What is the evidence that sound travels as a wam)od) x66r tz zba5+ngqyn+4r ve?

What is the evidence that sound is a foyz.r,rl8gprig + )c*.b c mpi-7qp4l brm of energy?

Children sometimes play with a homemade “telephone” byjaaqam0 sl11, attaching a string to the bottoms of two paper cups. When the1a asa1m0 ql,j 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 passes from air into wat knkwuu1z4c f (zdcq9 d6w)+s*er, do you expect the frequency or wavelefd 4 szu*cck1n6zdk ) uw+qw9(ngth to change?

What evidence can you give that the speed of sound in u dj.0,c2/m4xsod bnu air does not depend significantly on fr/xu sudcbn024dom .,j equency?

The voice of a person who has inhaled heli rkkd1 h+q/ )/rxs9zqmum sounds very high-pitched. Why?

How will the air temperature in a room affect nqyfsy/:nv j6 ,k+ o.kthe pitch of organ pipes?

Explain how a tube might be used as a filter to reducm,py-6tc),i bu 9fkjbe the amplitude of sounds in various frequency ranges. (An example is a car mkb-fij9byp, c t6,)u muffler.)

Why are the frets on a gursu7ym( bh /m6krti88 itar (Fig. 12–30) spaced closer together as you move up the fingerboard toward thsuyk8/m 6htb8m 7r( rie bridge?

A noisy truck approaches you jhpmx(c1qzceiw;3i9fg.) 1a from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-f3;(g i wcmijqca p.e1hf)z1x9requency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bd:+weynrr: 6 be due to “interference in space,” whereas beats can brwrd b:+6y e:ne said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would th bhq31xh*b0 ohe points D and C (where deb1o*h 0qhh b3xstructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting th anh-tnroo aqc3+)940rlxa l-e hearing of people 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 nroa -+qhcxral o4-)l3a n9 0tblock 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 sh j,iyc m/c01urpv;niwuy m; s)+c-c;hown in Fig. 12–31. Each wave can be thought of as a superposition of two sounu;sjh 1c uvycm c)c0n-i ,/+;w;mripyd 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 2h7d p1 6(u;dngc hxdkthe source and observer move in the same direction, with the same velocity? Expla67;dxhpgd1uk h (d 2ncin.

If a wind is blowing, will this alter the frequency of the sou4g;8/wmc po tqnd heard by a personq/;8pwgo c4tm at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion v h7*rq.:juvy(2xsl j on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for thxhljq:v* r(72 y jv.sue sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for s -e m7*yoe:ruthe echo of her shout reflected by a cliff at the far end of the lake. She hears the:-7*ersoy um e 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 th6eg/g6l-km 7lle t lj8e waterline. 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 point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not var gtkl78lg-e6l/jle 6 my significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths 8suz-mdkj(k 3in 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 d vb+ 7d xu693hjov+kfschool of tuna on a foggy day. Witk3 +vdh76 dvxujo+9fbhout warning, 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. The s tutez wi0r97,plash it makes when striking the water below is heard 3.5 s later. How h0wtet ,7 i9zurigh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the yiu/z b94;hsc:eynshs9,kj 2 concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did n:y ehs4y;9uk/i ssc2jhz9 ,b the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sf*)m u2o)rjy is fmt,:econd rule” for esyi2*mffm)t )s ro, uj:timating 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 leu,z3 z/5vnff)zic-f )qf*4 uhba3jxw vel 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 intens. ssl4n9+ydo;bmkf )mrh y) s9ity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fi*,q fai6l6 l(8jc ,muq6gbjbx red simultaneously at a certain place, what q8 m(6gfaljc,bqijl6x ,6b*u will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a ah :rmvq)1f3djp y52qcertain distance from an airplane with four equally noisy jet e q3f5r1j: a)pdvh2myq ngines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wbgu k2 .s0dtfgex3g1 (4 h(yykhereas for a CD player it is 95 dB. What is the ratio of intensities of the si y.x uh2yt3kg0dk(1gg4bsfe(gnal 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 nor,- lvsbjx:gzwz+ dw22s69nln 98hszceua - h(mal conversation. Use Table 12–2. Assume thh(us9wznjg-+zw ea 2 svc9sn6 l:x bzh8d,l-2e 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 ear gt 19v3udfqg7drum 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 250 W, while the more modest amplifier Bj vt (f*nkx8 :kc(8zdi is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m frnd fv ik(:jz8(8x*ctk om 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 regi8;q29ggdc l vxe;3f gnstered 130 dB when placed 2.8 m in front of a loudsqv;fegd9 lxnc 8gg23;peaker 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 del pjbru sn. * 3sqw/59med1sm3,mjstg z;c;g3 tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this m,ssselusjt m3dm qgrg3 .j1bpz5c39*n/ w ;;amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavep ricw-nyn8.4 rp :g1x is tripled, (a) by what factor will the intensity i1ir cpr4 p8-x.ny w:gnncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplit*fmzjy g*:2 qb) y-grwudes, but one has twice the frequency of the other. What is the ratij)* -y g:g2fqr*by wmzo of their intensities?   

  What would be the sound levelz-yb5d zle)::rsxv u, (in dB) of a sound wave in air that corresponds to a displ -uze5dbl:x :)yz ,rsvacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev q pel):owc7,nel to seem as loud as a 100-Hz tone that has a 50-dB: elw,n) cpq7o sound level? (See Fig. 12–6.)    dB

What are the lowest and highese2u4je q.n bt2gjl99 jt frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 49j.egj92 jnbt 2qeul12–6.)

  Your auditory system can accommodate a huge range oivcp8 :s zomm0+cqgyn 9:b 2b;f sound levels. What is the ratio of highescqsv; +gcnoyzmb:298i :b0mpt to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length ofx*gaxej80;x( 5lamnw4 eur,)xeba0 o the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? ,(u nx4;5x 0 emex)wr8xa* o0lgea bja   N

  An organ pipe is 112 cm long. What cq0*k - bxoqch3v *+vgare the fundamental and first three audible overtones if the pipe i-+c q*3g qov*v 0chkbxs
(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 expectzwilobhijo-4y594nk,7n h0 h from blowing across the top of an empty soda bottle that is 18 cm deep,7k5li0j h4oy nhzhwb -9 ,n4oi 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 raipnc,o,qws b:4 be(t4nge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths b 4nb: ,owic (qest,4pof pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 4a mu6q .4yxox92 emsjHz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengt9eq464m2.axjm sux yo h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long 3)orn-ykp n2cand is tuned to play E above middle C (330 Hz). nkorn-3p 2cy)
(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 (2f8 k aiodj/j/5b v8hxkx)j9o qv-4+bd62 Hz) when the tempe 8dj fv9 jdbxo4vk +ko /xbh)8q-aj/5irature 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 2vi2b k)-i .wt9wioby*0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o (9 :9ekbzawb( ql,gsef the flute in Example 12–10 should the hole be that must be uncovered to play D abov (s l,ze9q9wg:kbb(eae 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+u*+hw gs a7au Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why + u*us hwa+ag7this 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 resonawhr;-jkvw 2 tf v:v43ptes at two successive harmonics of f pw :3vk wj;2fhr4-tvvrequencies 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 vy uqwmjj4ydl 1h*hx zrgv9(//v17 .p$^{\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 xenq 3 jm1t0rhol22c *0hjy o6for a 2.14-m-long organ pipe at 0l3cj n2ty0oxhh2e o*r1qj m 620 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside ah4cqi8h ,mgt mp.o, )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 .hm,h8gqpt mo, )i4caof 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 b82ud wy b3bk8beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otheryu3kb8w2b bd 8 string? ±    Hz

  What is the beat frequency if mi nr;+y mv*m0ywjfp *l-ddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) op.qsdftp ku k3yn;+-ud0z22jperates 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 thy20kd ;fq2jp.ku+zd-ps 3 un te operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when ss pn/(o jq1p;zounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency o/o1 ( jspnq;pzf the string? Explain your reasoning.    Hz

  Two violin strings are t+1wv+fbp oe+b+ihbldui 9):dyq m6 l :uned 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 the two strings are played togethp1b+6low)+y::h ivl+qm9udb f +be dier? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fl + )bz f86-rgwffc-regutes each try to play middle C (262 Hggwc8 b- +z -fre)6frfz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has apmxi/ j4tmry 4)v734/jbn5ru9 qtqta*oo q4o 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 soundjyr 4x4pr)mvt35o 94 qqnt m/ *iu /7j4ooqatbed 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 ps: vqq6fa5 k.uerson stands 3.00 m from one speaker and 3.50 m aq uv.fq5 6s:kfrom 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 vibr/uco.;fj 0n4cc-nzh eating at 132 Hz, but a piano tuner hears threcnzc cu/fh04- jno;. ee 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 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 2cqui4* yqo (spu f*8u7.64 m and 2.76 m in air. How many beats per second wills*ofu i7*yp(uq c48 qu be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ 5qj(yni(4fkl ency of a certain fire engine’s siren is 1550 Hz when at rest. What ff4n(qly ( jik5requency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you pdnt:m1.fpz - detect if a fire engine whose siren emits at 1550 Hz moves at a speedfm.tp :1 pzd-n 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 at9 wlq4w3rixm//l*b1 wdk/hf+x 8 lvyx 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cloix1vbrf/wlm*3x+9dklx/ l yw48h/ qw se? $f'_{source\,movine}$    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 equippee y3g)y:mrw8 jd with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver mj3r)weyyg8 : 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 sa)4b-ui,va3 vjx k9oe3mg 5abound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receiv5-obma9u xib ae4ak3,v) gj3ved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a s:999hli yi1q1htmht hpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequencyhqiy th 9l91ih:t h91m does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba e uhw.ofsvb-g 6*qv:dg z1l7)t5mq0 wwas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency5g ts*vmuzqbv 7w6)1f o:whd0 .-qlge was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves 5pb 0so4xo26c,q2 wjwgz mm a6to 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 awa4 6mq5gojax o2sp,bmzwwc26 0 y from the sound source?   Hz

  The Doppler effect usiuxkg+ jzu7in (iqy;p87enecr+ cc 365ng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the win yor6evt3 b5s9d velocity is 12 m/s from the north, what frequency will observers hear 59e 6sryo3 vtbwho 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 spem w0zst;nk6c:4g/*y2unhu d ped 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 h6l ssa6/n,apsound is 310 m/s (a) What is the angle the shock wave makes wit s6ls6n/aahp,h the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of 7 qgk.cy(- yhvsound is only ab h7yk(v cy-gq.out 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 g 2jpqt9bu6rh8fkok)n9 g 2a:shock wave angle it produfb 2 9tg9khj nga:28k )orp6uqces
(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 )s 9xk.c8+w2 okry ba1s-fibk$/theta$ 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 f8a:jkwq; e 7aexactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane h wae7 ak:jf8q;as traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses 9z-zqp3uk f- fdownward 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 pulses (in fresh wateru-p9zf z3kq- f)?    s

  Approximately how many octaves are thereuphh kd 1x nbs+:)dgy6m *:tsx,x3m(e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cab9 w ty q6cjmot6,m/6.z wh,ponsists of many plastic pipes of various length6/c.j qzbww m6h,,a o9 ptmy6ts, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a souhcc;02tdq/6gf zrx,bnd close to the threshold of human hearing (0 dB). What will be the sound level of 100hfqgt;, /2dx6zb r c0c0 such mosquitoes?    dB

  What is the resultant sound level whxo+5w0l6-fi*. 8t/ulxp itvew)kyo jen an 82-dB sound and an 87-dB sound are heard simultaneously?uk p i6w/0 fet+o8jl)*owvi5 xy xt-.l    dB

  The sound level 12.0 m from a loudspeaker, plauyd,3x)0ikdk ced in the open, is 105 dB. What is the acoustic power output (W) of the speak3 y,ikd)kud0x er, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outhi8 5va3;wfa;bhkb1 i+fv6s kput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts atva; kkh5 ;+8ahf6if1 s3 wivbb 15 kHz?    dB

  Workers around jet aircraft typically wear pk2i .oo6fd9.kl d8bdxrotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, anx8o2d.9f ld6 ob .kidkd that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, tgcmkkr odf9uyz)t;,ev5f6)) he 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 vio/ nxlpd fz(nz6)gdx- z/e6l6 elin is tuned 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 ppv 8* 6dau4sf7b*jyzjoints with a fundamental frequency of 440 Hz and a mass per unit leng4 a7d6j 8y p*u*jbfzvsth 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 vibr 84xliwg8 ohu2wan;d2ation above a vertical 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 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 ag22h;d8w lnawgo8 x i4uain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one end3 ia)2 g8czz fay4ak,p and also 75 cm long. How much tension should be in the string if it is to produce resoz3zfya4 2 ,c)8kaagpinance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop3 qq(pkam-va 3r7)akr ($\frac{1}{2}\lambda$) 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-c1x)ga;c+t uc xvn4:pHz 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 )c ua4vxgn :cc;xp1t +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 l02ud xdx9qq( wpbg0 1is stationary. The conductor on the stat xlquq(0bxp1 g9dwd02ionary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a stegezsi*ljob bx(-)t6.r h5 z,iam train whistle as it approaches you is 538 Hz. After it passes you,eo ,tb)b6sz*ri(.jl h5 x-izg its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can .gv+cnu83-qx)exh w e estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a q)-x3u e vnwxh e8c.g+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, soungyx)/6; :l)(v3ll6nfi * jcurw1z pij r jh)lwding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How /:pjn)x()vlwf31cz6w*lj6 y; ilg lrir) uhjlong is the other?    m

Two loudspeakers are aiqw4(bj ebr6/f) ei,he k a-ad;3hue8 t opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, whata b3reief, h wde k-(iub6; /84)heajq 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 flowi3jok*l kjp4-aeyhx)*xan-+ in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wa)jnlxp- yk jaio-*+h43k ax e*ves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s w+ ;dwow8d uzk1hile the 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 batku+do1;wd8z w after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mk /xpd u8y3;pgoth. The pulses are approximately 70.0 ms apart, and ; p/k3upyd8xg 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usedvvjsa) 2nttc.( e9am / 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 m nv9 .tv(em)2aas/jc tusical 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 compromisex (wbhb c6q+y)d 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 lh 6c)q +wxybb(ong, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lowxl2 um 1/da45b r6elx4had8b ng, 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 r2hlderxdx 56u41 /lbama8 4b wod 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 th;;bhu (r7qy4 gy+5rk uplf9 ooe human ear at a frequency of about 1000u+b (;ryp5ry holk;9f7 o 4ugq 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 hnu u bu*-g71fn:2zf ts(wi 2cf5*pbodears the sonic boom 1.5 min after the plane passes dirgzd o1 u u2f25f: n7ib *p*twn(usc-bfectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboasde)n ycs+n a,ue r44pt7 qk1 d*l5:cdt 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