What is the evidence thatll;u* nia ;7xl,gc:el sound travels as a wave?

What is the evidence that sound is a ft eyw1m/(-x wiorm of energy?

Children sometimes play wtyam eer,a3( q8k1 m5jr;,t;mgew o) uith 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 j y,makm;w 1meqera(r 53tgeut,8;o )clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into wat:qyll m:;vkc. er, do you expect the frequency or wavelength to ccmlq;lk: v. :yhange?

What evidence can you give that the speed of sound in air does not depend sig53,wv a 6kaufcnificantly on cwak5v,a f36u frequency?

The voice of a person who u ,dyrg,rqabv* ke)8 0has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room(hbxvamz8;phm1 ;lm * affect the pitch of organ pipes?

Explain how a tube might be used as a filter 4,rv05phhrxi, kj 2tm to reduce the amplitude of sounds in various frequency ranges. (An example phmv, hk 0 itxr52rj4,is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetp zjkl o8v0fq,o) ;shl g5d*p1her as you move up the fingerboard toward the bridgepklzv q5 dfs1o8p0og; )h*,lj?

A noisy truck approaches you from behind a building. Initially you hear it but c xo k(fkxd3.gkplj ,;.annot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on d..(;pxd,k kgf3o jxlkiffraction.]

Standing waves can be said to be due to “interference in 8h8 /ecqn 3haofmr+jv s*2 g.ospace,” whereas beats can be said to be due to “interferejhe+ nmsao2h 8v*/gc .ro8q f3nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lox+xx*3zzmu3 fcll3 p-wered, would the points D and Czf3xm x3 l+*3xpl- czu (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in0sk1rvp wfd1 ,lsq17r areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise ,s1vk0r 1lw7r d1qpsf reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. bw8mr urq94 pqz9yuqj7(q)l : 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wh7 m)8ql :jrqqw(u9ry4bz u9 pqich 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 iq6)tx;- id9yvad7 zg same direction, with the same velocity? izq6)idv d-7gtx;ay9Explain.

If a wind is blowing, will th/9ncvl k8kt nbw2z 2 quu+1b5bis alter the frequency of the sound heard by a person at rest with resp9tz2kb lnv/ uw + unq1bbc852kect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion o5 .e+ 0 zivu7j5gsuyybn a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the so.+05jgbiu 5vyz7 yesuund of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeniezi*3/p l4pqp ng for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 sz e lppq*34p/i 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 hears the ecz w 4e++*24kodb ,xovmhf xy-rho of the sound reflected from the ocean floor directly below 2.5 s later. How deep isf4rx+eov+ yx hw2,k4d*- mbzo 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 wavelen2jiw mcs7ljsu2bu(q(d,5bn 5xev 37egths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. W)d9 ih(i* sn3 pbfm,qoithout warning, an engine backfire occurs on another boat 1.0 km away ( bs 9if(imo3*qd p,)hnFig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikingz9xylju ;d4n-kw *)wfi 9i z:trl 4f2x the water b wf92z)i l zjyixf: tru;4nk*dl-x9w 4elow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone sat4va0qg o ngl+op00f-2t p( ztrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact oo2(a+4anzgtg0f vpl0t - poq0 ccur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent en.1q pee js;*yrror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike ;syjq* ne .ep1if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paiewzkvc a)2a1 .iobh0 :og62az n level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a souwdm9lt 3h.jdunke0 1;nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 958tassv 7v+t7 pa,6wkm dB when fired simultaneously at a certain plsamv w 7pvas87 t+6kt,ace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a ,c *ai mysu9xm+mz* .qcertain distance from an airplane with four equally 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 all but oneyq9m, mm+*axzci *.su engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to hao)o: qk40 .qyyci9lp ygq+jm9ve a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the opq 0koymyq+ q94iclj g9y):.background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frqzxfr e67msbd2rt y3,k66yj 9om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on q2 my k9r6d,te67zjb3sfrxy 6the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum w;af7v* ;r b)you8yt vahose 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 ado /e8f;p x0jmt 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 loudspeaker connected in turn tojp8 0 ;m/dxefo 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 2.8 m in front of a z;fo8krf5i6c,* imdn c5 orin ,m d8;ifzkf*6loudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typical8k,n6ldol3 /yj( 7 3xx zcrqiily detect a difference in sound level of 2.0 dB. What is the ratio of the amlyjq x(,7/zlo 6 3iikn3x8c rdplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the ppks)7yed95er ev-lfj(s/ i jd:qo:2 wqa ((o intensity increase? Increasr:ojvd/ (q7 p w9sieyj2a s:-)qpk(l5ed fe(oe by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tc2segwls8v j rc*2u4)wice the frequency of the other. What is the ratio )*c w sc82us e24lgrvjof their intensities?   

  What would be the sound level (in dB) of a so;os;1 p26wdj ih2d5ta t9guix.0sudmjp3nb9und wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300u ms u3w2 nda2p;1j sdb6;i9tt50dg x .jih9po Hz?    dB

  A 6000-Hz tone must hava;uk)q: z kgs q mfsawn-k11-qeb4e w4.;p)ije what sound level to seem as loud as a 100-Hz tone that has a 50-d mk nik;ueg :ek.- 1qfsj-szpaa)b44 ;qwqw1)B sound level? (See Fig. 12–6.)    dB

What are the lowest and. fk236 lb :ygzt2anxn highest frequencies that an ear can detect when the sound level is 30 dB? (nk2b3x6tl 2a y.fz:gn See Fig. 12–6.)

  Your auditory system can a,r nkk 2vpra enrnj50x *9ti:jmv 9)/lccommodate a huge range of sound levels. What is the ratio of highest/ nrvnl9jta5*i mkr:r0j )x2n evp9,k 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 frequencyn u/*mfi1b-ikh g29oq of 440 Hz. The length of the inogfm2 /ki9u -h *1bqvibrating 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 are the fundamental and first three bsjm+9 mn(.xuthrk ;(audible overtones ;m j bxk(9(mnsrth+.u if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect fro(d9ktha-xkf ,m blowing across the top of an empty soda bottle that is 18 cm deep, -hktk xa(d9, fif 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 aj k i/t(w5lje,*9 9axuq 8sjhf pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range ofj,ljs*9wq 5 (ae 8xkft9uh/i j 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 w.m8d(gst g8fthird harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origi f8sgmtd(g w8.nal length?   Hz

  An unfingered guitar do/b8k. h)e irstring is 0.73 m long and is tuned to play E above middle C (3d /hb.ekr8io)30 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 le4egupgdzjhc0y ;r;57 ngth of an open organ pipe that emits middle C (262 Hz) when the4 yhrgzd;p;5 7ucgej0 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 20u90f q+ifmxm x3,i k7g $^{\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 123mnhls+ -.0indjzti*–10 should the hole be that must be uncovered to pi+n-3 tnz0jsl.*h dmilay D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 4hvl.7:6dzx 1llg/,l ad:q aiw40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an openzl6 ll. q gaw d7x:ih1:,/lvda 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 at9 kqr8,gs-90j1a w j) k7ljxovh,nsgt two successive harmonics of frej qgk ,-g9t0,nk)7w ljv8xa9 so1hjrsquencies 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 /++j5 fvyoybi $^{\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 orgs:a0o j. caoov: -*twlan pipe at 2so -0j.ota::lwao cv* 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to abohbi*:ed* ;1 o i+jlthe 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 relatiohd1ib:+jb** a ooiel;nship 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 trying to adjust twrpg26.,(x ,h9r 0sgbnjx vgxfo strings, one of which is sounding 440 Hz. How far off in frequency is the oth.x rhgn6 ggp,v, 2fs0xxbj(r9er string? ±    Hz

  What is the beat frequency if middle C g ssjdj-r0jkap2 do )658 psnf4 2ykfr5rsa,.(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 o;pwg1yyp g( iismz. 4rjn e437r d0u;fperates 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 frequency(yn.g41ypmu w;s 0p7d zi ;3jf4ergri 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 a709 hv(e4xa y0dnw bx2twqy5fkxk8 4m 350-Hz tuning fork and 9 beats/s when sounded with yaw44 (dtyvwn 29mh ekxxx078q 0bkf5a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T cprp *n7w 7ke/wsv 3nkc951tvhe tension in one string is then decreased by 2.0%. What will be the beat frequency 7tskwc9c7*w5vn rekpv /n3p 1heard 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 k1z qjdw *ugc3 mk...lplay middle C (262 Hz), but one is at 5.0°C and the othwqk 31.jm g*l.udkz. cer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B:gwlqg) h.;r5 aa1h ib has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. r ; lg:hahgq 5iw1a.b)When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from:0mbeq78oaii ep6ubiyw ;)r l5 v w;c( one speaker and 3.50 m fli 5pr obw)vm(w:uiee 80cabqi y67;;rom 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 Hz, but a piano tund, il f *wl8bji4usipm( :ga*3er hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what muudb*j f *,p8agimwl3 iis4: l(st 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 wave )p.q .eh;- dauvob7uhlengths 2.64 m and 2.76 m in air. How many beats per o;hvp7d) qb-euh . .ausecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of b/91kdt x f*+7bl(hws (eqzod a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you dexdh9/ *d+wzk qs( t(eb7 fbl1otect 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;rojs dki0i5 tjoj)) m*t t6 j1vz8w+w engine whose siren emits kj) 0)1ijoo5vrjwst*+ w6 djit8mtz;at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenq/ff80f9/vq y1zexp q cy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequfvqzf q qf/91ey0p/ x8encies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one iw10w7 1 kubfnt ism*o, n;t;xks at rest and the other is moving toward the first at 1;7s,ntnf0; *1xkw mbtuiwk 1o 5 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 ultrasonic sound wavyki5 .q8zaz .sfimk9e9nu u:0es at 50.0 kHz and receives them returned frk9 s: u zk58i.y 9efiaz0qm.unom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an 5u3 7* z-mbywnxtp jf6ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear b uw576z-x3t fy mpj*nin the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat (v7b4 noi ew6xyys0 5utrain car at a frequency of 75 Hz, and a se o4y7(b5 yu0n6evisxwcond 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 measure blood-flow spnfx9 y2h) j,nfeeds. Suppose the device emits sound at 3.9 yj)nnfhx,f25 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic /lgj/g91 mih egza kqqiv;;mco. 7t85waves 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 emitz n -kvlp7:ja9s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hevl -7ak9: jnzpar 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 speedkx4ucswyhudgq:. x y b-te8) b3+1k+k 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 *r: h bzc ;l+*.ri5sff*zfywai :ztq -2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction *-bw* f z5ci :zrl z;qi+a*s.fth:fryof 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 sound ixigdo26hpd* )jagmx/ 8k* y.gs onlpxg)k g8o2x yi. *a6m ddg/hj*y about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oce0f)gm7 a d6rdo r8hj2yan. Determine the shock wave angle it produces 6yj d 2ar0drh7)gmof 8
(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 ff diif(boc1vsk t;ks )4:d)($/theta$ 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 vdb q:g;xgi5qz5 *k6zjw+ie + the ground flying faster than the speed of sound. By the gvgwx+k;e j *5ziqzdi b5+6:qtime you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fro2myg6j w y1ou/35ol1spgd6 f ym 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 minimumj1glo6m5sg w6f y1/ 32dyypuo time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huma b1tyv1 au0d0,20vvqnjkw)rnn audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displays/n 4xkt - gbpy82 jvmv0;chg5 called a sewer pipe symphony. It consists of many pb4pyk8-2n;sc g 5gv vh xmj0/tlastic pipes 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 ta6.om6k otgz- he threshold of human hearing (0 dB). What will be the sound level of 100.m6 ztakgo 6-o0 such mosquitoes?    dB

  What is the resultant sound level 7 6apfg o*exg.when an 82-dB sound and an 87-dB sound are heard simultanxoa* gfeg.6 p7eously?    dB

  The sound level 12.0 m from a loudspeaker, placed inwmwif*nl :tp,c1q2 g8 the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in a2npc: mtqf8,l iw*wg 1ll directions?    W

  A stereo amplifier is rated at 150 W output at 1000 H76 cd e42krg vbfc4bp-z. The power output drops by 10 dB at 15 kHz. What is the power o 4p-vdkrc7f642be gbc utput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eaj e *go1dt)z a/xd t/+plv;2uers. Assume that th +oe/;z*1ltp/ de tvx aj2gd)ue 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 would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, k7gs*a :,mku ;drtvpadw5)6n $\beta$ 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 tune8 h6*s.ut(ft.l*cfrxga-gdm d 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 nuc.9zhh6mdn)9sot 132 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unih9d.uh9 m )nstoc16 nzt 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 abovioli v 1pj g*32+-6lywwoex.pe a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does jl2.o-*wvg e3 p16iwop+liyx so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube th9rywq k)4l c3jat is open at one end and also 75 cm long. How much tension should be in the string if itqljwc)r 9yk43 is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was oh1p3ri y)h i r,/jfhj.bserved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two ; obx; ikccmg ,;b(91pz4pvucsources. 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 4cx cg ;bvuo1 c 9z;pm(,;ipbkone source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. kci/qjgha x*+:c )j +mOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency jigc+ :/ qcmahjk+x*)when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you bqwly2 gqvl3 (0)wga 3yxjdx. :i6 d6sis 538 Hz. After it passes you, its fre3 6dyx:ib6vwa x02ysw) dqlgqg3 .lj(quency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can3h;(wh/ yvtc)ibm/,9jc sc39xbkn )4 rliwuj estimate the speed of cars just by listening to the difference in pitch of the engine noise between appro(wym3i u9 /bkh ;3hj 9n) ,jic/r4xvcwc)tsblaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sound7ihrdp rmg c;ckmi7 v;96+i 5ojm/.h xing together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is. 5j;7 xih9 kgr;dhicmr6i movc7m/p+ the other?    m

Two loudspeakers are at opmfo+6 t(0bfo 3orr29 nvgvi:a posite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the(62f3v+afrv0i:r g oo9 bo mnt 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 abo a6pj3cq0k*mc.si 2zg ut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wac3qg*i2s k0z 6ma.cjp ves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whep41ohre 1nh7 ;myd *.u(.hyhlyz8yqile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wha4e.dq e l7;8o*.myzhpyhynyh u1h1r( t is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freqvw 3wqnes, 0ylsfk9un9zy2 :8q 3 t:awuency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. y nevatw nw8wq zkfy,3q:0992:l3ssu 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 Alpine viaqhjgu/ 2 h* 3 89ge*tub5vmjhllage to another. Since lower frequency sounds are less sush* 5j tj93 hgvhu2g8mequb/* aceptible 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 lir h61-5; uz dkdbxxod+a4fr1,y cl5 zlstening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 mbu dkf54dxdl,ac h1loz-5y;6r r x1+z 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 w- )2ky nyr uqs g*f,p;ey3(wv“singing 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 to “sing,” or emit a clear, loud, ringing sor p ew *2-kvys)fg3yuq(wn,;yund. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequencob+ .g(mmi3jrem(;;a 8c lgtx+hgce; y of about 1000 Hjcli(rgea;mteoxg;+.m ; 8 m3(+cbg 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 2.08fkb 1g ;hqbpw*dbaw7lt5 81g. An observer on the ground hears the sonic boom 1.5 min after the pl5p8 d1k;7bwb8lw 1fbt g*hga qane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo,(bsz*0r dtlhat 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