What is the evidence that sound t sx:.byz4l -anravels as a wave?

What is the evidencekpusg0)gza 9. that sound is a form of energy?

Children sometimes play with a homemade fov(5 ik5uto6“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 be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave kf 6( io55tovutravels from one cup to the other.

When a sound wave passes from air into water, do you expect y5xr2( l: cukf(.kv sku k2p:nthe frequency or wavelength tlkpn:u:. xr(2ysk f2(v5 kkuco change?

What evidence can you give that the speed of sound in air does not depenx(r/ q .un0l+5wz85o 8vfouyda qjw/rd significantly onn5duu0qr oyqz5f/ j .(l8/8 oxw+vw ra frequency?

The voice of a person who has inhaled helium sounds very high-pitched.pa(l q;,zuyp6 y j84cewb;a :z Why?

How will the air temperature in a room affect the pitca+ 8tfid/ a8xqpors 3gg5wx*/h of organ pipes?

Explain how a tube might be used as a filter to r3 p 0l(ivte3iww*x em;educe the amplitude of sounds in various frequency ranges. (An example is a car mufflerit;vwwem*ilp(3 03x e.)

Why are the frets on a g. /qbo6abn+m iuitar (Fig. 12–30) spaced closer together as you move up the fini+6nq/ob.ba mgerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hej3sj e+c*3rns ar it but cannot see it. When it emer3 rs*+3je sjcnges 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 be0f)b -9 2dgn,emfrcnq due to “interference in space,” whereas beats can be said to09) ,fq2mnrg-ed bfnc be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point c3 jia*-5sk bgr y-4.pa9dsgfs D and3g g59jbdksy ci- .as*a-rfp4 C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting- 6rpapmaes d;)qz+ ehul.n83 the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device isr+z ;ae6adq esp8pmuh- )3n.l 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 xtj 76z,z(v k:we*job3oc.utin Fig. 12–31. Each wave can be thought of as a superposition of two sounz:zu* 7 kt6bcoex jto3jw ,.(vd 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 sh6b6/vq;hevu zift if the source and observer move in the same direction, with the same velocity? Explain zv/ vhq66bu;e.

If a wind is blowing, will th4zx pmaxc:r 6:is alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocit xmcr:4p:z6a xy changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monihjxdw *4u07d,q c)el jtor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning. d 7,cuj) wh0 x4j*delq

  A hiker determines the length of a lake by listen; vx(n 30yp88fq sqbxcing for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimateqfxsnv xy8 q08p3(cb; the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just btk 6 t;x1t;uk 3c-gyn ax:xb,welow 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 1560c-ykn;;kttwgt a 3b:uxx 61,x m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtkf h f,qze,7/ths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just a kj4+qv i7r-rsbove a school of tuna on a foggy day. Without warning, an engine backfire +r 4r7 kjsqiv-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 clibva qz(dw 23,iff. The splash it makes when striking the water below is heard 3.5 s later.adv(q i 2z3bw, How high is the cliff?    m

  A person, with his ear to the ground, seh9:j-)*9wf7 wwa8bayz g eie q1aooe1 es a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othe7 bha1ojwq -ee*9 w)o1:9z8ea afgiywr 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 dis+mo vcp0fb3)d l1rf:qtance by the “5-second rule” for estimating the distance from a lighofcb)fd01lmr 3v:pq +tning 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 120x gd77wxx6z5 e 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 is660 qlzygif 0:w xei 5*:zodf( wfzgx4 $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound let rk4/2 d17yuf qb0481glo6 lt/aov4opjelaavel of 95 dB when fired simultaneously at a certain pl1 rbo/8oaed 41tk6laq lfa4ov7 0p24/ulgjty ace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy je;0y ,/peuo wxit engines is experiencing a sound level bordering on pain, 120 dB. Whe;yw/ ,pu io0xat 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-tou8o b-39 8bxfsu7rmm at21i hh-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intsamx7tbo19f8-ubi 3 2hmh u8rensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of 7rvgk *mby9 *wr+j9opsound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly umk 9+ brwr*9p vg7jo*yniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardru12)r1aqd+ rg(xjyf4n7 un cedm 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 ratel5pl8,-fk v4)tn unxld at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound k84 nflx)tp,ll-u5n vlevel 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 registeredgv(+rmwv-eeehbd8q z.o r rz-2de0 m 4ji1(; l 130 dB when placed 2.8 m in front of a loudspeaker od mv+l1 r 0(qo.4 (;je gbw2erde--zr8 hivmzen 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 differencwolvu+06 t a6te in sound level of 2.0 dB. What is the ratio of the ampu lvot +awt606litudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavew m5m3t39ffjd1gfyy0 d*: i nw is tripled, (a) by what factor will the intensity increase? In3fmwy:59dfn 1t3yjdwg f*mi0 crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, otsvzi lzg56cg:s1bf* q4p*0but one has twice the frequenco f s61spz **tqgcvgb4ilz 05:y of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a so2bq 78(qq/nobnra 3i hund wave in air that corresponds to a displacement amplnb7/biqhq (o83r nq2a itude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem aspw:r vm4 0 mz.inta8cyj4e-)l loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.n:tcm-jl 4wa8)mpz.0e4yrv i )    dB

What are the lowest and highest frequencilu)o 5cc40+xwvn buu.1t.ahces that an ear can detect when the sound level is ) vbcuu c5 uc.wh 41+tol.0nxa30 dB? (See Fig. 12–6.)

  Your auditory system 7a aphefxzz ,j729bs2can accommodate a huge range of sound levels. What is the r7pazj ,hsxefb292a7z atio of 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 fundamental frequency of 44t96rjuz5)cb v 0 Hz. The length of the v v ub)6jct95zribrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What ardh 4kena0i64y e the fundamental and first three audible overtones if the pipeh ya06 44ienkd 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 topq sy, ynblz:w:n2x6qf sw);v9)ir8vx of an empty soda botz) 8vxsywq)nbxnv26;riwlfyq, s :9:tle that is 18 cm deep, if you 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-d1qohbb/eu k3. 0h/ncwm c,b s5f a8e4tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?h n48,bse c e. aw1fkd3om0/ ubcbh/q5 $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmom 57he zqm 6c tqhfnjl7:8ay4.nic. What will be its fundamental frequency if it is fince4aq7 .y ql6 mf8hj7zht5m:ngered at a length of only 60% of its original length?   Hz

  An unfingered guitar string -s1qr8 -oak phis 0.73 m long and is tuned to play E above middle C (330 Hz)-1-p8ko hr aqs.
(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 opeylu* uy hb .266pjtzg/n organ pipe that emits middle C (262 Hz) when the tey uh6 .gp 6*lb2tu/zyjmperature 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 2opjqm 10byr84 otbp300 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the f5 gwgdky8u10ao *4o otlute in Example 12–10 should the hole be that must be uncovered to play D above midd1 gy8 gdook4 ou05taw*le 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 pip gx ke;cn1/e4hd fx:mt/sce18e can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open ot/1x;m/dg shkce1 n x efc8e4:r 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 az4 ij*ihnv6nn.zh(l)m 5lt.tt two successive hart4l)6j zmi hn(*z .n5htvinl.monics of frequencies 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 4 ).0qid;csf gul; rj1t subx9$^{\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 d6q6 kgluphs .nn7-0fthe audible range for a 2.14-m-long organ pipe at 20 fsn06h6pl qdn- .gk u7$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm ln5 ron;aa*zx ,ong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of t r;5xn*o za,anhe 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 t,qi/ mx:yelkwf1p5 2 krying to adjust two strings, one of which is sounding efw5y1:/ixmqpkl k,2 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an c mu7bdqpt dfw1((z(3d $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates 8 2fdm-p0pyljat an unknown frequency. If neither whistle can be hearfd 2yp0p- l8mjd 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 whenc3-f-iin y+ ls sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain3f-+i yc-slni your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tens3zqtrb g+u*u;ion in one string is then decreased by 2.0%. What will be the beat frebz+tru* ugq3; quency heard 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 play middle4i/ ,qo;*rdwtk u(mu z C (262 Hz), but one is atu/ 4tzq;kdm (rwi*, uo 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 a frequency of 4 tf glfo6e0*0w41 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 beat frequencies are possible when A and ft w60*goef0lC 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 kms e.hg uj)527n wk nbnb6n*.m apart. A person stands 3.00 m from one speaker and 3.50 m from the othunkskgnj6*nn2 e bh w.5.b) 7mer.
(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 suppod6 qz52l mme6zwo ,+ hm -3eyvtv(omh3sed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mh2m lwvt6 eommozm +vzyq,5- (36 hde3ust be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beatsi4bpek 3c2g(uxbe .x: per second will be heb.k u 2px3g e:(ecbxi4ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirenoumip9b257fw , nutjm.(cvl 3 is 1550 Hz when at reu wcljbt29n f7uo(,i5 vpm .3mst. What 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 freq2iug5fpz tv +o l9 )ut1(phmj;uency do you detect if a fire engine whose siren emits at 155pi+z1t;)(p9t j5 muo2gufl vh 0 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-Hz source is moving toward w8z)( yl5 vu(p smvv; id)0flryou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactwydrvzuf0 v8;5)s)vi( l (plmly 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 equippe/e l o-ldrz/4h /16p 3vdiqziad 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 frequency of 5.5 Hz. What is the frequency the hornshz zel3d4a/o/r-1 dv i6lpqi/ emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHzynhuom 7b9 ,l2 and receives them returned from an object moving directly away f2,oby ml9hn7urom it at 25 m/s What 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 baqvf(p w.aj5ses 7mi +/sy8of7t emits an ultrasonic sound wave with frequency 30.0 kHz. Wasfm/q7f v7o wpei5 8.s( js+yhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl9dzcm:tk 7c:kayed on a moving flat train car at a frequency of 75 Hz, and :c9dckkz:7tma second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mea; gr7a l:l 2u.ytum.xasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tigua.x.lym7 a: ltru2 ;ssue 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 ox/ z2xv o3dep),3 /ayxn 6llbr6,f cxdf 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 x 32lgbd*mq/ b8ca4wy5f eh z)570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers qxb82c/fale zh3dg5 *)4 m ywbhear 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 speedugesd*9suwz /ig 9,)l u:j,f f 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)8i4iif0loa ,3ukk m dhyk1 u; the angle the shock wave make1dui ik0oa,lmy4k 8)fk3hi u;s with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of 8:jdk8r. oi .vi)z5h+grwc pysound is only about 35 m/o r:wh v8.+)ycipdjk gz5 i.8rs
(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 wave ani rktecpay4n;.r 6/ pys7u29 zgle e.y 9piy7tzs24ca6r;u/ prn kit 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 i ccw 49,9b;0 mhmmu2o.awmcx$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ov6 1e//jyeccwp r g+*enerhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34.6c/wy+reje/* ne 1pcg 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 s5.*ckbuolleex3-+ y eonar device that sends 20,000-Hz sound pulses downward from the bottom ofx.+u5 *eyb-ee cll3ko the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves 6d45ts 1 y vprerpatbb -gdm-cp9/ y*+are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympld+g cow73,m )dfd )ishony. It consists of many plastic pipes of ,m iwlof +s 3g)dc7dd)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 clo (lw ct7:swl*8 r9kopva+ bhdi-etg-4 se to the threshold of human heariws toc-9 4gl h l+*rbtpv8wa7kdei:-(ng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an6nmfqpl*3 7pt 82-dB sound and an 87-dB sound are heard simultanp tpfq637*mln eously?    dB

  The sound level 12.0 m from a loudspeaker,x9pp:v9j u6 rz placed in the open, is 105 dB. What is the acoup :99 vrx6puzjstic 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 q ta22x 80j22shurgih c*1ybg Hz. The power output drops by 10 dB at 15 kHz. 21q8aihx*bgjrs g2 22yuth c 0What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tx q52ll,(sk;qb l dkkvl13 zf.heir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of slk2xv.dlf5kl 13bzql q k;,( 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 syebnc 1a-ug7z 3gx9y l3stems, 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 t(4q1p z p j;iaz);h,tnwky;*jj5ejyfo 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 fixlznv3t *dyo2 j vr* l.dc)kreag:o)4 ,ed points with a fundamental frequency of 440 Hz anal:g* l*d, 2kodje n. z3 tvrcr)y)ov4d a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set be o:7buk ncq.v09a-ginto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level isoagec uv:0.q 79-bnbk 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 mas/)qcfbl8/ bbk s 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with thlbqck/) bf8b/e third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t0j vx0kff z*m-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 pure tone in the 500–1000-Hz range coming from two sour2lot+zk 1v2 brw ge0d)ces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, 1v )ogzl+edkb2 w t02rthe 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 whistlrc1r 0 labj s1h(7be6ies. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the 67r0clb(j be hi1r1asmoving train?   m/s

  The frequency of a steam tn zc4hux2xi;e08y- snrain whistle as it approaches you is 538 Hz. After it passes you, n0x si4hc2nyzx;-e8 u its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spx 0e y,fd-buis ;1-nxieed of cars 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 is it go0b1i-iyefns; ,u x d-xing?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz.zdpw 8vsm ) s-n:y- 9xy7yhx(x The shorter one is 2.40 m long. How ly-sd- nwv9xhy:p )x xs7(m y8zong is the other?    m

Two loudspeakers are at opposite ends of aj ju0qh5ib84q 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 observer8qjubi045q jh when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 shj(f/w3lc l 2m/s what beat frequency would you expect if 5.50-MHz ultrasound waves /l 3 2wcjshfl(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 xutv.qqa2uk89 69xrd moth at speed 6.5 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 frequency of the wave detected by the bat after thaxt9q6q9 .kardu 82xuvt wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches asj f9pr(5lpfqg(vt*3 ju0c3 vq 2i4r*ykm 7hy moth. The pulses are approximately 70.0 ms apart, and et52uy 3rj g f qpc(hq79mvfl(4k j 3rp*siy*v0ach 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 chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send ,u ss)vmcm7g +o duy 5,w;or9vsignals from one Alpine 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 in,cou)ssrodm;5v vgwy7 9u+m, strument, 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 8(7ym8wsvjva / /ab wkcompromised by the presence of standing waves, which can cause a8w(v8b k/wavs/7 yjmacoustic “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 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long ;j t9c)yno::mm1w cnsnlpf)r(frx0:, 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 ma)9c): m1mnwj:cf;y (0rnopstfx: l rn de 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 fos y4r ej-b; /8n, up,ya4yglccr the human ear at a frequency of about 1000 Hz iynrg, yyc-a; cl,jb 84 up/se4s $I_0$ = $1 \times10^{12 } W / m^2$ 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 2ql .2hkp qeubo()v/6d.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directl( h/el)db o6.2kvqu pqy overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo co mx7 4wqg1 ix19p.j+ye 2ykt1xjil5at 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