What is the evidence that sound travels as a wv2wcd5 5 pbu+iave?

What is the evidence that sound is a form of enerecyaj.y)b 2 f2 ypv09c(zk1pygy?

Children sometimes play with a yuo51w0kl95akw95 jx3a tyl bhomemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child spe0bxa5u59wll9j y3tka1y k wo5aks 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 you expect the frequepahv02+ wyn ;m2hn; fancy or wavelength ;vfa2yhw2+hp; mnna0 to change?

What evidence can you give that the speed of souohm)dp-3p8 iw nd in air does not depend significantly on fre phmi)8pdwo -3quency?

The voice of a person who has inhaled helium soun y9p n*dxjj; n+md+q1scv 1:odds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?3 sls kg61xns1

Explain how a tube might be used as a filter to reduce the amplf9lv8e :q ckh 7mj8q,9kz ck7mitude of sounds in various f7ck,chv9qlqfm e7z9k8j km 8: requency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) 6sz7sj.f2x6 f5x1rgkl7b xmm spaced closer together as you move up the fingerboard toward the bridge? 7lff6m17rx. sgsx kz xj25mb6

A noisy truck approaches yjq9g6:yo pjh fvy 189 ufoa:6cou from behind a building. Initially you hear it but cannot seu 6 :j:acgp8oy69hqjyf 9o1vfe 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 diffraction.]

Standing waves can be said to be due to “interference in space,” wp9nq a b6i;+ re(lj 2sb4 tt)+sxtgj9khereas beats can be said to be due to “94irxg2 lje)ts6 +ks tb n pb;+qa9tj(interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point k l 1id-gig2si3)a ciu6v*mx3s D and C (where destructive and com26d 31sgi)vckai3 gu*xii- lnstructive interference occur) move farther apart or closer together?

Traditional methods of protectizy yb0zs )cppr46 * ecd6vv56png the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or zpzr4dv0 c) 6p6e6yv *5yb pscreduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–3xe/mx3zy0 t3h1. Each wave can be thought of as a superposition of two sound wavesyx33 0/xemzht 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 source and 6 1s1ac1shk;ta xt5r uobserver move in the same direction, with s 15 csk ;6ar1ahttu1xthe same velocity? Explain.

If a wind is blowing, will this altenptr/ei ;hzcea su9,az5 d: 0)r the frequency of the sound heard by a person at rest wia p:e,rs;u59 0t)zicehaz/nd th respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mon:mes -at57lqzitor is blowing a whist 5l7tq-:amzes le in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of agk+wy+b 0; cr*zfcr:g lake by listening for the echo of her shout reflected by a cliff at;ybr0kz+r :w + c*cggf the far end of the lake. 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 below the waterline. He;p;7 gk rwif/n 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 1560 m/s (Table 1r;ipg/;7kwn f 2–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a vjjyani+enl+811,i1xv d- xyt 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 tuna on a fl4vl6 3xgqkfje,v /(joggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fishjx ej3vvf( k46lg/l,q,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes x 9rvptez8(f:w53 kpowhen striking thetw(53okre zv8fp 9 :xp water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground,zh1ph,l-j kgc l3,3cc sees a huge stone strike the concrete pavement. A moment later two sounds are heall1ghz3jhp,c3cc -,k rd from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by tj9wic +/t5lc6 6axz wthe “5-second rule” for estimx tcw+iwc/ 6aj6t95zlating 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 the pain level of 120 dB? hn,p1)apr4sz x4 qdi2    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 inv lvptnt0k 1ajr:;d;, tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce alseorhp)e ki 0d gd0;hr*-k4* sound level of 95 dB when fired simultaneously at a certain place, what will be the sound 4 0i k err 0*hhedo-g;)pls*dklevel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equalo-d2 uu;dq znbjzy /86uh/ *,m(rtrru ly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down allq2,rtr*uoduj-/z8;mbu r yz/ 6 (d uhn but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hj*+nzc7 9j pkzave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is thepnjz zk 7jc*+9 ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in*sdg p*d6nxu8 normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a d* xu* dspn68gsphere 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 acz9e i)zz6rfg mwv; 54axx/)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 amplvsb2 pipr4)e *(fpdz6cfa p:/q, lg+gifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poinf pc4dgpi e2(p rb6psfg+/v:,q*z )alt 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed i0 sli3io v4 st,;(p4ybqlw 4s2.8 m in front of a loudspeaker on the0i4tp4,sivsow l lsyq43ib(; 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 detecd,wc0e+ -dfcst a difference in sound level of 2.0 dB. What is the ratio of the 0ccs -ed+f,dw amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,v55hxw,:by- w8-; x lmg wal/ubgj*xd (a) by what factor will the intensity increase? Increase bwxubld/ yx a*:,-h;b x mv55jwgl-wg 8y 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 3 b3bouk 0fy1pthe frequencyk3 p3ub0fb1 oy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspondr.nw9 o8isryfr x5 +o(1 khsg1s to a displacement amplitude of vibrating air molecuo h1no rg89 .k1s+s5x(rwyrif les of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whatdee(mns; .et0 vmh 30stn- mg, sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? 0( tg dsnest,.vnm-;eme3hm 0(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear 9jlg 8sqnj)k5 can detect when the sound level is 30 dB? (See ) q9n5slkg8j jFig. 12–6.)

  Your auditory system can accommodate a huge range o((heh8rgwwxf8 ( 5x3eeq bry* f sound levels. What is the ratio ofwq3f(geeyhew(b* 85xxr 8(rh highest 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 fufmf3 /65n+/y6q doy8 wumqxyls*e ek7ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a masslm+f6k / u *7qxyfm5y s /ywe83qodne6 of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lmjmt5 kb, cq(jfk:1da,z84y k ong. What are the fundamental and first three audible overtones if the pipe is 8k:,5( mqkdjykjb zf1a mt,4c
(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 r;g pt3gboi72 tnp4t, (r.nrqexpect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed 7p q.gtto 4i, gr;tr2 r(n3pbnit 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 pipes spannr*dro 3*q-ro2va7 krpt f8g( zing the range of human hearing 2qf-z3vk* t7 orgr( r *roap8d(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 frequency of 540 Hz as its vvme/e akmi e0;dk,;9third harmonic. What will be its fundamental frequek9e e/m0idv,a ;mvk e;ncy 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 pmyd)y ;45bxqkk 9,itx lay E above middle C (33x yk4;b)m, qdtkxy5 i90 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whe-yfm2q0 df6e en the teqe ymfed 2-06fmperature 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 b4au 2 aj;1kemnbpj(/at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole b/hpcs: jh 5ya5nvs:d.e that must be uncovered to play D above middle C at/pn5:j5vh. :hsya dcs 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 h: b h5m9i q8ahimp,t-lsgy;( Hz, but not at any other frequencies in between. (a) Show why t yl(9ih 5ig q- hhsapb;:mmt,8his 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.cmdtnydd: v + p/e9 qwsw3pyl*i90u2 5/ih)m o80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 3wl3+ pmiihdn*/m2vyd09p q w5)9etc/ :yodsu30 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 /) jnppxm5l yky9;w. f$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-loncen/ )thwvl j7,. j)rig organ pi./j)n cth7) ervljwi,pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximated dymwu:l1-qqh z4j *7 c,uh1rly 2.5 cm long. It is open to the outside and is cl dlzr1*u h-4qd cwy,hjq7:1umosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryg x/r(*:hacsmw xh,k-7 av )uvug/6iuing to adjust two strings, one of whv/m*:,rx7hi kug6w)ag(/ xhscuavu -ich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fremyav.ons3 xapa)zf 692(jo/ iji0cl; quency if 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 opertvv- m*isl+ 8nates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequen*l-itv +8 snmvcy 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 t kq/r dnxzw7,vu7,h6vuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What v nx,wv7q6/7rkh,u zd is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tens.00z doss-j cyv.gdk+,-5 yab wb5gtmion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played togethermbayo.-sbj 5s0 5- gw+kt0vcd. gy,d z? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flc+tjb)/qi3xx7rq l gn g 0:mf70s-- sq*c dfrsutes each try to play middle C (262 Hz), but rs-s*3 jqdtxrg+)s/f q7cl7x -i0qn mfb0 g:cone is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has s6o44(rpdo7ep8 x :d 0u ljuxaa frequency of 441 Hz; when A and B are sounded together, a beat freeua (4 6s 0lpxxo:dp4uoj7d8rquency 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 s9ffwgsn 15m8 mc5gzjg; av7;t tands 3.00 m from one speaker and 3.50 fa85sg m9tgfz ;mv;n5c1g7 wjm 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 vibrating at 132 Hz2a ou)afu2u; tt(o+b x, but a piano tuner hears three beats every 2.0 s when they are played togetbuo;ott2ua) fu+xa(2 her. (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 *mg 50n mkvv(jzl7w/ yzf;i6h wavelengths 2.64 m and 2.76 m in air. How many beats per secoi(zvvwzmy l7*m6/f;g 5n0 jhknd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engin ixkid;jueg d3s -91h1e’s siren is 1550 Hz when at rest. W-kgsd;3id1 jeixu9 h1hat frequency do you detect if you move 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 fire engine wh( p,f9(kjnbz tmou94f8 jtky )ose siren emits at 1550 Hz moves at a 8y kt ukto(jj9fn),4fpbmz9(speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift :g+dfw 98vyqlwyhj;+ in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/8vf : jwdyy 9hq;wg+l+s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped withucnbwxhl7 c8 4k2 t;n2 the same single frequency horn. When one is at rest and the othe n82hkb wx24;ntu7lcc r 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 ultrasonicarau i (6 dvxk hz2g(eef.j:;x 5s4r7i sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whatf kix :(5ar6i;d2 r(4esx haejgvu.7z is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emi vp4xcqw42m8igb2ly: ts an ultrasonic soul:q4ywbic4 m8pv 2g x2nd 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 on a moving flat to:2 ,cm(zlrtarain car at a frequency of 75 Hz, and a second identical tuba played the same tone while a a:,rmlo zt(2ct 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 ultrasoun :la2x 7 9(lx*o2o(dpsiawczbd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound sourcazoabw:((pl o d2*x9lsci27 xe?   Hz

  The Doppler effect usix pei) wj,i 9/1fb.vspng ultrasonic 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 Hz. When the winreq8 k;y6:ti xd velocity is 12 m/s from the north, what i:y8re6qk;xtfrequency 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 +e;yoqryde zr+3eznse *5r .;rg4 ,poat 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 isazokd:h hzhdb -89-w-5v( jbg the angle the shock wave makes with the direction of t-: -5a w hvoh8hbk(9 gdz-dbjzhe 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 planetjom0/ylk1q 9fu1nw d 9 where the speed of sound is only about 35 m/s dmn919u0qwo y/f1jkl
(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.y(st i+ olu98ok6va-j Determine the shock wave angle voy 8jols6-9t+(ukia it 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 50wu1gmfcz . zh3qf.1akqo i6$/theta$ 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 the ground flyiu47 aagcuhw0.4t q :ryng faster than the speed of sound. By the tu0thw:7qg 4 .aa 4cuyrime 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 8-vxp b4nvac ui6w46v20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh vicx 4p6navu-84v6w bwater)?    s

  Approximately how many octaves are there in the:c7 zf: g-coul human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ut6 0keeyp.x6 mwny// many plastic p . //etepwy6ku0m ny6xipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold*ktvz 5lvn -4n of human hearing (0 dB). What will be the*k -5tzvvl n4n sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hdt ld9k09iwr yv-os- pbsv)90eard sim vwbsvk9d)p9-l ri0t0so9y- dultaneously?    dB

  The sound level 12.0 m from a loudspeaker, pla*wf)s2epkm /3 bbkbh1ced in the open, is 105 dB. What is the acoustic1 /s*m23kbhwbp e)fkb power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powe-bbhfpmjv5) mol; 07rlmqf51r output drops by 10 dB at 15 kHz.7jf;- 1hplfmrl)b0o55b qvmm What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typical 9v ur):3rftimb d.n3vly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at u3r:9vfb rnv) it.d m3a 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 communicatiotg:t 3cxu-rb 3/e ,gpsns 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 isfwssv/h we2 )vd90j 4m 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 fixed points with ku r ),9/qe0qyyc-oz oa fundamental frequency of 440 Hz and a mass per /e9oyr)-u0kqc o zq,yunit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical op7 8z khk6a:nz6p ckh)fen 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 lez7k) hk8:fh kcp66zanvel is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar s)nd*/o8ye -ugi 0r rdwsb+k*rtring of mass 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 st n dr-esbu/r8yg*w)*ki0d + roring if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wa8 p 7p y(9 ud+gtre7x5umekc.fs 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 50s+,uno (+ig07l rtmsk 0–1000-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 other. What is the frei +unk lrms(0t s+,go7quency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductorcbwyx8z rh -0j7j7o9dtj62mf n98f,nie zlx 7 on the stationary train hears a 3.0-Hz beat frequency when the other train approache binj,rcnx0y8 9jhfjxzz l 68t 7owe9-df727m s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle +*.fsqj3gh g has it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. g3.*hg+sfqjhHow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of chs7b i0 ovt;ff.g3t2u ars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast o.b;ftg 3hi ts0v72ufis it going?    m/s

  Two open organ pipes, soundio 6+shlgn6-n.is -v p5v,c33kz;zvrj l 4 yqonng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How o+6ni ;zgj5nvhzrnq--s o.6 l3k3vlv,c p y4slong is the other?    m

Two loudspeakers are at opposit0e r,5o,dxa w bye2*ose ends of a railroad 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 they so,rd2,be ex ay5*0owhave passed him, at C?

  If the velocity of blood flow in the aorta is normallc5h 6;r oj2rd8*heuvh ri ,yp)y about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wavejhr8 ecr,p 2y;)hu*vh5dir o6s travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.m+u)tp9- b/z umiox.x 5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frxuuzp-/ +o)mt mi9 .xbequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenrp vcgmf6bb4q5csgt5 )0 ,zp4cy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chir0r5bpqv56 t m4fcgg4p zs,c)bp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vzkcfe7:w 8 **4jduone.tr s ,lld *y:eillage 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 an op o8udnc7eeszwf :y*jrd :k*,.e t4ll*en tube.

  Room acoustics for stereo listening can be compromised by the presence of standicz p5y13 hla;lng 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 frequencies for the standing walyla 1c z5h3p;ves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “sifkec 5i52gf 3tm k3se3nging 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 practice, the rod can be made f ecgik 2e 535ksfm33tto “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 thr tn c:/z2xbrao03 vp,yeshold of hearing for the human ear at a frequency of about 1002yno, vpa t xc/zrb3:00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bda(s2)ogre2 bvfo b80 oom 1.5 minvbg orfs 8(bo202a)ed after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1gyfv*d:9 o,97 enotlikb 8uy sj893dx5 $^{\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