What is the evidence that sound travels as suib e8l8--z ao (ov//5-vsm;igfukra wave?

What is the evidence tv*zka2/ 5asclhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a stringh *sx.5b5ozkl to the bottoms of two paper cups. When the string is s*b sl o5zk.x5htretched 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 wa9u* 3dg2s/ptheb; b xyter, do you expect the frequency or wavelength to change?gy e2 pu;b hxs/3bd9*t

What evidence can you gek b ut.sca36c.e7e t/(ynm5 cive that the speed of sound in air does not depend significantl.bac t3ek ets(./ ccm7 euy56ny on frequency?

The voice of a person who has inhaled helium sounds very high-pitched.p9 x 5ksnr1zu- Why?

How will the air temperature in a room affect the pitch of o wp:c1g*2fn ny)kw f8brgan pipes?

Explain how a tube might be used as a filter to reduce the amplitua5;.gjkfvzm ) de of sounds in vaz .;k j5)famvgrious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tro*b j ;k nv:h,3kmms3ogether as you move up the fingerboard to3 v:sbj kr3,;monhmk *ward the bridge?

A noisy truck approac6wdmy uy.,w xg+osx +i 1j:i:ches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sudcm6g yj:i, ox uiy:+1xd+sww .denly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be du/9ohx+bb da-9ib knf3t1wt4x e to “interference in space,” whereas beats can be said to be due to “interferenc dxnhox/9+bbb 9w t1t-4kfa 3ie in time.” Explain.

In Fig. 12–16, if the frequency o a0kwcwi-jb uyohdmw) 6/)*(a ++h oa vdj8da1f the speakers were lowered, would the points D and C (wheredb)1+a6j(ha ova wy)+*k-d dhwm jcu8iw a /0o destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of pe upjf,z 99804ukzzcinib d)5wople 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 detedn w z 89fb45)90,cuj iuizpzkcts the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a 4: 1o(o oxdct9(2gz, )arvwjdy+ albisuperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.4 x:1 ioot((jy+ 2baord gvd9)lawc ,z
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move g250)qmeob kgin the same direction, with the same velocity? Explain.g025)kbgqo me

If a wind is blowing, wc,oj- f ip3pdnl -c(i6ill this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or pj-,d3-6 oci cn(pfli velocity changed?

Figure 12–32 shows various positions of a child in motion on a sxq ya i2eqz(- 5bvx68swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequ(sa6q8zb5vx2e iqx- yency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ech+ ka0at to1lfio0pi-* o of her shout reflected by a cliff at the far end of the ltktiif-pl0oa* 1+ao0 ake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just b..uhn )dha od9 ph36eaelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is a)u dh. 6paoh. hedn391560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength g3x.8zrlcglmw.n ;. os 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 drifting just above a school of *(etuvan/nuvp;9k 7ttuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time ela9tv/a7kpn(; uue n*t vpses 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 vrfod5by bdnqbp b9 ,y;7oed7+5 yy . ;nsq-r3striking the water below is heard 3.5 s later. How hi5f rb,noyy9 ;b.nr d yydqv d3- obe77qpb;s5+gh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cw) +0vhykzb9:6 jy.5gwjioxsoncrete pavement. A moment later two sounds are heard from the im +w5.vzi ghjy xo6:s w)bky9j0pact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of jgi40bq kq . 3 3aov,xeb4lbrae.h+8x distance by the “5-second rule” forbaobkr8g4xqe3b 0l .vi +4aj3xq .,e h estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at th bv6p c m*9z8m r4+muh9qk1pdbds w-v)e 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 sound whose intensity is iv4uqaal y2n9.;y ge7 e/ fzj;$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 ds )xnnukj :pp 21+2yukB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: u+2nxspkju2) : p1knyAdd intensities, not dB’s.]    dB

  A person standing a cov-b/4gw 0euspllggy1 ;sa 6 1ertain distance from an airplane with four equally noisy jet engines is expw0ol/lvg bgyse6 ;a-su 11 g4periencing 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 ratiou 0esi 7*ohm suorls:z67yl ;) of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eachi*ez6huy7 s om: l r07)o;slsu device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output xnd6qwa6vl(ngd2e 3uj5u 65 sof sound from a person speaking in normal conversation. Use ux g(d652n nw6u jdae3qs5lv 6Table 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 str;3us5 3 cmlnzbikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplu rx809x,uwsx0dlq fd7;o ) i q1bht*/a;buqsifier B is rated at 40 W. (a) Estimate the sound ; 8d7; h d1b)b tafs,or9u00qulswqx x*i/ xuqlevel in decibels you would expect 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 registere*cncea+) f,iqt*s; lad 130 dB when placed 2.8 m in front of a loudspetqa*nflciea ,*);s+caker 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 i)a nsvnnox)- .zab oc )z8-j(dB. What is the ratio of the amplitudes of two sound)n xn)8za(ja- zvbs .)c-onois whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inteni +j8zygc ;y4usityy;yzj84 u ci+g increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice theoodawn+ n4qd q p,0;(w frequency of the other. What is the ranw4od; +p a w(d0,qqnotio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thezrt2; f 2n:/ jee+nyyvg*:qvb 1j2ohat corresponds to a displacement amplitude of vibrating air molecules oo tzyb22gene2;enrv :fj+q h/1j: *vyf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to s0ssqv) 0 nv3gfrbk/f 6eem as loud as a 100-Hz tone that has a 50-dB sound levffqv /0s k3v)brs 0n6gel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear ca:h. m+aa- fdtbbq5 l,an detect when the sound level is 30 d-,bltqb+mad5fa: ha. B? (See Fig. 12–6.)

  Your auditory system can acc0,p ygz umeqabx q,w)8 l1m5/9 apfcf(ommodate a huge range of sound levels. What is the ratio of highest to lowx, ,qqf 1)wb u y8cla0fge9 pmm(/pza5est 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 .w26m (dolxk oHz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under whwod .o2l6xmk (at tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the f-0fws-uyegnr .9ru n/undamental and first three audible overtones if the swrn ngfue0-y.9-r/ u 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 yout nv1se d 1p(.4ff+nwf expect from blowing across the top of an empty soda bottle that is 18 cm deep, if youwnt(f1vd epsff1n4+ . assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tubeoz)tzz14ax. h pipes spanning the range of human hearia4.ho )zzz1xtng (20 Hz to 20 kHz), what 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 csmke1g20hd.1vm k(3r 2ui bsfrequency of 540 Hz as its third harmonic. What will be its.s12se2ck31( gm 0rvbkidmuh fundamental frequency 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.j3vt,r q q69edhljx, 7ak1ci E above middle C (3301 d.9eq h, jv7ilarcq3x,tjk 6 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 leo)e gq: /57c1i mzevjingth of an open organ pipe that emits middle C (262 Hz) when the temper/)eg z1oqve 5cm7jii: ature 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 atj2(x 3qwgtoxx-v ml53 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the vaoj6 )4, mmbpj hq +yct6n7us8sep)8 flute in Example 12–10 should the hole be that must be uncovered to play D above middle)oh8s6m,by+u 4pv8mj7 ne jt 6csaq)p 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, a* klk0 z2qkps ; k4c:3d8la ajt0qgo+and 616 Hz, but not at any other frequencies in betwep t4+ck akz a2q:0ds;k*akl3o0ql8 jgen. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at f2d uwkse. :(ytwo successive harmonics of frequencies 275 Hz and 330 Hz. What f ysd. w2:(keuis
(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 i i(g 8blq7gww ii,u2y6n*iu tv(+ .yl$^{\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 within82/qqs7 aj)wb kyb v-gno()oq the audible range for a 2.14-m-long organ pipe at 20 yj2bo)qvq/ - gqoawb (sk n7)8$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is499 aissv1how open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in t1 vw4 h9ao9ssihe 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 b2non 7m+;acu89l vpc0 :jcd tceat every 2.0 s when trying to adjust two strings, one :c 7c2 ncac;+lndmv09upo8tjof which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if-sunm2zbg5v4;)(skowd jw 8s middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another r.ada7,gd: q5vanijuv:h c7fx;kkx 3o.+jb6 (brand X) 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 simultanei kd,d v3:+7uoqc .ax:gk5v6b f7ana.jjxr;h ously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz 9l))vfa-zu(wut1z g u qs. 2qwtuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency9fw1(slwu)z)- g auvq.2qtz u of the string? Explain your reasoning.    Hz

  Two violin strings are a) tl32i1 ,jax pds1( 3s6dknmlq vm4mtuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hearmpd12amd1kq)s3ilxt3v jn6 lma( s 4,d when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to p5ucuf4oo l (6play middle C (262 Hz), but one is at 5.ouop4u f(5 6lc0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencywnw,+hfkh p/; of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What behkwfph + /;,nwat 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 perh .x;qzri0;gpson stands 3.00 m from one speaker and 3.50 m from the ot.0r ;iq;gxphzher.
(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 supposedm.txmxt-950 93j k hvv pnphpnew,j5+ to be vibrating at 132 Hz, but a piano tuner hears thr,xkjnx9.h0 vh 53 5 -vpetp9mt+m wnpjee beats every 2.0 s when they 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 of wavelengths 2.64 6sj d85wtgelpju ejv0k;94 e3m and 2.76 m in air. How many beats per second will be heard? (Assdlpt kj v0ese63g8u;4jwj 59 eume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fiil5-) ipynd0bbms+ v,rg7 6.tyi nw 0yre engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed o.-,0b +vb7 6yiywr) pin 0s g5itdylnmf 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you 1 e +sdp(,dmoodetect if a fire engine whose siren emits at 1550 Hz moves d, o+psdo1(meat 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 too (oo:x, sgi5f8zbla0-.k he gward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are.lgai8h, sfz o0b:ex( o o-gk5 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 (g 2spf6ykwcile1 e,zq6qj,0 with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequencyqf6i1 ,zep,ejy qw2c6s lg(k0 of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sw/:yy q sr24;9 o)akxwupm;k gound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is thy:w4au;y9/o gm 2p sqk;wxk)re received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sfi ;7k qjcps81;slf g1peed of 5 m/s As it flies, the bat emits an ultrasoqj s gf 1l18;f7ik;pcsnic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played+qjinhb 2 ol6 arb rprj(m (:tg5,9,0rrmgdp- on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while atgmr-rl(d2 r5nr ,9br6m,g o0 p:+i jhqbp(atj 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 wa6q u:cp.9e-udxi /hs cves to measure blood-flow speeds. Suppose the dhdp/x.-qe6:u iu9 sc cevice emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fr)eu+c 4nve+md equency $2.25 \times10^{ 6}$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 Hz3f 2stzuhq73 a. When the wind velocity is 12 m/s from the north, what freq 7tu32 zafh3squency 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 land if its speed ir:x x07yb+hds,/iun at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is yrt4 hipebx3/lii441x : e )sethe angle the shock wave makes with the direction of the airplane xy hp:ib)e ite4/x4l4 srei31’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 +80beo7ywjtuv y o7x1 sound is onvy8ob+y7ojut1w0e x 7 ly 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 strikes the ocean. Determine the shock w7r ;6.5uacz /dzji;xyoh :kua cwn38a ave angle it produccnr8wa6a;7 dz.jzi;y3hx ua /koc5:ues
(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 8jd 66rvuqbh 1x8ky: e$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see*.29w ijrik xykw: eku:0apw2 a plane exactly 1.5 km above the ground flying faster than the speed of k:yxw pu92wikj*2ik. re:w0asound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000xkl *id0x3.gi-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is des* d.lxk x03igiigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves arwl6xkh+q osp k1 3yedfq, :j iw;vi74 x.qef+(e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists tf61 t r rw0mf anc/iux,;wd)3of many plastic pipes of various length)in 3c,dfaumt6f tw/rx10wr; s, 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 g jpl4jfrp*r/bzt;;2 the threshold of human hea /;;4fp z g*btjr2rpljring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound ac :d/7 g7jzeo 8 wa9* m8r0f3nkbzvxyynd an 87-dB sound are heard simultane0/z ykjfxmac r8w7y*b87z 3e 9:ogvnd ously?    dB

  The sound level 12.0 m from a loudspeaker, place1 7, ybnriq,(rldpar) e4x gh5d in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass 14gplr,yrqd5(xr a7ieh , )nbuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powe;c5pp+5 rya megwsg + z;a2.bggogo88r output drops by 10 dB at 15 kHz. Ws 855m2 p;.pzeo +gwb 8oga;+agrygc ghat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicaly44kc)qm)7a lyyc y3 kly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30)3cak4yymq)k y y7l4c 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 communicje /m7 bkf ve0amnka9 ;dlt2,7ations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequel3;)c2utsun t ncy 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 po udd6v3c 44fhkints with a fundamental frequency of 440 Hz and a mass per unit length od dkuf63chv44 f $6.1 \times10^{-4 }$ 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 fill j7stw+4raiz2 z0 we7ked 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 agre7wat s+4i jw z7kz02ain 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 aw7n- h 4;bzdgn7ir1dgt one end and also 75 cm long. How much tension should be in the string if it nh7ginb;7 1 wdgrz-d4is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wab wtxw6b8l;/-rm so0 as observed to 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 pure tone in the 500–1000d;k1 v:1iijq;mjf 8 kd dz:t,d-Hz range coming from two sources. The sound 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 otherm; kk:v;zddd f: 1id1j,jq 8it. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One trpo +v6e 6eb gxr:7k3rgain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the othevrke :op7ex3gb6r+6g r 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. b,zvoe82c:rw ;l sk0 eAfter it passes you, its frequency is measured as 486 Hz. How fast was tb;sr:lzv,c8e2 0e kwohe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the v3 9t wvre*gb6diffev9rvb6gwt 3 *erence 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 ,ch:,,jon*vs .d gg qu *jfg0ta beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othergdjo t:*v. hcsnu*f g,, 0qjg,?    m

Two loudspeakers are at opposite ends of a raf1ri m*rzs fk )whu 3dav.4-7xilroad 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 frod.)4 i*frram uf 1kzv-h7wsx3 m the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about /s +e2cqr5vwp0.32 m/s what beat frequency wovcsw+r2/e5q p uld 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 at3t cdq0dsp3gt2s1m3s speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sou03cgdss13q2p 3 smd ttnd 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 )zeg5o0rt-zs7sh 8 dgs2oe- c qf1h; jas it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chi7 hj8; 0oz tshcz-q s21gfo-g)eerds5 rp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alp ,idkn8- s-zee4 hsa3tine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as a3e8sh da-si-ez,k4nt n open tube.

  Room acoustics for stereo listening can be compromised by the presenct)6-d bf5(wmx a9yyvde of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencb-9 t 6) xdyd(5ymfvwaies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lo935 1okxlyc+zt kg79 pz* gghbng, slender aluminum rod held in thgxozk3gygb l*z 159t p+ k7c9he hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-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 theg)gfd;9n 4l we human ear at a frequency of about 1000 Hz iswg 9ln )e4dgf; $I_0$ = $1 \times10^{12 } W / m^2$ 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( zv99pr,dd yxke3)b7 uyqw3o observer on the ground hears the sonic boom 1.5 mi)yo7q drp9zye k3xwu (,9 vbd3n after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat n;h7u1 xp2 jgy99ou zxis 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