What is the evidence t84/j s;.kukf agidbcz 49qocp6x8 *wthat sound travels as a wave?

What is the evidence that sound is a for2k-8lyfpk1 en m of energy?

Children sometimes play with a homem lew+yzs8h9 ,xade “telephone” 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 bw hxlz +ey9s,8e heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequen3vq, y. zho0-sz 8hc (hk j46mwxgox2xr:w4sa cy or wavelength tox hjrkh,q-a cszh.0gyz 3m (:8osxv4w 2w4xo6 change?

What evidence can you give t9fujfjyy+f d6l 89 w2dhat the speed of sound in air does not depend significantly on frej+dj9 w 8yyd9fl2f f6uquency?

The voice of a person who has ix ;.aj0qkxfc0wc: cxhw )6f:tx1j 8mu nhaled helium sounds very high-pitched. Why?

How will the air temper6 ryfw(705k .m2jqacjn3e gsjature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitu5lsbpirjb28lv yq.7+de of sounds in various frequency ranges. (A jil2.byr q87p5+sl bvn example is a car muffler.)

Why are the frets on a guiv9tg)q 5tesrg- at;jod wa6+(p1be7utar (Fig. 12–30) spaced closer together as you move up tpe1ag o+dettgb(sa tqu j v;7r) 6-59whe fingerboard toward the bridge?

A noisy truck approaches you from behind ac4u /h njyuq:) 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 y)uun/4:jcqhon diffraction.]

Standing waves can be said to be due to “interference in space,” w0ru7+dai 1gcmhereas beats can be said to be due to “interference in time.” Ex +uiam 7g1c0drplain.

In Fig. 12–16, if the frequency of the speakers we3f p8 s0 m4shd0fhjs:lre lowered, would the points D and C (where destructive and constructive interferenc0s4 p8dhsff3 mjsl:h0 e occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplejxy. 2kz: 5a7fx wi053quo qcc who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. 35qqykofc cjxa5u0wzx.:7 i2 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 noise reduce the sound levels reaching the ears?

Consider the two wav8p) 44nrqql tbprab:hw 0,df dc2y0pdn.in/:es shown in Fig. 12–31. Each wave can be thought of as a superposition of t/ :bqnr2l.4: a0 q ,pd 4dnbptphfciyr8wn)d 0wo sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the pdad1aw 2q9;/nuf ct,source and observer move in the same direction, with the wq pc,au9/dd2 ant1;fsame velocity? Explain.

If a wind is blowing, will this alteza5/qyl:2 cix1 , wfxs5mk- ozhldb .*r the frequency of the sound heard by a person at rest with respect to the source? Is the wldz bq-5l sf:1h .o*5 cimxwy/2xz,kaavelength or velocity changed?

Figure 12–32 shows various positions of+q f: n u,;ql,jr4saboxi3k+v a child in motion on a swing. A monitor is blowing a whistle in front of the child on the gj 4;+ isb+qnlk, 3a ovrqfxu,:round. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines trjd8d8v d(-9 f;yarqxhe length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the 8yjrf;daq(xd d8r - v9echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearteel+k- *fzc,s the echo of the sound reflected from the ocean floor directly below 2.5 s latelc- ,*ze+ftker. 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 wavelengths in i8sklk m.mcmo8*cwj n7r3q e26- vd+x 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 i- jy nl4ophg/)i8;d c 0f3bqnns drifting just above a school of tuna on a foggy day. Without warning, an engine backf/ndi0o8)n 3lfq yhpc-g; njb4ire 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 splash it makx3onj2l z q7fhfggp/ g m5++*fes when striking the water below is heard 3.5 s later. H2 3zpj/*fmh q+g5on+l7 gfx fgow high is the cliff?    m

  A person, with his ear to the ground, sees a 9tn7gy+a/ wq;si6q lrhuge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occyti7wa9q;nl+r /g6 q sur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made r)b0v vj1x4pzy**yder;e dv 9over one mile of distance by the “5-second rule” for estimating the distance from a lightning strik)*vrx y ry4 01v ;pzvee9ddbj*e if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain legcbz4jci589 ivel 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 sound whose intensity i*xre- cnp u8fm22q;b *rhkm)as $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu5 f3t;h4tsmor ltaneously at a certain place, what will be the sound5h st4fm; r3ot level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with forccz tr1 9eh ew.9*ax9 34gpe6/miopdur equally noisy jet engines is exh3p 9e 9 gc9.xr odz14t *a/ermeipwc6periencing 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 isn ;zwjw0*) hxy said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noisyhw j0nz )xw*;e for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soq28 p, fnnuow4fhg*9 dzx gayh )7ls0nnb:5*q und from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cent5q *gn8*ubgwfnhyqdn,4no :p 79sfxh l20)azered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose areavi9k,2-wq ekb3wzl 5r qg ip76 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, while the more modest amplifier B is3q) t; qlex1kr rated at 40 W. (a) Estimate the sound level in decibels you would et) ;3k qqr1xlexpect at 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 aabi ttj:z/s ;,j; kfi- b1,vndB when placed 2.8 m in front of a loudspeaker on the stagfazs1ivkt a -;j /n,,;:ib btje.
(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 diffe;j 5y.0 zqa luxacd8-dun 69tgrence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? y6a5 gnzj0 tl;-auudq8d9. cx[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by ,7a(13wv fju b7rmgbhwhat factor will the intensity increase? Incre bhf, jv1gwr73ba u(m7ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but on q,s ;o,gvp2une has twice the frequency of the other. What is the ratio of their u; 2s,vp,o nqgintensities?   

  What would be the sound level (in dB) of a sound wave ino6:qdd+o gkn afh499a air that corresponds to a displacement amplitude of vibrating air mole9h:g6 qafkdn+ ooa 9d4cules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud 1j zzyr96ms3bas a 100-Hz tone that has a 50-dB sound level? (Seb3 zj9my r6z1se Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can26b +x6v 6pbp ty-vyxq detect when the sound level-+v6b qt2p ypv 6bx6yx is 30 dB? (See Fig. 12–6.)

  Your auditory system cg subw2fsvuq 352v +5qan accommodate a huge range of sound levels. What is the ratio of highess5bvu5 3g2+fu vwqq 2st to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Thiwtdg)bqf-y5b5 5 ux2u50 p dye length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under wha5u ptd0)fi- b5q 5y2 dx5wyugbt tension must the string be placed?    N

  An organ pipe is 112 cms9y -ez o7vdb:wh,bt1 long. What are the fundamental and first three audible overtonessy:eo-9 bw7tb hd,1vz 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 blowing across the top of anqy(netm, l5r3 empty soda bottle that is 18 cm deep, if you assum eq(,5nlt3mr yed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube w g 9pi/1 dbn)rns,wrx+3ucc- pipes spanning the range of human hearing (20 Hz to 20 kHz), wh/ ipc, wngdu+bc9nxw-1r)3r s at would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a wzuz :56slfd; frequency of 540 Hz as its third harmonic. What will be its fundamental frequen5 :zu6lwzfds ;cy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E absc ehksp 6,,7tove middle C (330s67 sk ,tphec, 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 lengthl; ev0pa k *19c q*ng6dfsj)dc of an open organ pipe that emits middle C (262 Hz) when the temperatqk)fg0 1v a* ;pclj dde*9cs6nure 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 1cl/ykm/jxz :hj n2m/ ebw*;a20 $^{\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 bes9zr9j9 3no dik6)h3hz q ghr( that must be uncoidnhk9g (3)z jq3rz9oh96rsh vered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, buq6hz)x oi64ipby0.uw z j6;jxt not at any other frequencies in b ) 4iiyj0px6j.zobx 6hwuz 6q;etween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. yr8y- riuj9 94cyxrg/It resonates at two successive harmonics of freyry x9gc4ri 8u9j/ y-rquencies 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 h 6ke1f( l-khfhs q,b0rr/1vm$^{\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 m/a(w7l . uztpwithin the audible range for a 2.14-m-long organ puta/(wz7l.mp ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appjg 0cvjoo8)+ jroximately 2.5 cm long. It is open to the outside and is closed at the other end by the vj+o0jo)8cg j 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 2.09a:bho;k 9z6*+dgfpr q 7zqv u s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otherr9zh 79dok qfvq+z*pab6: ;gu string? ±    Hz

  What is the beat frequency if middlek;ir sptf9s*;o g/48x r tyv/q 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-; 91d np(dnmro3mjgl 23.5 kHz, while another (brand X) operates at an unknown frequen -(gopnl j;rmd1d93m ncy. 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 of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andtenou 2khu8 u;e8((sqe y)ugrr)tmr p).0 )fa 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explaih) k)tn0 t; (2r rruo8eeaf.) e)qusy(pgu8umn your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Th79nxk lokcpt+l3 5e,4 7accpfe tension in one string is then decreased by 2.0%. What will be5xktk +9pc73plf, 4cn caoe7l 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 identi438ptbnmgve, cal flutes each try to play middle C (262 Hz), but one is3g,m84 pntvb e at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,uf31necb q; eg+:r* hdd(f7se B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beasgeu3d :q*rf7c1h( +bdne ;eft frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an)oik.k0gs4xrza k 9t :d 3.50 m from the othit4a)kx ks.:kr0z9g o er.
(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 suv 05fb;2g+0yzk)ktim l(ujkc pposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If onvl0yt )z(k jm k5f c+;0g2uikbe 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 ofi6 h3 g1f8ifqt wavelengths 2.64 m and 2.76 m in air. How many beats per second wilhgi if13t68 fql be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a wwou5ppt,:uwh -))gvcertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you mov :uwp u)),hgpow t-wv5e with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fireri /pu-nhu( ihmy 2bc91lp;i2 engine whose siren emits at 155 (92il1i/-hibphpr2mu;ycun0 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-Hzsp4pkj ir )(dx ::pr1g source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequepr)p jx14kg rpd(: is:ncies 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 hornf mwz-7l ql-; jf))jsu. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat sujq-f7 lfmwj;)-l)z 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 and receivesk,3xg)e+n.tge tlo:x f ig-keu;twx j f2- h7- them returned fromxx,;i tl2xw-.g)g + f-gek7n :e- khjo3tfteu an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of :nh:lz 6mmx 9 8n/ghmr 1l)jin5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequencyjnmn n i h)rhl9z:61xml:g8 m/ does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moviyb +fe )(br*eong 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 appro*(eore)f +b ybached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultraso258u jpnskznhy7d5b ly 4 aw-.und waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of soun5hy2 y-n8p .57swanu jk4lzbdd 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 the sound source?   Hz

  The Doppler effect using ultrasovd pbtge.wy 2 ,,cio h55+gak/nic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 H0vc zg 2wqp72rz. When the wind velocity is 12 m/s from the north, what frequency will observers hear v2rc0 w7pg2 zqwho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 2ak fnnkr-) 2mnre:h r7p3 y4w0c c6j:r0 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the bs :-*upab y6aspeed of sound is 310 m/s (a) What is :* -6busabay pthe 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*+ tmw/bfz, p/rkfqhkf(ok15 atmosphere of a planet where the speed of sound is only/r/ ,t (z5 p+w1fk*obqkmkff h 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 8500 m/s strmu pr4 .+eqh4vikes the ocean. Determine the shock wave angle it prodvm h.+44puqreuces
(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 zi2kgaqr/1 )+0jruvb$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead j1i2p0kjux0ry uy)7sand see a plane exactly 1.5 km above the ground flying faster than the skpjuy x170iu r )0y2jspeed 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 send7 1lt/ nu18iwdk fzx/ss 20,000-Hz sound pulses downward from the bottom of the boat, anl/18xsu wti/17 zfdn kd 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 many octavesfh j; k6-g c1gujdw,bc:m p30b*gk /me are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sea l;5(-ge: 7tp,2ju:ckid -sqj5sawo0k r ur dwer pipe symphony. It consists of many plastic pipes of various lengths, which are open on b55s(wi : o:p2uk;dur,e k-lcj7q-rgtsd0aja oth 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 f+8xn u *j,8(icasuja+nd5csv5m g g)from a person makes a sound close to the threshold of human hearing (0 dB). Wh5 vd+anu gj 8*i8f5xj c, sanc+(s)gumat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound af r*mgco-vhj46 c 7a4und an 87-dB sound are heard sia 7go u6m4jhfrv*cc -4multaneously?    dB

  The sound level 12.0 m froxbz*jrlnk 2oq68op ranfnx3d 4 4,b-2m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (Wl2doxzn6rbop32- 4 kbxnn rj*,fq 84a) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power o z c*+)x v/pdo :a nnbq)p tl:vubqns)-5;jxa/utput drops by 10 dB at 15 kHz. What is the power output in wata -:* pnx)/;sj)v un : xqlt/d5qbao+ cbn)pzvts at 15 kHz?    dB

  Workers around jet air2mntv; o ,rkv 6(o4c0cntd(ficraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, atnvc(6fv ,o4m2(ik0r nt do;ct 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, thigy vyo:(jg0hoa+ xuea 7y 0qyg*3l7cu4n0 w6e 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 frequen:h2q2;hw s;ycc dvqk1 ckx(9iagv4m )cy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed snojy cx45 5q-i deh8cg,:q-ffjlmlb80 1 id. points with a fundamental frequency of 440 Hz and a masse y50qmc .,i 41j8sqhl-fo5dn- g: f b8jdcixl 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 in),e9qi my jmy2to vibration above a vertical open tube filled with water (Fim2ejq iy,y9 )mg. 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 again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one e9ww w7wewb fw ;s*f/8ewc)3fgnd and also 75 cm long. How much tension should be in the string if it is to produce resonance (in ib ww8wcs;/ ww 7ew9ef*w 3fgf)ts fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tj9zd-,r xc/mg zvy5b -o resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a purp:m i4ca*ipb8u ke5y;t5ezf; e tone in the 500–1000-Hz range coming from two sources. The s;p5cizy*mik5bat:;f p8 u e4eound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on t;, pb(bt-xbs whe stationary train hears a 3.0-Hz beat frequency when the other train approaches. Wxspbw- (b,b t;hat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches youu 2x8khlv7u v6 is 538 Hz. After it passes you, its frequency is measured a6 7uh v2x8vklus 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you cas(fxotg99z4lu5 3j g an estimate 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 z549aft(jluog 3xg s 9certain 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, prozbe ,3-o q3ersduce a beat frequency of 11 Hz. The shorter on oeq,b ez33r-se is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stafih,pk0 .lkwn z f;efy6,y7 4ltionary 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, 70lw,;pkff e h n 6y4kilz,yf.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 blg,qu3h z9+bmfz-q:2 9 ycurm cood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the q,cy qg+u3zz-rf2 bc9uhm9 : mflow 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. gy1ym/;q x4b6pi* cvn5 m/s while the moth is flying toward the bat at speed *ym6;p/nx4big c v1y q5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mowv:r,juaelw,,2 8mc fth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detec,a u8: , r,fm2ewvcwljted 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 )8 hqq6qxu )aysend signals from one Alpine village to another. Since lower frequency sound)qq) yq uh86xas are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised r1t irx/0u3l b,xg+nmby the presence of standing waves, which can cause acoustic “dt0n3irbm /xr ,l+xgu1ead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singkac/o3 v uyl57nv,k.0 ktd j(r/v,ot ving rods,” 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 pv 0 7,vl5k,o 3 (jvy vcdo.ktrk/au/tnractice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humvo7c zkl wh 4es+ot 93(-fpr:yan ear at a frequency of about 1000 Hz isf h l9(t7-keoy4:przowcvs+3 $I_0$ = $1 \times10^{12 } W / m^2$ 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 th 0(/tffqfj,kgyg,1y be ground hears the sonic boom 1.5 min after the plane passes gby ( t/q10,k fygfjf,directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat vy6nhd8rva82 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