What is the evidence that sound travels as a uuhk mz(a3( sw ,.nk9j,l5oa bgj;zk7wave?

What is the evidence that sound is a form of ene+rg :vqp-m0l urgy?

Children sometimes play with a homemade “telephone” by attt pfg2xaubt-2 4.-ffi5cna,x aching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the f2i4n-fa.t-f a p 2, cxbutg5xsound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequenq2 xw(w-bwag)ux ,jts7hq h;5cy or wavelength to change?u) hts gw2xq ;wwha, q-jx5b7(

What evidence can you give that the speed of sound in air does not dependzjwrs67 jk:kxw/1 a8 t significantlytz76x:js jkr1 8wa/kw on frequency?

The voice of a person who has inhaledvs)cq18:7(blodw q f o helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch ofw.s )2 pqnw0/*:6y f4 saiucaqinvob - organ pipes?

Explain how a tube might be used as a filter to reduce 7pcqf ocb7ta3+4 n nsj;:2phg the amplitude of sounds in various f; jq cshfg+t:37na po4pnc27brequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as y)my ejp n;rq07 xp-zr;ou move up the fingerboard tow yp;ex7n j)0zq rr;-pmard the bridge?

A noisy truck approaches you from behind a build(:uaumty53uo a mr+b- ing. Initially you hear it but cannot see it. When it emerges and you do see it, its-u u+ ay:uot5ramb3 m( 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 “in q,cp uey(-rc3terference in space,” whereas beats can be said to be due to “ie3 pcc(u ,-yrqnterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakmkq39 x/f4c bbers were lowered, would the points D and C (where destructivx/mq9f bb4 3cke and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who worb xcu 5t)t3 gx8sf0hd*k 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 detecth05s gb8 cu)xft x3*dts the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eo1s wiuidmito , 8o6;.ach wave can be thought 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 frequencies farther apart? Explain. w,o6 tmiou1i8 s;i.do
(12-31)
(12-18)

Is there a Doppler shift if thew j+xaoi)2 y5b source and observer move in the same direction, witoi+bw)yaj5 2x h the same velocity? Explain.

If a wind is blowing, will this alter tru1iq ca(p q.-a-dwh- he frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocitya(pu 1-q -rwadch .q-i changed?

Figure 12–32 shows various positions of a child in motion 4hlq b:fl i,p5on 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 frequencp:qb45h ,lil fy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of :* srbud2tbggwik,6xqm3 3 m3her shout reflected by a cliff at the far end of the lake. She hears the echo 2kmd2mg btbiu rw*3s3gq3:x6 , .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 waterline1 9ik4ny8 fnto. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at 9o1 i4nk8nt fythis 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 at kl 0 )pee39i cqu9 /5tkoz+jrp20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school n i ;)b+hy*rsod 3ww7rof tuna on a foggy day. Without warning, an engine backfir7)n w;bh+ r*3wrdyiso e 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 f, 6:iiq0+pkvinbe );xdkhl8yrom the top of a cliff. The splash it makes when striking the water vlhki;0d ex6y)qb k,+p i8 :nibelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pavea 7gtvr(f 0r.pl/.gqq 8r7xlu ment. 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 dix f7.qrvg0.u8(la7 /qpg trrld the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error muvnrif:4u/ v +ade over one mile of distance by the “5-second rule” for estimating the distance fvuvf/uin r+ 4:rom 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 level y ()d(75ahyace rd.x tof 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 is +n-h qqx5 d 35y/piq5 ofdmnx-$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simjd lg.g/ 3,foxultaneously at a certain place, what will be thx3fj., gogl d/e sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wil8+ jkii2p -dcth four equally noisy jet engines is experiencing a sound level bordering on pain, 12pk 2+lj8i cd-i0 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 bz*bq/etrfh;ngp;tb..z 0b3d3*ns u of 58 dB, whereas for a CD player it inn0z3sbg/ .qp*u; thrt*b dfbb3e ; z.s 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 output of sound from a person sperorwvtilca/7(x+h+( m) rvs ,aking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ov +cts+v,rl7(ohwr/a )mr x(vier 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 strikea92/c tpm34 k9rkha ,jel upx(s an 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 250 W, while the more modest a13: zohc/rhy2 k f.eczmplifier B is rated at 40 W. (a) Estimate the sound level in decibels youzhko1/rf c zy:3 2.che would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB metel a7eck4e)nr91 a( rk ple6hhd-)yx2o r registered 130 dB when placed 2.8 m in front of a ( axrarep e) l1lc)ko-yh6 k2dehn 749loudspeaker 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 level f7oze/rt)xe/of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: Se)/te xo/f7z ere Section 11–9.]$\approx$   

  If the amplitude of a sound wavb5p: zzd4 t)hle is tripled, (a) by what factor will the intensity increase? d : 4)5zlbthpzIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freq yd 7svxci)tfy/ e+bt.- 45 nows:m5uruency of the other. What is the ratio of theif/stvxst5dce u -+yn b7.o mw5y) r:4ir intensities?   

  What would be the sound level (in dB) of a s/ar p+*jdyu2e0d(0 kw7i kdtbound wave in air that corresponds to a disy dbkae7d00 + ikt (/d*2jpurwplacement 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 100mo);l6r std0zx6d z:llc, s y9-Hz tone that has a 50-dB sound level? (See Fig.o :y0z;xls6 l)mtsd 96dzrc,l 12–6.)    dB

What are the lowest and highest frequence/yiogek7 khub(m t -7am5m; :ies that an ear can detect when the sound level is 30 dB? (S /a;m5umkh77 eyk g mio(b-te:ee Fig. 12–6.)

  Your auditory system can acco0 x63ksn-5.xztko (e rrcgfw,mmodate a huge range of sound levels. What is the ratio of highest to lowg-t,560wzrk nfoek c.rx(s3x est 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 lenyvz y4wi1j ( to(j.vg9gth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensio.y(zj4 w(otivy 9j1gvn must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thregc1 e.9ug7eiuf 2xa1w e audible overton .9gxu1u7fa2i weceg 1es 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 top of aniwuu ctn*t8)-pylbm jh4j, .+ empty soda bottle that is 18 cm deep, if you assumed it was a closed t-inj)4jt, mw+8ly b .u*uth cpube?    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 range o9(u ra(yc+j(z sxu5l6r mmk2k f human h akl69rxcru (s2mju(5 zyk(m+earing (20 Hz 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 as its third harmonic. What wip4b6) (pnrh,9wdocy s ll be its fundamental frequency iw cnd),p6 4boyhpr(9sf it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string isq(5y r nn6g1wb 0.73 m long and is tuned to play E above middle C (330 Hbrq65g1n yn (wz).
(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 angdwbyqos t h)afs +4zu4+w2 08 open organ pipe that emits middle C (262 Hz) when the temperature is s +h wazdy uq24+80gbsw4 oft)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 at9fmspvi02 9kwy) ma0y 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shou1 2 /lui0m7f,wmfdjiq6 ,fauvck+y1p ld the hole be that must be uncovered to iu1i df v16m0uj q7a,2w+p mffykcl/,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 264 Hz, 440 Hz, a4 w(u:sn m5*fev j2mxpnd 616 Hz, but not at any other frequencies in between. (a) Show why thi5xusm:j24fp n e m(vw*s 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 two suieoq5k f f i/5*5mrv*f3heda:ccessive harmon qf*ihefm553 *d/re ako f5:viics of 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 gf6eg nrtmt (r,vkn n45l;s,+d6 wj4t$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgaex- 61ea9bil au7cb-hv8,+ xojz qo6en ecb6b- ov,1 i o8ua6ez-j9xleq 7hxa+pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal iv5a:u :or gc df70tc8ts approximately 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 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. ugcf5 octd0: 7:av8 tr12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trtcn yn. ,48/ qx:ziyq v4qe2wsying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±,xwy/tizqqnq.8ys :2ev4 n c 4    Hz

  What is the beat frequency if middle C azrisp qfrpu28j.9kd fo(8 6 9/pjf+w(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 atpz uj c ml2:yu/ cavotz 1vq7l*:s3p6* 23.5 kHz, while another (brand X) operates at av pl up c2*uzyv 3cmj:ts /q6*za1o:l7n unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 5lf;h1upx;4im xofm8 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. ;xfi8;5 pommlhfu1 x4    Hz

  Two violin strings are tuned to the f - 2yvd0gwv3nctn5v9)d2sf hsame frequency, 294 Hz. The tension in one string is then decreased bf0)2ngvh 3yndd9 f-ct25 vwvsy 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idnzlufe;7p3h:nk6q f 5sj,8oy entical flutes each try to play middle C (262 Hz), but ou,ek h36ony5 8fqpjnzl s7;f:ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork5pq 4h+ hg w td4xv sze00ny*1;8sx8i crz:qpn B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 H 8g q+sriz0x:ys*4ht zv81wnd 4cp5e nh0 ;pxqz 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 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 aparf cd7)iazx./b 3 fnb0t1aswv,t. A person stands 3.00 m from one speaker and 3./0i cx1bfsfwd7 zvb.)a a 3tn,50 m from 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 tuner hearig1okj fz53h1y.sr2o s three beats every 2.0 s when they are played together. (a) If one is vibrating2 . zo11kryosghi f53j 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 2.64 m and s7b / jw1,jb:uzpeqc16 u8 wzhq-+ag w2.76 m in air. How many beats per second wq+u6/uzbwg: wz17j wjac1 she p8qb,-ill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certkktj fs7.n), mvgrv/) ain fire engine’s siren is 1550 Hz when at rest. What frequency do you dejvkvs,7 /)r)m.ft gk ntect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fi50yy7i5 wa8 2yb(aoko dlge1mfz7qr9 re engine whose siren emits at 1550 Hz m(fa7o59bqeyd y 12owk 807 ryil5 zgmaoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency ifaeig /v-ti 4(r* ohd6h a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Ari e/iah(ro 6v *htd4g-e 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 freq*j64pzxfw l; buency 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. ;p*b w6 4ljfzxWhat 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 receiz 2-ecfmro1x/ves them returned from an object movi cmo2e1rz-x/f ng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, th7v f.uk1s stegux9t3*iq/h.d e bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected ev thukds*1t.i3 f9 7.gu sxq/wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl 6-bln sar2hn-b x:.l4eljxn(ayed on a moving flat train car at a frequency of 75 Hz, and a second identical trnn.b: e- xx -2l albhnl64(jsuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usz7lps*gi41;a:vh uzl.daa 4 jes ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood isd j*i4sl71 u 4zaa;lzavp:gh. flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usinioyqi-y-w)ikp s*6 l, g 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 wind vel48hl: g)mt.um xkhe8 yi2ia6p i.3qof( 9kmolocity is 12 m/s from the north, what frequency will observers hear who are locatey 6u: iigmm8poq( h9tx34)8f kai.h2ol.lkmed, 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, q.s7by7kzu pd13(d, jpv f b:tfzd:o moving on land if 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 sok 1/tz(kkg 7mlund is 310 m/s (a) What is the angle the shock wave makes with the di k /mtk71zg(klrection 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 whe1gq o;(xpiazyizp8fk,q,: q:re the speed of sound isi(ki8fo, pq a,zxq1;gzp:y:q only 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 8gm qmlh7nqi/poi2.z,v 0yc((500 m/s strikes the ocean. Determine the shock wave angle it produceszq.,oh2( 0/cvl mn7ym (ig piq
(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 /- bxbaq(p q;v$/theta$ 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 jgz2g(lg u+.gexactly 1.5 km above the ground flying faster than the speed of sound. By the time you heag (u+2jggg l.zr 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 q/ct urn85/bm20,000-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 bb8/nq5rc /t umetween pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibmv:t+b (1t k-3lp vrag39h ulgle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a di k5ih,q (sq7gssplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whichq,sih5sqk 7( g 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 sb r8,th d:oz4 j)wx*gcound close to the threshold of human heaz4wht*) rgod8 cx :jb,ring (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound ep5v+zwomwos()5) qtlevel when an 82-dB sound and an 87-dB sound are heard simulta+zopvwqm)5 wo e )(ts5neously?    dB

  The sound level 12.0 m from i 3h3f+g6py3k cstl)xa loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally ik)ih33+ x6lpy t 3gscfn all directions?    W

  A stereo amplifier is rated at 150)jzz,fy :u m3s W output at 1000 Hz. The power output drops by 10 dB at 15 yuzf , j):zsm3kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsbb7h /.j7xojuuy9 ,zi. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. Wh7bbj .zi 79jx y/huo,uat 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 syste37jwhxcv b6g 9ms, the 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 viol0* nndz jhb0*tin 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 fixe*nk 7 hw m;2w/8i0if) x)mgmdnlyyah7d points with a fundamental frequency of 440 Hz and a mass per unit lengkxymmnhg/2 07d)w8m;)7ni*w ilafh y th 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 yu ,(gde ;wf5s9.utfa 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 again at 0.395 m. What is the frequency of the tuning foy9fwae gfuu;(,.5d st rk?   Hz

  A 75-cm-long guitar st6ccvv1v2.s db ring of mass 2.10 g is near a tube 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 vsbv2c1v.d6c (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fullzeu yf a7xhk:(19 (lsi loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from t+r7 z ifr*eci1tbuli* (r/7zzwo 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 of*fu1 czii7b r l*/+irztr (e7z the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the sr2j 6u plcgm n6,rs(( srh),istlr(sj,sh66cip2 ng),r (umr sationary 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 steam train w)hx2qpj ,l-rx histle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train x,p-)xj l2hrq moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thefkb2s-susyqt 2b:hgyzi r38j /*(k g1 difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fas2zhb3t yqj1r s8 gksfsug:kb*2i y-/( t is it going?    m/s

  Two open organ pipes, sounding together, prod*m3tv 9 7ydrxi:s-k gnuce a beat frequency of 11 Hz. The shosin-x3rkdt79 v:*g y mrter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at op:dfc d c/kh xa(-6)verposite 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, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) hkv )x-cf:ea6/dc h(rde 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 aortab/r2*ms + i9rq qen5nw is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blowi rnsbn qr9*/q em25+od 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 moth is flying towarl2e *emv lt,bh3xg2q2d the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the *ghllx,ee 22mtb vq 32moth?    kHz

  A bat emits a series of high frequency sound pulses as it approacg* v6 nz dr-f-8v phols0nuu.1hes a moth. The pulses are approximately 70.0 ms apart, and each is about 36vlprnu -1v g un.s zhd*f-8o0.0 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 to send signa usgi4ni*m zm* *g)6wwuj)om8ls 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 ones4i 6gw ngm8um*zo)iju*m *) w 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 listenin 8dwljkjywg6xqj9an +e7xg+ -8/v g8og can be compromised by the presence of standing waves8 +yg-k ej/dag w8l+qx7v8jow n j6g9x, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratiofrq ru3x *y. vrci-l57n, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The*rv3cqy- flu5ri.r 7 x rod 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 hearieoi lfv49.o :gd4tdi54k we3 r 8t:gxst5taa6ng for the human ear at a frequency of about 1000 Hz iao44d 8wii g.tt3: ef5k6 9:godtrtsae5x4vls $I_0$ = $1 \times10^{12 } W / m^2$ 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 hears the sonilk d9q*y2sd gk1.8dbjc boom 1.5 min after the plane passes directl1y2d*s dk 89dbqk.gljy overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 3yiuw,4gexj yw bd o2,2g,gx315 $^{\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