What is the evidence that sound travels aax- qq)ng 8pj4hw;wx0 s a wave?

What is the evidence 0* g: hdxewf2jthat sound is a form of energy?

Children sometimes play with a hor q2zt8/* pky:mma,c,9vhqcomemade “telephone” by attaching a string to the bottoms of two paper p* q/cvmry,8,hazcko tqm2 :9cups. 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 travels from one cup to the other.

When a sound wave pasf6mj9af-icv ) 1i.bwxses from air into water, do you expect the frequency or wavelength to chcim-w6j)vf 1a9ixf .bange?

What evidence can you give that the speed of sound in air does not de bg 6h yq;x-ecy44qxk(pend signifq 6exbkyx;qc(y g4-h4icantly on frequency?

The voice of a person who has inhal,qxpa4 (3sn vi9i,ip3sd io* eed helium sounds very high-pitched. Why?

How will the air temperature in a room affb 45+ncwona4ez3x s 0ject the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitudet6,x ycfowz1 6 of sounds in various frequency,yxfz c 6tw1o6 ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacejj1 3i m+keq7 oz/m8iqd closer together as you move upmq+ eq/m13ii87kzj oj the fingerboard toward the bridge?

A noisy truck approaches you fzdd7ym*,g4z7b t( 13en npsmlrom behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its,tbz( 7gm*7myp s4ded 1lnn 3z sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas 8lz;hee/ 9 lp 8/qyubxvkn+y-beats can be said to be due to “interference in time.” Ex/; ylybk eux88/nhpv el-+zq 9plain.

In Fig. 12–16, if the frequency of the speakers ef) p7cgcas r*w07i3rc0u i8qwere lowered, would the points D and C (where destructive and constructive intc)78f0wrcqu 0*c psr7ia ei3g erference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who w65eii8fzm os 7jet 09work 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. Inste j5e6w7ozis0e9itm8fad, 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. 12s,owekkva j)x . -bp(0–31. Each wave can be thought of as a superposition of two sound waves with slightly different frvx jo-0.s k,ew(bkap)equencies, 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 own p96j8 5clr4wjg5mdzd6y (5ll jc/ move in the same direction, with ld 6no j 46(lljzgwyj8dw/5pc9c5m r5the same velocity? Explain.

If a wind is blowing, will this alter the frr x j75si-sr,vequency of the sound heard by a person at rest with respect to the source? Is the wave rvir7xjs-s ,5length or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A uo c9d5wl 49nnmonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child heo duc5n9nl9 4war the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake- gjmluy2bn 2ormhi(9rtiz..32j3 zk by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0yr .22m3gt3zni- u mloh9b (rjk.2izj s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wattns0,c*lex8h(r9 d v0 ckta0s erline. He hears the echo of the sound reflected from the ocean floor directly below 2. naretdl sh0cv,ct(0 k0s9x*8 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 wavelengths in ;m nw /xegr42adyz3*x.mq 7tl 7bgi 0iair 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 ql9 nq1ar)):9 gbu tmsk t6p.br0 y5cgfoggy day. Without warning, an engine backfire occur1lag)t q)u6rbt:ry k50csnpq9b 9g.ms 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 f ia4 b)j,x hvbm/ g;-taoo;+utrom the top of a cliff. The splash it makes when striking the water below is hearvgubtx,a;o)jamti / +o;h 4b-d 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge,pt3 kgma4t7ur/6*w x7 n9pq(fr e php stone strike the concrete pavement. Aqf emptu* pr9n/ a7r p4(px7t ,w3kh6g 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error madeqy)6n5yd dr7a+8q m 87q sbsca over one mile of distance by the “5-second rule” for estirq)yay+b86ns77sd5 ac qq dm 8mating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain 4d dc6i - ev)4gyfiiu9level 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 ofumm-g7 bp5d9e,yq-cl /o o+ x 02wmaib a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuli1j1 7d ccv-potaneously at a certain place, what will be the sound level if only one is exploded?1dcjp i-o1 c7v [Hint: Add intensities, not dB’s.]    dB

  A person standing a e+q 5xanq+h b+certain 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 n+b5aq h +q+xethe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sigtn. 1y xeex.k4nal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sen..t1ykex 4 xignal 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 normal -vnk8kv fvcz0,cm 35zka,1w9vii(wm conversation. Use Tazfiz8wc5c vwkkv1n k,9v0 ma3,m(-ivble 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 eardrum whose area is fq t/8fyjmyc yz )6*3y$5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B (gm +(djl8ztvy0 ik0nnawqqy0 * 1s9vis rated qiyt0 v d9j8v001zqlma(skw*( n ny+gat 40 W. (a) Estimate the sound level 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 registered 130 dB when placed 2.8 m in fxd2.boj2 9cbqront of a lodb2j2xoq9 b .cudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically det94rs wdsqb8 d1ect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thi 9q drs1ds8w4bs amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facto 2jbm q1no*o)d,fh1p 7s--csuen.zjor will the intensity increase? Increase by a 1sp *-q .b,ons7fe -1jnzhod2ujc)o mfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicoe ay(8.fvvp 9e the frequency of the otherev 8 fv(.oy9pa. What is the ratio of their intensities?   

  What would be the sound leveglj3q)2kv :mqu8o(ac l (in dB) of a sound wave in air that corresponds to ao ju3l2 8vcqm )(k:qag displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level i m yyxd+;iv+5g9+qk +xt3kpwto seem as loud as a 100-Hz tone that has a 50-dB sou ypkkv; g+ q+i3i5dx tym+w+x9nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect wh5 nh /rl,:n hdp)3jhwo vic3-ien the sound level is 30 dB? (See 5/r -hp,) cwjhviho3ilnd3n : Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounr;ppo+uoc4 q( d levels. What is the ratio of higr;oc +p qpu(o4hest 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 fundamenta gpa*7 lw,bsp:l frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pl,sb agw *ppl7:aced?    N

  An organ pipe is 112 czug 3u:a3xkod:hc ;p ;m long. What are the fundamental and first three audible overtones if: ;:33 uxzog;a dcuhpk 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 f*l4f eo (si34.* f tlawn7vbqvrom blowing across the top of an empty s3l*nv(o iffs 44l b*qw.te7vaoda bottle 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 orgj slb.uy vm-+-kkqv29 an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be y2v-+.ul- sqvjkbkm 9 the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequencywsx*mv +9v )ztdwwr /) of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered swv x vtrw) z)dw*+m/9at 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 above midd*qxie:x9 t4r7:b ry xdle C :x*4r r y7xxb9:qe idt(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 xyhm z86j 7, ,txdb3gwan open organ pipe that emits middle C (262 Hz) when the b z376xwjy,8h ,gmxdttemperature 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 atkque/j f8lru5ntwp9( g8 m7/m 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Examtmekn2aa 7d :m(;di 2- ix0aymqyw8+ uple 12–10 should the hole be that must be uncovered to play D2(akyx nummd08ed : iaa; tmq2-+w7y i 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 H7dj(8i5tuo eoz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed p d7(eju 5oit8oipe. ----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 hr ov)-lap,mb )bar 46 xh*p7m x.yzt2two successive harmonics of frequencies 275 Hzhhlbx,m tv.2y b6mpp4 a)x z r*o7a)-r 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 r9 6ij 2; wvk):hpkrl ;thm1gt$^{\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(2gjswib s n67zih .3h1vlb2f pip3f vb2( 6l s7bji1ig h2wzn.hse at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm kq )qs) y1jtp l( sjn9q)z/zc,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. ( zk1qsqy 9nsp)) jj/tz lq,c)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 two strings, ov *f5u qu0gn10o i6 hakzv-adbxa+-i-ne of which is sounding 440 Hz. How far off in frequency isguk vfi0-hi-qz 6an1oxu50da *- ba +v the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and h(7ndb e h .c0oj7ounyln:3r2$C^＃$ (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 (bse/2 fr3gbt5 orand X) operates at o2t/g3b erf5san 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 X.    kHz

  A guitar string produces 4 beats/s when sounded with ri -::onids 9 t)xab7h;vo53 inqdp+o 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? Explain your roni 7do5pd3vroiq +ti:ans;hx 9) -:beasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tene 7mnj -u,oljin*21 kasion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toge nenu i*2-oj7a1 ,jlkmther? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will 7q +gnagtj3s8y 8.ju nbe heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the jn7tuy jsg q a8.83+ngother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A o;znn8n --o-(qaktdv b dbe.1, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounoe dat bn--; (.-vz1k8 bonqdnded 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 one spevlcwop6c .+v )aker and 3.50 m from the othe p l)owcv+cv.6r.
(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 tpk-czhu*w 63-hu3k i f 8shw1vo 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 must be the frequency of the otherwph8u-i -shkw3v6hk 3 1fzu c* ?   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 soundbv )uu;ck eq a0z41kn8 of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assn zkq 4ue b10k)cva;8uume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi7lysshoou1ps38 8* m n;q4bxaloo5(tre engine’s siren is 1550 Hz when at rest. What frequency do you detect if you1lu ho8*3xo8olsspmo4 q(7ab n ;y5st move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose x z.x*yhu/( aqsiren emits at 1550u(* xq /xyzha. 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 yo.bj /q75 nsgkq-v7 nvpltnc/: u at 15 m/s versus you moving toward it at 15 m/s Are the two fres nt/ :j n7/.qbnv 5lgcp-qkv7quencies 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 i2yqqy u 0t29yrs 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 rt0uq yq292yy Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz ai,d k gm71 roa7vv(tm*nd receives them returned from an object moving directly away from it atov *7mtar7vd1mkg ,i( 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 u xv12(xewca9m9u bf5xg zu*h 1ltrasonic sound wave with fre xzxgxh5 f2a 19 uc*v1(ue9bmwquency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppfsu -a 6a t,w gjm:zsp25vt6t,ler experiments, a tuba was played on a moving flat train car at ,w:2t-6 5m,vgastzpfats j6u 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 the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavesqk3 nse 9ces(8 to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away fro(k3 9ceqens s8m the sound source?   Hz

  The Doppler effect using ultrason)my/m khjp z--8k pb e4awkr5c 3xp,u2ic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind gp9sb f,4b t8w gexy6:velocity is 12 m/s from the north, whaty,: fpex wbg8t49g bs6 frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20vp*,fdre6qnq ;h-xk8 $^{\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 sj5v80-kp3/ kopjy +jxu acq4is the angle the shock wave makes 5sj043-avk/oquypp cx kj+8 jwith 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 wsehl y 1(j;5uahere the speed of sound is only ae;ua(j1s l5hybout 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 strikex6+.pynqha-l yv8kkh-ixp z :h0 d21 as the ocean. Determine the shock wave angle it producez qx:2 hniy8 0-pav.+h1xdlp hykka 6-s
(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 ri7hmrrf 2m3e9nm /. q$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see asv yj*l. vt4t9 plane exactly 1.5 km above the ground flying faster than the speed of sound. By the timvs 4l* ttvy9j.e 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 sonara4c (z*l/bno q device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for wh n a4bcl(z/q*oich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?m/vs0st4du7fzp;cq6 f0o + nt 3l;-fir ims)r $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. -) ugoan: lique3eo 04It consists of many plastic pipes of various lengths, which are open on 3 i)e-4:nuua0oogqelboth 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 ngd9 nof);quvsf5bmif50 z:1cx )(bma sound close to the threshold of human hearing (0 dB). What wil:0(f);bu 9 mc m5 xgvszn q15ib)ndoffl be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound 9:xc8rhvkolc qgdjcu:5;t 0 )are hearj;lgq98 r hdo5x:k 0:ccv)cutd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,t dyl39dcpixs f(:4txl db,36 placed in the open, is 105 dB. What is the acoustic power output (W) of the speak4x3sdf,pc39l (yd 6xlt tdbi: er, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ou va4-ovnn/(e tqwz/s1 tput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts a(1qzvn /4svwenota/ - t 15 kHz?    dB

  Workers around jet aircraft typically wear dkkf 8k(7 ns6nd/7jhtprotective devices over 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 would be the power intercepted by an unprotectenjh(7k/ kd8t f 6nsk7dd ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th ma/ .0.ymd0kk tr(pde7 e*name gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenjny1 wdoimo4*5g32nvpys j+ ,cy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental2iv m5q39 c3kg+vvheb3hz c /:tc -sfu frequency of 440 Hz and a mass per uib5-zs/ vc3 u9gq cte:3 fmv3khh2 cv+nit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical e0 ooah93:rge 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 wat e:g0a9h oe3roer 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 2.1)c vr8idsl ex2.;i4pu 0 g is near a tube that is open at one end and also 75 cm long. How much t rd.8) 2x;pecu i4vilsension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop6zs ch z5 n-kt8;uh-nw ($\frac{1}{2}\lambda$) 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 twojrlkeh ,-lww:si(jy(5a3 zw * 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 th(*h iew r (a szkwwjly,:j-5l3an the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductorbyl:jvqg/6e -4 gss 7x on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of 47x:6sg segj- lb/vyqthe moving train?   m/s

  The frequency of a steam train whistlezfy 9zew8g.v9f6 ov(9; jm vwh as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veloc mo6ezh;v9w9.g y8vj9fw(zvfity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thsi /di 4j-ib+oe 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. Howsio/ i-4+idj b fast is it going?    m/s

  Two open organ pipes, sounding togethi mgfmh44 /o,7vum en;er, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Ho om hne 7mivmf,u;/g44w long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it +.ugy )xw -jeejsul:;j k dvb5p.b39 lmoves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is betwpbe xel :93)kgjsy 5;+bju -dv. uwj.leen 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 normallyessf/+*t,g,b /ay m plibb0n 1ba2pr5 about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assus/b p by/,nstlr2,map1ef*g +0bab5i me 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 igttte: 0 eho .1v mz0u*0taee+s 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 that wave reflects off the motm01 *0:vzo.eh gt+e att eu0eth?    kHz

  A bat emits a series of high frequency sound pulses4 dftnzw/ wgis(2kf c,:x k)3n as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns bg f,x24:dn/sfwzik wn(c t3k) efore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sigf89t2s*sa*kz w4ulf9e epwf: nals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensik*p42 su:f 9lsf*wz8 tea f9wety 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 x;v dfip2.br:5dao 6 y9b:ev in2 jz+lcan be compromised by the presence of standing wavese xbavldf oi .9 2+2;::pdvbz 5yinrj6, 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 demonstrate y5..4klf i3:doaxjaion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod ifl4jea a3.:io.5kxd y s stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thresho .m kuoptn ueo5)m)jca)1 d;x0ld of hearing for the human ear at a frequency of about 1000 H05m adkteuomu x;)co 1) ).pjnz 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 nhfvd*wjxj+cu 8 9+g7Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’w9g +v+nj du8jxhc* f7s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatdzv+7h,3dj j+1r awr+,in s.oyau d:f 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