What is the evidence that sound travels as a w:(r 6mebsn u(bave?

What is the evidence that sou0( gq6,nfafd7lr. 02vnga a tend is a form of energy?

Children sometimes play with a homemade zt 6;dv8hbvma-wm5z7 “telephone” by attaching a string to the bottoms of two paper cups. When the strin v7- tzdh6avw8 ;mbmz5g 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 passes from air into water, do lyv3g kkh8:p,ve( b3 tyou expect the frequency or wavelength to c k vtkg:v8ep,bhy 33l(hange?

What evidence can you give that the speed of sound in air does not dec c2/v5zvoq 0wpend significanto/z0qcvv2 c 5wly on frequency?

The voice of a person who has i bhxv0pe r7zevicj))2d ))a8mnhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affectjui;)hs/9 a ud the pitch of organ pipes?

Explain how a tube might be used ;j )4ljjve7 c3lr j y9tz4ej;:k kv.ozas a filter to reduce the amplitude of sounds in various frequency ranges. c4ljk7 rj3l.y 4jzj:9o;v ezv);kje t(An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced ojox;: -xgh a9closer together as you move up the finggox-jh :;xo 9aerboard toward the bridge?

A noisy truck approaches you from behind a building. izm9s x4yp p4sb326xj Initially you hear it but canno96p3 i x zssm2b4yxjp4t 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 diffraction.]

Standing waves can be said to be due to “interferaykpdjvof kz2d q112k, ;7pw/ence in space,” whereas beats can be said to be due to “inpdwv k,1 2yk/17pj ;azd of2kqterference in time.” Explain.

In Fig. 12–16, if the 10:n/6vvbj2yjqd5gis 9 h o/ tkmzv)h frequency of the speakers were lowered, would the points D and C (where destructive and co2ti s hqykgd5/:hz)/0vv jmo 1vb6j9 nnstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopl 7+ux52qw vdr8li.vtc 5uf;pt e who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, u twtl52qirvdx8.fu v;p+ c75then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tho)gfmfneg1t 84 ught of as a superposition 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 frequenciee8)gg mft4nf1s farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in t:9g bzdf:b;mghe same direction, with the same veloci9d mz: fg:bg;bty? Explain.

If a wind is blowing, wi f*y5knb ) njye,ehfc(cv1uy4o99z p(ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velociceznp91y,hkvo 4 fyfn (jyu eb95( *)cty changed?

Figure 12–32 shows various positions of ptgkp :z y ihk4+k7q256(vjsia child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A +iz4v7tqpiy s k h6:kjg5( 2pkthrough E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lesj)c 0i.q5l6fqifbfs0f14 pength of a lake by listening for the echo of her shout reflectifi jsqqf6c0fps l54e 10) f.bed by a cliff at the far end of the 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 waterline. He hears the1 z tpl/3lofgr 7srg30 echo of the sound reflected from the ocean floor directly below 2.5 s lat/13 sr3r70lzo gflpgt er. 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 air atb qyt/+e *u uectb5bj 9.2(sen 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 driftij2mft-i jo6a 1ng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses bi afj j1m-o6t2efore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top oxxszf-w- q:5llby 0o: f a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clox-lzq05yw:b : fslx-iff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrprofk1kam3 gaq :9h :y *j/e5jete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and 9k gy*mq j:513rj /ke hapa:ofthey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent err u r6oh+w o (wbgiv:2)ob0mg)nnkua*2or made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the t+)bh()kbmwr20u o2 ow 6: aong*vgiunemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at th m,zdxeh52 p30(lwe ,fly, geye 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 intensity )vocg d;n0+auzsqx) -is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when f*l;pw-,3qtjcl b.pj .p arg)y ired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.] b ltw-jar;jplgy. 3.q,*) cpp   dB

  A person standing a certain distance from aq -keor3z c1 9yzxy5 r7m(uh4yn 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 downx3q o7yye( y9-4rzkz m5u crh1 all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is ;n if 7,.//ixddv lbyn6xzu9yr8cr ;m said to have a signal-to-noise ratio of 58 dB, whereas for a CD pll;nrc /,fx. vn xi7b yrz;98iudy6dm/ayer it is 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 ga +iwozpo(h: x)8cu.output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere pu.oxh) g a zo:(cw+i8centered 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 ag ayb:0oh 26rfn eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at put bf63g2qx eijz(on 0 ;r(,r250 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 cofunib t( 6r z(gx p2,3oqjer0;nnected 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 pl+ en6c6i nkva2aced 2.8 m in front of a li kna6c 6+ven2oudspeaker 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 detect a difference in sound levelpkh5: kd-trj2rah b*e- jkhn:s1-b q ow2vp79 of 2.0 dB. What is the ratio of the amplitudes of tw eo2vtk-jk q p1h2*:b:a-bshr -jrhndw7 95 pko sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave maaf:c5v:,o3tb q3b :vxu kd: is tripled, (a) by what factor will the intensity increase? Increase by q,:x b kmbt::ufaavd3vo5 c: 3a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement3l0w 2ym4l)d-o z dlsrlw6jxi 6l +qd: amplitudes, but one has twice the frequency of the other. What is the +6w2)ylqsjo ld w l-dlx 0dirl3:zm64ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in ao,jw 8emw/ wm ,p ,mm94d1rvvokar1(sir that corresponds to ak(evro/1r4, waw m mow91,,8mmdjpv s displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a je fy;( -xe)5:pe wjqs100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) sf); y5xq e(jjew-pe:   dB

What are the lowest and highest frequencies that an ear can detect when the so:0yh8lrgi*2e eozp k) und level is 30 dB? (Seez*ri: ek o0gy h)ep8l2 Fig. 12–6.)

  Your auditory system can acx*9v ufts0j /c7nc8jhcommodate a huge range of sound levels. What is the ratio of highest to lowe tujvh scc*j/7 xfn890st intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length o l k,dbz,wfq1j, ry(bb+ 6(cp0ajrqa -f the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the brj( (q1blk+cdyjpwzqr,6 b-f0, aa,string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental aj3dxa5kw- m2uithwl 0 6-de 4tnd first three audible overton 4it3j k 0-ld m25xeda-t6wwhues 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 from blowing across the to6n60 j qqyi7m/bty x4np of an empty soda 6j4y ymqt 0 q/ixnn76bbottle 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 orgap evrez.s w8y6q;q469* f othrn with open-tube pipes spanning the range of human hearing (20 H6ryz4*hf8esvo w;tepq9 rq . 6z to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz asc9thspk8lcu8)r n x:; its third harmonic. What will be its fundamental frequency if it is fingered)8c n lh s8xkp:r9;uct at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lonha:3)z siqd;bh3fjz*)p3gi eg and is tuned to play E above middle C (330 Hz).dsaz;33f :p*qe3 hih))ijb gz
(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) wfjw1 v;c6 qyv5hen the temperature is 21 ; qvy1v6 cwj5f$^{\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 2dvq )fb(ty r))0 $^{\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 swa4( /wnmj- qyhould the hole be that must be q4w jn/( yaw-muncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 2s9k* doie(+yj 64 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why th* s(9 yokd+ijeis is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at u*hygydkp3 pf ;2,z1pvevul2 i5*,j g two successive harmonics of frequencies 275 ;py ufghge 1*p,52jvduiz*2,kyvl3 p 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 khxip6vdj:y .*, g *kn$^{\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 trjmv u 2 68bov2p3drt6he audible range for a 2.14-m-long organ piv 66 d3r82but2mjp rvope at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cmz+. wiuu 7ux1gon58 de long. It is open to the outside and is closed at the other end by u.zgdu51n7 e iuwx8+othe 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat ev ow fxqf c)k*68u(x.ffery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strff*xc. wkq86 ( fxuof)ing? ±    Hz

  What is the beat frequency if middle cagr 4ey+;v3()rnuhkC (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 atz:z) inu:iff8t cfs9 +fey9o1 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 5019i fs fi:y9:)zo ef8tu+ nczf00 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/sy83hyps jd0ipk )4q. 2 yfmfg/ when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is 8j3ypgsmd4iyqf.0h y2fp /)k the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are:n)(hq tp-u d z;czyfbb4+d v9 *r2lzo tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when cz:z4 un(dhtzby v *)b d;pof-+rl 29qthe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to ezyqno4 qvb /))t8gs,play middle C (262 Hz), but one is at 5.0°C vqqyn s4/e,8)gtzo b) and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A,0* rdegh5 ;vub 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 frequebuvgr5hd e*; 0ncies 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 one speaker and 3. ati*lmq2d7go zi /5k.50 m from azt7mdk5iq/g *.l2o ithe 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 1ol l2v,l:6 pvb32 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one isp 6ol2lv,:lb v vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths -mkv 6eygq8m9; e l)vr2.64 m and 2.76 m in air. How many beats per seconevy) m9k6 ;gem-vqr8ld will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s 4)z:o9x.a9k ;8ag lkz*nkxjb 2njs clsiren is 1550 Hz when at rest. What frequency do you det9g kkxa2 zos jb.x zl)a;*n9cln4k:8j ect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stil+utjhr,+ zs9,w1 4 *memdj*di zgw;qx l. What frequency do you detect if a fire engine whose siren emits at 1550 Hz movesm9z,w x4 +r e;wq+1j *hmgzjsti d*d,u 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 you at c,k/ t20cy ds yq0e-cu15 m/s versus 2ktuc0dec,/sq cy y-0 you 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 with the same single frequency horn. When one 21 cv tmn:frc+is at rest and the other is moving toward the fir+vf1tmcn r:2cst at 15 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 waves at 50.0 kHz and rece6y lc/l1t(ehr +u4lwrives them returned from an object moving directly a6 lu y/ cr1elt+rwl(h4way 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 8q:klv/ /nziv6 mge r85 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does tv8elzqi8v: / rn6gm/k he bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origina m /xqx/s*ta0al Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same toneaqax /xt/0s* m 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 qyf/99ni) n3sht qhy, waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound qn)tq3,y hn/9ifsy h9in 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 ul us/ ydpwgj56-trasonic 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 b eq23 fe3ni4)5s xvppHz. When the wind velocity is 12 m/s from the north,2 es)fip3nqx v5e4b3p 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 8hlgbh a;5h.(eqrb q: its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) W xw6-n;3 kpsvdhat is the angle the shock wave makes with the d6kp nxw- vsd;3irection 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 hz 7ebq5 3(l1epl)f 5ab5eir 7qu/abt planet where the speed of sound is only about 35 m/s belh3lq(et55 afq7bi1/za5 ub 7erp)
(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 t-p5+ f9q i+v 7rxzaon5vqw6gthe ocean. Determine the shock wave angle it pr6 5-tgqir7f+5vw x av9oznq+ poduces
(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 pi a80sb/:vbf$/theta$ 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 ground rh64qast)*cxp:f o*sa kvomflq3424 flying faster than the speed of sound. By the tia)hsrtv*k 2q*4f 6mo:qcxl3 o44 aspfme 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 20,07twdt9hr vx5- 00-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between d5rth t97 xw-vpulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rang8onn5f7t l,,bi fhjw4a,vo c2e? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ie c3vf;1( o:b+hvl:itgb vz;/i5iid a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. ; v id;b+zbvhf: /t3ogii 5lveci1i (:
(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 apx ,/vr9:cmwg/.now5vv.os d person makes a sound close to the threshold of human hearing (0 dB). What will wsxogv n:/m /vr.p5 .cd,o w9vbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level whe i a0:fyxabh f:qvogl*, b;7*tn an 82-dB sound and an 87-dB sound are heard simultf:iv*:qb h;7a yl,afg b 0*toxaneously?    dB

  The sound level 12.0 m from a loudspel3onu *cgf 0q*)*gjum aker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates enggj uu)ocl*0f q*m*3qually in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power an,u+1;hzt 6bjij9n b+lye18uh il8doutput drops by 10 dB at 15 kHz. What is t9z ,htii lejuj h+ b8ul ;y1a8n+b1d6nhe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective device/* d/sw(ers wfs 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 huedw/frws *s/( man 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 gazxi1gztnhl kj0 /,s /)in, $\beta$ 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 f)8,cr ni7bcxn requency 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 fundamental qr;cq k4e)t 1gf-evrt(+vnc 8frequency of 440 Hz and a mass per unit+4c efgtkec8) 1rrvv t (-qq;n 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 t. ls00f7rl5 hb:9ushaowwib, 9d zlu)ube filled with water (Fig. 12–35). The water level isob9ul.lrws) w50d:b0za 7f hl h,u9si allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level 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 tqy v6ej24fa8evc-n5-mr y.r m(od s:wube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in en jqw-(vmmf e4y2syrrav5co - 86:d.its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on2qabd0euk5di3 /6 xbk e 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 500–10/ixfid-i2rj e2uodivq 69ed ).aj8a-00-Hz range coming from two sources. The sound is loudest at points equidistant from the two sourc8xe2jjeau- oiid 2di.f-69r )/vai dqes. 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 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The concu0ax9v .:irl wl; 0feductor on the stationary train hears a 3.0-Hz beat frequency when the othex00ic9l ; .l:eawvruf r train approaches. What is the speed of the moving train?   m/s

  The frequency of a steahdel vlycx dew*/r0w ) v0t6)9m train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (*vv)tw9) y6lw0/hd0delrx ecassume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening tobblyio59 mq4 0t(4 coh the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as itc4 b9o (ib0m4hq lto5y goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 2z.a7wki hzxgc0i+ :f Hz. The shorter one is 2.40 m long. How long is the other? i:ckgi axh+ z7z f.2w0   m

Two loudspeakers are at opposite ends of a railroad car as it moves past a s9m0(dtia1c * d auygr7tationary 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 between the speakers, at B, and (c) he hears 70t yrma dd1 gac9ui(*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 be(4: gl2x filiaat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the gl(24 ilfa ix:waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying :n9g rg/jz1em 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 reflectsg:e/z 1 mg9rnj off the moth?    kHz

  A bat emits a series o: uw fs;kek7a1/; *ygk7ejiobf high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and esw/eufeykog;17 k *j k:7i;ba ach is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used qa*sep)t yo3 ah de-oi(:zz2lcv.d-a 6w7,fito send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create d( -ywavs3fpoh- * cq7li,d:azd2tae)e.i6ozeep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be cok4d; csl- 8v8x2x); hudbja azmpromised 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 mb xad; csvzu 8 -lk;hx28j)a4d high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” in (w(j3ly8f1d u my,widom5ii :volves 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 wy3uyj:mm8df 1(5 l i( d,iiowrod 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 ok1 tk ;g(ekwn+y*xe0 lf hearing for the human ear at a frequency of about(t+1k*y g0kw lee;x kn 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 obserck(u7k,-i: ux3w-j chvjt8 yd ver on the ground hears the sonic boom 1.5 min after the plane passes directly oj t -wj :u73hcvx-cdy ,8kk(iuverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i :3xbqp +2fwlsw7;d-p11 uqoccc ana nxje704s 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