What is the evidence that sound travels as w,m tjw a6+wp(7xysr5a wave?

What is the evidence that sound is a form of enela/u)l*x 1drlk.kx8c rgy?

Children sometimes play with a homemade “telephone” by attacl6+ yz;- y7cdfrqo al2hing a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the soq yafcl7+ ;2y-l zd6round can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency xgl1 ruwne+zdc8 c(u a97.y*gor wavelength tn9gayz*lx 8g+1dre. ( w cuu7co change?

What evidence can you give that the speed of sou/eeuux.c ui*wr j8g/ukoy/l3bd . 0*b n0sm9 und in air does not depend signifi/u/ uex.s*yu o3 ku/j.8l0 b mnrcbiue *dg90wcantly on frequency?

The voice of a person who hr /jly:pd- ,kesu 9osd+ oc(t6w: wvx2as inhaled helium sounds very high-pitched. Why?

How will the air temperature in a rolrsqr (x0qk 9 ,viz24tom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplit no(zqrn+3 a;pfvzjt4r- w8m/ude of sounds in various frequency ranges. (An ext/zvz f qp4(r8njnrm ;3w-o+ aample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yto+*30 n wijrxou move up the fingerboard toward the bridgejox i*3n +tw0r?

A noisy truck approaches you from behind a building. Initially you hear it q3uv 0k1si cy)tiv h ,0n2lc,jbut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the hini,iy 3t2cj0lhc0v qk )usv1, gh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfwtqg*g4)gzcvn 4 bon*2aw,9 herence in space,” whereas beats can be said t9*c,nbz nw g 4tgqha)2owg4 v*o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spea srus wr0y,aos3-m.0h*6 s mowkers were lowered, would the points D ansrsmmsw6 y0s uo3*or.a w,0-hd C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with w uk9di1 9. 4/nngy(mdqfns+ hvery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new tecnyd.(fhdin qw9+/g41mnsu 9k hnology, 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 Fizfdus-+dv e0nj )20virz4 hy* h5 wvy0g. 12–31. Each wave can be thought of as a super)05vediyyu0vn 2 *f+4-s rjdzh0zv hwposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction tp u,7sa0yzh9-,b-hyqpyb;x n, rcw4 , with the same velocts 7;,qhypn za4,xy bbry-,u9cw 0 -phity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a t1 .mfao 0+n/pm6hk)go mn+od person at rest with respect tko0/n.o 1 htf gpmam6+nm d)o+o the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a z,(/ccdt4u mbchild in motion on a swing. A monitor is blowing a whistle in front of the chil/zc4,tm cb(du d on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake 27bu-b e-52xu*z q aw4 kaizhnby listening for the echo of her shout reflected by a cliff at the far end of thw4u52e x-ub*k-a zb2qah iz7ne lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wat0m0a ak.pi yc n qsc9n1ggh.9-erline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this 9a0 apnq 9sc0 mkycig. g.-nh1point? 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 wa.93mps+d+nvcer ki* n z)uv h/velengths 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 sm9hgvy (wj 9rx09z15l6 pu mmxchool of tuna on a foggy day. Without 9w9( 1 phm rgy6ul9xxmm 5vjz0warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Th+ vb8r2u whs0uc3r (koe splash it makes when striking the water below is heard 3.5 s later. How high is the urb3u(h8+sr2o wkv0ccliff?    m

  A person, with his ear to thel g-*i el+j)ov(y t8yb ground, sees a huge stone strike the concrete pavement. A moment later two sounds ae+ j(o*i-b ly)tg8ylvre 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 made over one mile of distance by the - (uw.xteaw6 h 4pmiyk3;hl -r“5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 uwlwh; h.pi- ka 4e-ry6t3m(x $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounceb8dw m* r4vk9u71qdd at the pain 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 sound whose inte, a5y:pt:b vwf gs w37k)cr4dpnsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whenm yz06x2of *c/s6kve uor c(6n fired simultaneously at a certain place, what wilz( 0uc6s xcmre6k2 6yn v*/oofl be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equaf64r m0b1v-d0gfqm-xj50d8 *qpdj u 6peihbolly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the ca4qm 0qp0u-rd bxme05fbpd 6hd6jg*1jovfi- 8ptain 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 of 58 dB, wher4p:4hd54b monim lhb, eas for a CD player it 4 mmlh: dn5b4,4poibhis 95 dB. What is 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 ot+f,dal 4-u6k ddy v4yutput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered dlaf,y -4dk46u +vd yton 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 ar/v hd (.fs8rb znd/w,zea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whilev5haope:.c mswukg()u m:( m5 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 connec swm(m (p5vu:m5:hk.uo g)aected 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 dBy+xh:4bap/ ry meter registered 130 dB when placed 2.8 m in front of a lo/:rh p4 ybxya+udspeaker 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 dete,ii.b sg l99jys 6;ayrmcs)v5ct a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hiia56 9 igs)9msl.;rbs,vyc yjnt: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is hr,+ocluyjprcl.c 40f2i ,1g tripled, (a) by what factor will the intensity increase? Increase by aj l1ccy+h g,r.2p, irlc0 4fuo factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemekdy pxarddfg8qt*06 c5l * ap63 8oi9znt amplitudes, but one has twice the frequency ofzogqtaicf*l dk0p8 yrd ax6*p69d5 38 the other. What is the ratio of their intensities?   

  What would be the sound level (in yqvyp3f1w: s(dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air mole1(pvwy qsy:3fcules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level toet9a;r/ i 7ilx)ywi;l seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. w tieali;7; /9rly)ix 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecvp4ms gw n+.s8mm 25 + r-0sqdhgbk4hdt when the sound level is 30 dB? (See Fig. 8sdm+-b.4q4hgpg+ ns0 dw vrm5hsm2k12–6.)

  Your auditory system can accommodate a huge range of sound level +sw 8fv adwe+;12w;l+w wggtbd9m,ycs. What is the ra8dc9+ds;1l+2,w ;f+ mwgewtgvawbwy tio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has 69tfm wk,cq:xx oe8w* a fundamental 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 6qwofx tm*9wk8c:,xeaced?    N

  An organ pipe is 112 cm long. What are the fundak p,;74lflx366osch- ste re hmental and first three audible op -hs7h;l olsxrft c,e63ke64vertones 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 v/7t9dr rm(2u mhhj/-i gvg)gfrom blowing across the top of an empty s- mv7rd)h/(mvgt2 gg jhr/u9ioda 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 organ with open-tube pipes spanning the rangkw*rg:igxjoi)2s *9 k mzz,b .e of human hearing (20 Hz to 20 kHz), what would be th iz *igw9:j)r.2zk* b,gsko xme range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar striniqb1kn p-2i9f5hz,f 8,fiz fcg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if iqfp ,zfzb5i2cki f ,hf9- in81t 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 a: h4bz+v piyu+bove middle C (330 Hz)+zuy: vhp ib+4.
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz-nqfc6-*uh 2s h+zhsbeqd5 e5 ) when the temuznf ss+decq5 65 hb-e hq-*2hperature 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 20 rqvhiq 7b 6ylxw-16+/ nfx+z f$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sc2you- qah *mdvs nr)h-1.vf;hould the hole be that must be uncovered to plarhc f-y1a-vqo2 nv msdhu.;*)y 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, 440 Hz, and 616 Hz, but not at a8if7cyul h0sh vjbv/6z6wfc) - i5d9gny other frequencies in between. (a) Su5v-hfjwy)dv csf69 i l z08cg6i7h b/how 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 islt:.yz,c3bz *r 5 r)lctwt*lu open at both ends. It resonates at two successive harmonics ofrl,zryt 5 lbz*t)cc*twu. :l3 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 , +:jma 3ywuc+yxudq /$^{\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,b4w*+lcs01zgih u7em9d u by2geo5q within the audible range for a 2.14-m-long organ pipe at ,y*go7+9 4dczu qsibm1e0lu whbeg2520 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approw4 pex5f:qg0 dp;t q(iximately 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 audip: d(qefg5qxp;4 w 0itble range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adf 1dpu-ut (q0zu 3os4 1bhutj2just two strings, one of which is sounding 440 Hz.(d joq0utub 4 tp1u2zh3fsu -1 How far off in frequency is the other string? ±    Hz

  What is the beat frequenct/t06tfvo; 6 b+qaqx vy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while rhx4f0)f3kvzow 7 (ab 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 5000 Hz occurs when they are played simultaneously, estimate the operating fx0a rwbo fk7(h 34)fzvrequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz t +8b4nqioj3k guning fork and 9 beats/s when sounded with ao ibgq+8j3n4k 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. The tenl833bf;1 ttppv2*n mqo q)cqysion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1o318l ) *v3;tnftbqqp q2mpyc3.]    Hz

  How many beats will be heard if two idencug.rcl02 ul.):2 vxt 3dqhod tical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othlco 3q.d.2rlct:u20 u vdghx) er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whenl(d1bn:h b (ki8d s5dc 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 freibds ck(5bln 1(hdd8 :quencies 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 1.8hxo6zwo c9/2r 0 m apart. A person stands 3.00 m from one speaker and 3.50 m from 2zo wx6hocr9/ 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 1c;hh9vebp/cfqv; c 1 -(:kb wnbi/nftuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be 1/ hvehnfbcbbi/k9q1 c (c;npv-w;:f the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Hok.vek5 *,izqfw many beats per second will fvk,k.5qe *iz be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh)l3zg hpc h3 ypv6 pox(d3( k*m-zamh3en at rest. What frequency do you detect if you movex6 -()d(zmhk gvzlo3h hc3m *3p3ppya with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency q-by2tp6xe.1 p. blgqzj/u l+ .z uok-do you detect if a fire engine whose siren emits at 1550 o+6pp k/-.zqxljul. 2 b -yuzbe.tq1gHz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fj qnwp3n ((vk7requency if a 2000-Hz source is moving toward you at 15 m/s versus youv (qn pknj(w37 moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped wmh( no0r .kwwz-dz *k0ith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequ-m kr*nkhzo (w.d0 w0zency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrat v7on;7 :z4su4m0dev 88 :dejbukmh vsonic sound waves at 50.0 kHz and receives them returned from an object moving directly a ebsdo84d:;87v0euh4 7mvzjmn:vt k uway 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,4v 3n :4+mh m(;svs3b ehmhvwqm1 3abh the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whm(m v3vm3+ vbh:; a4s31he4q nbws hmhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatnm e( f pi2qnm6l07(bw+ zgue, train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the raii0un w +7m mq(p bzen,lf2(ge6lway 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 blk0xp y;1. lqr4dcra l2e ggl:(8cy+o good-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound syo(xqpdgg0gr+e ca kl; c y:l 14rl8.2ource?   Hz

  The Doppler effect using a l9j6kptgdrs. wyd2y, . kpo2jq3+t6ultrasonic 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 wi a m5oplp4,;lojrjp0- nd velocity is 12 m/s from the nora5p,p4j;jrlpo0m - l oth, what 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 2 x ocki2-1adi*(hds(t0 $^{\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 thegt0*1kgpt * ut speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the aigt 0upg*t1k*trplane’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 s y+:( licirg o2pw 1cf5q73yjoyyqy38peed of sound is onlyfiyc:y7wlo3rq 8 py2jqgyio1+ (c53y 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 ocean. Determine the snozwp su5q*/9hock wave angle it9np qs5/uzw*o 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 g*ortpkx p+ m:3r-cq 8wk(4zh$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grouawc,:.fc lhy7 nd flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–acw, c fl:7.yh34. 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 downx or6q z6/ md: rgqo:za3n)b-pward from the bottom of the boat, and then detects echoes. If the maximum depth foq:zd 3nxr:gzo/)qb 6po a6mr -r which 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 t4(nqcxc f ;*5n)ngn4zumw m3qhe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer p/lyl*dd lt:k s6 z6n.nipe symphony. It consists of many plastic pipes of various lengt nn. :dkt6d6yl*/lzsl hs, 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 n on9(poz/a7j*tp7ax a;a:i ql4i( oc a person makes a sound close to the threshold of human/j :po9a ot7n74a a i;* xzl(pqoaci(n hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 0dae/p9gs8is82-dB sound and an 87-dB sound are heard simultaneoupa08esg s i/d9sly?    dB

  The sound level 12.0 l )3 sa5kuwv+ vgxc rta0;l(v,m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuminl)v+( xlv53u,vcr a0aktgw; s g it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output 3g ,xxvr/ ipu 5l/10 3exlvrapat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the p /evx 3gxiv p30lp/rxla15r u,ower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically 1q 1 rh7wp1rrg:rvkx(wear protective 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 effectiveh1(x wrr:71kvr1 rpgq 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 ge/.e3q d c;bt .u;vlhgain, $\beta$ 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 tune-zbhl 4z*nsiitp*9/*lh(c n dd to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a funda7u 8,7 fibk;wytvw-zj+2 wyjlmental frequency of 440 Hz; 8vjyk w, lwty7z-b2juf7+iw 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 vibration above a vertical open tube fil 1sze*:m 7-wyhv/sxifled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from wsmvf s ix1:*7e-h/zy 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 stlzg dt -3-b0bhring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension 0b-dz3-ltbhg 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 remi s( ;si1 -wy/ j8/,a8rztnv(d werlxsonate 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 l;qp fu9lnnp k -frks:l53. 3cin the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of3 .l3cnq: 9 r-lf;sflp5kpunk the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. ltz /-, jl4 -d-a:a k,t88d kaxvbcdhrThe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving -v/ka t h4-d,j-:8ac,b 8dartxlzl dktrain?   m/s

  The frequency of a steam train whistle 0w,k9r g.md prpirq+0 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 con r,+ q9pk0 rrgpdwm.0istant velocity)?    m/s

  At a race track, you can estimate the speeg(n xv5g yc n5fi .mch:z3fj/1d of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the souc v5iy z1fcf 5g/nx (j.:n3hmgnd 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, sounding together, produce a beat frequency y-924lywgcudgwl :q( :m/so fwko-4a of 11 Hz. The s wkg/l4wq(f2d ouym:g-:aslcw 9y-4ohorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves o5xm b1ww+x h:gvp8ks2+ z a(xpast a stationary observer at 10 m/s as shxgx5w o z:sp+x2awvm(+1h bk8own in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat bb8hmk enj9n4afhr: 78 xn 6+tfrequency would you expect if 5.50-MHz ultrasound waves werem htnjb+fbhk8x 9enr:n4687a 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 while the dd)e gj*p oryx4pb+2;moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat af* ;o+xjdp4 bpr yd)e2gter that wave reflects off the moth?    kHz

  A bat emits a series of high freq,l yp3zxo rs4 1fv,lkao1,x2 ruency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fzr,y4fl1 v1xxa rpl s2ko,3o,ar 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. cv2c7 *xan nnkma4(2z 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical 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, anc ac4ak7 vznx(n2 2n*md which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for s-kh3wdx j( -qy 7h6hvgtereo listening 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 5.0wh67-k qg-3hhjvxdy( 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 “singiazaw enq1e ( :p0d,enduxl1 *4ng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod0e1ddx4:eeunl,( a z1n wqa*p is 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 threshold of hearing for the human ear at a frequen j8jd2d;6iq brroew;.cy of aboute .jdr6 wq;rib2o ;d8j 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 heax5xdo v8wb1i9 rs the sonic boom 1.5 min after the plane passes directly overhead. What is 9vi bxdo x81w5the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 10 h6 gwddd2ie:5 $^{\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