What is the evidence that sound thq(cyhagf pqc;7 a9;w ps3q;4ravels as a wave?

What is the evidence that sound isf08rrzva; g zdu41mz8 a form of energy?

Children sometimes plxm/ cv2p0 wtu3ay with a homemade “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 utwpc32 /xmv 0sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect thet7okb o+u)r v; frequency or wavelength tko;+ vur tb)o7o change?

What evidence can you give that t5-nbobz4emqp r,/(qb he speed of sound in air does not depend significantly bqr ,z5bpmq (eo4 n-/bon frequency?

The voice of a person who has inhaled helec5nnfpn*lu 3x c -4g:fl;xx7ium sounds very high-pitched. Why?

How will the air temperature 2tg .t+s0nsm ny tfi+vf:c;:rin a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce fw0pox9p xe+xuq +3f(te f)3qthe amplitude of sounds in vax)wu e0 ex93+p+ftp qff(3 oqxrious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toger;) 5k+t ohqt 4v7nyefther as you move up the fingerboard towar5n4 e7)k foqt;hvyr+td the bridge?

A noisy truck approach g)tkak5k j3) rv(;wwres you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenlk3)ww;gar(kk)5vr tj y “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,” whereas b,chd7ty )mo7eeats can be said to be due to “interferencyetoc7h ,)d 7me in time.” Explain.

In Fig. 12–16, if the frequenzsqti)3 -l*iuom+fgz3l- w h0cy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closerius h 3-m wgzl+q-zfit*l)o03 together?

Traditional methods of protecting the hearing of peopls1sre :g/h+t awuj(;xe who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new g;w1sh: x/ (ajues+trtechnology, 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. 12–31. Each wave can be thought of .v4t7 oium+j 3fa1qvtas a superposition of two sound wavo ti m7v4.31j+uf tqaves 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 observer move in the same dirx -5j yfc 7zjqmin.,7qection, with thefyc5jq ,-xi q.znm7j7 same velocity? Explain.

If a wind is blowing, will this alter the frequejduan0 )xca0+ ncy of the sound heard by a person at rest with respect to thx)0dna 0+ac uje source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion onh8*fl.hk4y n y a swing. A monitor is blowing a whistle in front of the child on t8yk.h*lnhf4 y he 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 a lake by listening for the echo of her sh7x82u7u qew f( alcku 7lq3q;;3g y y)gocr,udout reflected by a cliff at the far end of the lake. She hears the echo 2.yeg 7;3 ulq7 od) 2rgyux8uf (;7ac uqqlc3,kw0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his t*2e3g+qd 0pscvsua es 9+e 5eship just below the waterline. He hears the echo of the sound reflected from the ocean floor d ve9pu2es3 st5s+ea 0d c*+eqgirectly 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 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthhbtr x+b3.qfsf49t() cmol))f x dbv1s 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 j2n,o k e9: (bvzu uvipa65ax53iizf+above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km,f 5xbzin(a65z io+u2e jai vk9vup: 3 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 f9 n9-t zgtkezsn f)/0crom the top of a cliff. The splash it makes when striking the water below is heard 3.5 s lac)-9n/g9tekt z fs0 znter. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the z6sy .+:e b ycp1epoy3concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, andb y:cs6ye .zop31+y ep 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 iv*8gu 2kd 9ht,tgr i:y)lu1smile of distance by the “5-second rule” for estimating the 2i*uutk89h giv,dstr 1 :l)ygdistance 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 12046(i,vt jbeab 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 sou nnzq64g/zej ,+vwhd+ nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d mmcp7/ 9j 255goxzyn) oi3upgB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add in/) 5yuxz9 n3mj p5pioo7g 2cgmtensities, not dB’s.]    dB

  A person standing a certain distance from an ais8ooylp7f0t 9rplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What soopt0o9f l8 s7yund 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 ratio oi+/h0mu n /jtynt, ; 5wcqq5coytdw, 4f 58 dB, whereas for a CD player it is 95 dB. What idt/ i,jn +;/w uwtqmc,qyny5o 50ch t4s the 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 normujpi69wpz . +hal conversation. Use hpui6w 9pzj.+Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an a 23,unmjl8wleardrum 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(6 )/hc3 n k;5l(oufar qlkpmj rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a(/mljho( 3nrfk ;q 6p ka5)ucl 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 mecs q1x3l d;yc,g a8e6zter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stags; y3leacc z,dqx1 g86e.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whatpqy/gz076n qe is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–qezp0n q y/g769.]$\approx$   

  If the amplitude of a sound wave is tripled, (sy-24ua4u s z6,ijf lba) by what factor will the intensity increase? Increase by a -2uf il ysjs,zb4au46 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice t0 a:iu dpck5;hhe frequency of the other. What ip:dak; ci0uh 5s the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air pvuplmoh4-9+5q 0 e mtthat corresponds to a displacement amplitude of vibrating air molecumuhoe4 l0t-pq9p 5v+mles of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as dc zzw 3-nubh,zv:).cloud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12b u,h)z-:zcn v.w3dzc –6.)    dB

What are the lowest and highest frequencies that an ear can de a+xtg6 9,)lsd*mjovep ) rd*;oxwn8i tect when the sound level is 30 dB? (See Fig. 12–6.) o+)mgpv8 jiaxlo 6,x9nte ;dd*w*rs)

  Your auditory system can agxx -j z28qz*rv2v-xv ccommodate a huge range of sound levels. What is the ratio of highvzgv8- x-qxz vx 2*2rjest 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 frem sjjf i.0w6ai/1l,ooquency of 440 Hz. The length of the vibrating portii./1 fooi,6 s0laj wjmon 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 are the fundamental and utoxj a4.ru:rqaa 0z/b(vu932 x+8 gwnm1hmrfirst three audible over zqo8 auu+: j3ahr u/vxamm9n.bw4(r2x gr01 ttones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency wou+th qq)jtl8v r2z,(w ).6cr0zjamb qdld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed a+ 8t)0q2 lh,rcdqjbt(6w ).vq mzrzjit 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 hj7q .h60mxeg pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would bx0 6hqe.h7jm ge 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 third harmonic.k5t /ay4 tbh1)wtgf ps4g79kg What will be its fundamental freque /gph ) 44t7ak1 fgsgykt95tbwncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abov.l*vm: 1intxq 0e5ykxe middle Cm tliyx0kq *n1:vex5. (330 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 thax:hqmqg l06wr8hs+ub+ .ttqp66ynaxt pq250t emits middle C (262 Hz) when the myq6 5t8l+un:htr0wh 6a6.tp2+gxsqpq bq0x temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at h/zm ;w*lyx-hd :ywa3 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpip.* uc3 lagp wn08ws.iece of the flute in Example 12–10 should the hole be that must be uncovered togl.p3 uscn* aww80.p i play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at h2o8qwg+lh7m.; 9j maqwgy y+ 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between+g wygqlhq8a;27+m hwj9oy. m. (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 two e hg/;*1 wgclqnrj3+tsuccessive hanjt3g g ;*1celwrq/h+ rmonics 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 8u osw,g ld/ y7fyf4 932fmjbu$^{\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-long organ/yx0xhu5 9 4;ultcp/nq 4 msmd piu54m/yt0 qpsh 9d4lx/ mun cx;pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatenr6z8 ,4xna cwly 2.5 cm long. It is open to the outside and is closed 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. 12wxr4 zn86a nc,–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one *d3y(jgff zdh3qfnu /y(q9k+cws2 jju: m 6*jof whisu6*n+f 3 :y(fwcum 2k3zydjd *jhqg9j(/j qfch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency ifj ws3zi2p +:znk1/kou 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 (np gep q(*d+p-/vr+djqj9cl(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 simultaneously, estimate the operating frequency of brand (pdd(njl* -p+revgqj9 cp/+ qX.    kHz

  A guitar string produces 4 beats/s whea2 ;h4z.brey j/ 3ph/u9ule ;m w(ayxin sounded with a 350-Hz tuning fork and 9 beats/s wabpjh/x 3yh9ueu(izm;wyra2 e/;4. lhen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned b+nb7 y8vem0m to the same frequency, 294 Hz. The tension in one string is then decreasedny0vm8 e7bb+m by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will b31 v3 t7sar8sj+ mh ,5newd fh4.p9 of8trsxqse heard if two identical flutes each try to play middle C (262 Hz),waf3 te sfqrp9,r 871jms+thovh.5n s438sdx but one 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 a frequency 5weyrrk5f(2th f0, s dof 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 possiryfd2s(0khwfe,t r5 5 ble 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 ag ukwto. r4gut( bjp;t -7 qy-+wea6h+part. A person stands 3.00 m from one speaker and 3.50 m from the other. .y+4tub7tu ;jeo+rh 6gw-qgwatp (-k
(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 Hz, but i hs.7p bpeacgn j( /s4md nnj2/16ai-a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must bei np pd i.g67c- mn(/ba1es/n4 s2jahj 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 2yk2w/7f+k p zhykb3t 8.64 m and 2.76 m in air. How many beats per second will be hearkw+ y 7pbk2zk3 ty8f/hd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequh .fvj owk5jfbsi a /;.s)bm(1ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency .hms/ib(ab)skj j;v w51.fof 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 h+uswt gn7p3 *you detect if a fire engine whose siren emits at 1550 Hz moves at ahpt3w g*u7ns + speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000bx8 )os43b csv-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the )v 48bosbsc x3same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with ta;0h4k jo4hzghe 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 horns emit? Assumg4oj z;0ah4kh e T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoudzssc23rl37e iewas.y3n:x h :uc7:nic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/su7ecdu: r sw lzhes2ixynsc 73a3.3 :: What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a kg, e9k9fxee/au6- m,x*crn j8 lvpt0;qff 4jspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wavc9p rjuq;98t 6,fefvxek a k-m x,*e/ljf0g4ne 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 plh //vz/fl s7iqayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if tqvi7 fs z/l/h/he train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measu:qcd al6 qq/1r8 3yvoxre blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is takenv8qa1x q:o6q/ld3rcy 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 usingu8n; 8d(,tm rpno*ghm 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 oe7*h jnv mfc*u3zxt )5f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observersf)zhu5ec7*n m*v jx t3 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 , sg76oeel,7i ogwbn 9if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of i/ 4z4lk 9n+nvro*minsound is 310 m/s (a) What is the angle the shocik4i*4nn z/ ormn9+vl k wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where thes uv* 7zs krobmtlh3(w5 :0k0q speed of sound is only about 35 m/s(*0l usbrv:0 kq5s oz mw3htk7
(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 st2t*;*kzbbfkf/wgne1 hp/ if -rikes the ocean. Determine the shock wave angle /f;nehg*1 p fz-i/ wbb*2k tkfit 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 nu v;9q dq0 8rgzjw-z-$/theta$ 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 theaa cs5i wr*/l3 ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horaw/il a35*csrizontal 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 sicanv j:y(zh (a 3x(,qends 20,000-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 puxai( 3q:cy((,hvjn zalses (in fresh water)?    s

  Approximately how many octaves are there in the human o4ahopk (iy8; :utqnh2e4g b bkrxy8*;j6 in(audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer 7(;ayv hv,rnc:zcd fp (4)bchpipe symphony. It consists of many plastic pipes of various lengths, which are open)(c ca7d;b,4(zch fn vv:yhpr 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 ogiletfe/q721 f human hearing (0 dB). What will be the sound level of 1000 suchile /e12qt7gf mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an(o.t 7g0y0o 7bj -jvt1 pklf7pwg pq;p 87-dB sound are heard v 7 7 -t(pb; 1tplgyo7fkpg.wqjpo 00jsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is7 )2xpq cddm6g3+mgxs 105 dB. What is the acoustic power output (W) of the speaker, assuming+ mdsd3x2)6 gq gp7mxc it radiates equally in all directions?    W

  A stereo amplifier is ratedoq +us+n tzz0tg51 py: at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is th+ o1n0z :5tg+typzqs ue power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices yz ujk.k, zn7f3. 2zfkover their 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 2.0 cm. What wojf k.f 3nz27.k z,kuyzuld be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gas:0amdvvf+ 80y td7 kgin, $\beta$ 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 tunedt, )xi r8m( t1vlh,rds 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 withkaij 8ca 3,v8ntb q;.:oif;js a fundamental fretj;c,avb3;fos8i qk:n .ji 8aquency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibrati ck 7zgfrp rc*a370odz.w ds;;on above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so,d wz;pagocsrfdzk7*r; 7.30 c the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near ll4y+nve/fq3 a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tfl+v q4y /l3enube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate 8z3anfgw,9n b, 9uo inas 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 cominguh/y .q8 pue- u0u.bso 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 i/puu -quby.s.8o0 e hus the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statio4 om7yf(lfy 0nnary. The conductor on the stationary train hears a 3.0-Hz bealy (nfoy 407mft frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as i0;nx (i slpmgqkef 1,8t approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the trainen i(;slf x10p,kmg8q moving (assume constant velocity)?    m/s

  At a race track, you c8xlms 8v -z6qkan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppm 8x6q8lkzsv-ose 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, ss u6u39g-h xn mc;2xk:;yg cyj6jd ,ldounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 x6y j du3nlgkj ;hu2,9;xy-cdgc ms:6m long. How long is the other?    m

Two loudspeakers are +2 qo;;(v ymtq4o*vlx0pbr qaat opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–4 mrqo;qoaqx t*(;l 0v+2vy bp37. 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 have passed him, at C?

  If the velocity of blood flow in the aorta is normally about i7:tze7 xxbx: homw(g 906ptis*tf +r0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refphzr7bi* t7x xiox90+f: (g6 stew:t mlected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is fly p8gq(-t/ (g8z9mgr e7noxq/ gu0zeouing 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 7q (zpruzn qg 0m8o/xgge9u8- eog /(tthat wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachesu-c3q6 y4spc r a moth. The pulses are approximately 70.0 ms apart, and ea- 6u43qcyscp rch 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 signals from one)9t lheiu ws9 gka.z 5e;d9n-u Alpine village to another. Since lower frequency soundeweghl) 9ud.u9k9ias;5n tz -s are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by thf+v3 (/opnnv w :rg8dke presence of standinr3n+pk/8o dgv:(v fnwg 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 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv d (1k6siv.eoiolves 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 to “sing,” o.v d1o6esii( kr 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 ,qw(cel3 9ftahearing for the human ear at a frequency of aboutc ,3fqaw9let( 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the 9o2iptob p)xv..+eq osonic boom 1.5 min after the plane passes directly ovp)i 2+. o.bextpovoq 9erhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 27rr :o3hlf dlis 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