / 0ybd0 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 1 e.b1r8zxf dl9s)3o o ybxsa6$/theta$ 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 tj n iihu)pd6c 0b2k)r+he ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane h nc2 phburki6+ )j0)idas 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 sou54j bjgx*zjy )vxd9/lnd pulses downward from the bottomjjj vb)ydx 4zx/59*gl 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 water)?    s

  Approximately how mao o2csf+r z3v-ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipebidda85v.d-lvz -8ba symphony. It consists of many plastic pipes of various lengths, which are o5v dda.bizdv-8 8-al bpen 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 thresho3paj vl* 0 pgfqjn+kc(bgn (;4ld of human hearing (0 dB). What will b 4nvgbl(3 *a+f( jpj0gk;np qce the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dz- 1w7r92q/f, -ujyejiudt +i wojzv6B sound and an 87-dB sound are heard simultaneoj wqju,zvyi+ 7dz6w1 u/to 9f-rji2 e-usly?    dB

  The sound level 12.0 m n.k:;tn;wnmwpyfo 4e j1m *5 lfrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of thekwot*;n p.m5l1nfynjw4 : e;m speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power omkd/ iatrsieqt+j 8*/g/9n5at 5 p0 nwutput drops by 10 dB at 15 kHz. What is the power output in watts at 15 gpa/ t50n rtk//wmjinadiq 8t*5e9 s+ kHz?    dB

  Workers around jet aircraft typicalluok+jo-s3* qm1m9mpj e)zwih- 25ju g y wear protective devices over their ears. Assume tha o32j+ mjmwq zis1o-*kj gem- 9hupu5)t 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 from a jet airplane engine?    W

  In audio and communications systems, the ga 0 pff8bfunaha,6 o;g(in, $\beta$ 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 violif5 /s/. mu/d2bmbfki +1swgci4c x 3fbn is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between f+8l/ ir6v0d0adw ccqab 4rju05ohzq-/s5in a ixed points with a fundamental frequ0lzn rri sh0o+8c bu j 40vc6da/i5a/wq- ad5qency 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 verticad9f6hd7c vpv*l open tube filled with water (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 when the distance from the tube opening to the water level is 0.125 m and again7fvd 9h6* pcvd at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of maslb2k c+hhz:4b bqt(m7 s 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 its fundamental mode) with the third harmonic in the tube? kt qm72z +:lhbh 4bc(b   $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on)j6r nk1 i ;,r*n2dw qoynqqd9ckkw(- e 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 ranfm z4hp:z .p7ige coming from two sources. The sound is loudest at points equidistant from the two sources7: zfhz4pimp .. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stlzvd io6v05 6eationary. The conductor on the stationary tred 06vvli 6o5zain hears a 3.0-Hz beat frequency when the other train 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. Afth0ua1rmo5;c1z vb 9j ver it passes you, its frequency is measured as 486 Hz. How fast was the train mov1z9cvrbuo m1a ; 0jhv5ing (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of:bx wy w/1n*9hohx( s;agkb rj)rim,5 cars just by listening to the difference in pitch of the engine noise between approaching and receding cars., )mb;og 1y x (5/i9njrxw:hbkwsahr * Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequeng( bnivu+h .opr;wy-+fxok i1oc29 c (cy of 11 Hz. The shorter one is 2.40 m long. How long is theno.(i ifc 9+pgu-o ; bc1(2ovhwyrkx+ other?    m

Two loudspeakers are at opposite ends of a railr +ko6w2 djsr,noad car as it moves past a stationary observer 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 r wk sd,n6jo2+they have passed him, at C?

  If the velocity of blood flor3 m/8gocz tp2 2zty,lw in the aorta is normally about 0.32 m/s what beat fr2z, lt y2og8 3zmpctr/equency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying touniuy;ijxpez:3r 3)4 ward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave ; rzi4yu :iepu)3 3jnxdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulm5 o cod8qflgy,9mk4zdn; *: cses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is a:mdk*gm9d5c 8fcq,yno4ol; zbout 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine twn 6lg93d0 ccvillage 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 fr6cdl 9wg03c tnequency 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 be compromised by the presence of d4 1 jz9+ he.zzonj,nrstanding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a livdrn4n1.9jzj zzho,e +ing room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sia1 98weilooxm,b6v g 0nging rods,” involves a long, slender aluminum rod held in the hand lvx wabg o086,mi1 9oenear 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-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 het;b csg.jqk9 3fxk m:(aring for the human ear at a frequency of aboutfsk3 j g9b(.:cm;qkxt 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 hearsrv+a;foge.l m2 7w/gz the sonic boom 1.5 minalz27+em.frvg/ gw; o after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa pl:c+92.l c cshtjj*it 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