What is the evidence tz4 -+axj hb:kphat sound travels as a wave?

What is the evidence that sound is a form of nn.x6 70ou5sks.gq i a ;q6uyvenergy?

Children sometimes play with a homemade c2/e 1-xeg pvw1+yvc u“telephone” by attaching a string to the botc 1ew2g ce 1/vp+yu-xvtoms 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 sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you eafr16j pjpzs,w 8.r2fxpect the frequency or wavelength to cha82,jarfrf1 .wzj p 6psnge?

What evidence can you give that the speedc.- q 7(p0vef)fmzsjrn u+ d0m of sound in air does not depend significantly on frequency?p mrnv-(md0 7q 0)z.+uef sjcf

The voice of a person who has inhaled helium sounds vqua h*uri;z+)ery high-pitched. Why?

How will the air temperature in a room affect the pitch of orga ;- d5rcvvcvd4n pipes?

Explain how a tube might be used as a filter to reduce th x6aytbpi35 s:e amplitude of sounds init:pb6axs35 y various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethi51owls6 :bc ker as you move up the fingerboail: w1cko5s6b rd toward the bridge?

A noisy truck approaches you from behig87tw(4. fzgn o6mfznnd 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-frequency nmwtofng n8z(6zg7 4 .foise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas dh*gthb8z r v.)t-x 9xbeats c*)vh.bt8xdrzxg-h 9tan be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points vjbi/ cj 1po m5z l;,vlpwz*-1D a wmizj1vz5, 1*ppllvj/- bc;ond C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work ifcf0g* wfkr, ;pm9tk9n 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 detrfk cf9w ;t, mfg*90kpects 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. Each wave can bw tbgz0d .w+9pe thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18.0 wbdg.zt+pw 9 In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move iawzil2f6m /xn s22hs.jwyvuz 17/q+x n the same direction, with txv/wyj1xq6 am u7/fh.2z22nl+zisw she same velocity? Explain.

If a wind is blowing, will this alter the frequency ogvb+vociur0h-5 w- (df the sound heard by a person at rest with respect to the sou0wuhov5g+v(- d bc r-irce? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion onzfe7hbbfbs g 9+;-7 8t u9+hvoke3wa ly:v /bh 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 the sound of the whistle? e b zughb;/fv738: fae+w7vtboh lyb- 9skh+9Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh8 /wukx /2 y/ksgnw rc7dtvi.(out reflected by a cliff at the far end of the k87xd.y/ w(u/ r/scvw2kit nglake. 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 pq:u6r-z -7bdm q6g jyjust below the waterline. He hears the echo of the sound reflected from the ocean fl mjy-r qup6q-db7:z6goor 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavtkv gov*g8:4jz8a.vs elengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above oc 4o;1dbmv/kzj7, pb 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 before the backo/m7bj vz,c;d4kbp o 1fire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make6- rpok fxfft 0lpjy98iyo* g /fi77/es when striking the water beff jtp-l*g 7k/ipof/6i9e07fxy ryo8 low is heard 3.5 s later. How high is the cliff?    m

  A person, with his exi 53cprjk)6.jo/diear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are he .3keir)j /c5xp6ojd iard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sec;o o )eq5tdbu6ond rule” ford o5otq)ebu6; estimating 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 level of 12qv,7x r. qs3hq0 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 wk4xery x/; 6kohose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouss;;b3zvxbg (w ly at a certain place, what will be the sound lebz;(s g wxbv;3vel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distanctkmnoih+b dm5.( mf9t:g ,d.ge from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person gmtmh9:k(, .d tom nb+dig5 f.experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said tog. qu(tjojvn4+m. k(-o 8 yghq have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is t j8gv(j..+h mo ntoqy4-gq (kuhe 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 speaki- ii:6dgmk e nt)vev4(ng in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over -nmvg4i dt)vek e(i:6a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whvr99kj0 qw 2wmg99bqnss8i 8vose 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, xsu qmg,n08ajz7k8k g - 3zc,swhile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in deci 8mu0j3gc,x ns,8kkzazs - q7gbels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dBxw7 w -6 z(rwd7z. b5eyd4kcds meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage754brzw.yxk -ddd c6sz (we7w.
(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 of 2.0 8*5lwtyp8d 1y(evrxzr.t mu+ dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section.pdlywr8um 8y(v1 *5t+ erzxt 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor w3)kq:hk0m fd bill the intensity incre:3k) mbkqfh 0dase? Increase 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 freqmd f9de/ooi:96z i ljdzt7:4xuency d: 6:9z47meod/z ltfjdoxi9iof the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) o v oi df-y)i692p-ym mfyl h54,nvtbn3f a sound wave in air that corresponds to a displacement amplitude of vibrafnyym o3 il9 nh mfi- )4v526td-bvy,pting 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 100-Hz uut)p tknjx1q2j9ly46r1 66i xpaq 5tiysj+/tone that has a 50-dB i1)5a6 yxr46p qnk uput61jli9x/tj+sjy2q t sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies:v-bl fu9 9obrvtz.i *;5milp that an ear can detect when the sound l.l;r9:9lvmif tib-5b* upz voevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is t8k,p qyd3dh 5she ratio of highest to dhk5,yqs3 8pd 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 fundamental9a8q*zzg t 6qh+wa:jh frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strihqz q*tw ja+a8z69hg :ng be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and f*1w: ybrj: s9orehre7irst three audible overtones if thr7woy re1:*:hjresb 9e 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 an q mfro9(+btrpo 7z8:dempty soda bottle that is 18 cm deep, if you assumed it wasp(+z 9moqr7 rob8 d:tf 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-l7f 7vqt awwx 2o4-bc4ojunl7r u+9b organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of u7fb2olbr 4-x+otqn9 wvlc7 w 4au7 -jpipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string habk0c*n tq;- q -mua3 uaq +;aatsn.w-fs a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its tfq n.wtqn; qc kaa;-+*3am0a- -uubs original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above br h+7f 5h/m kip*:ry5hez8aq middle C (330 Hz+ayf m*pzqkh5b7h r i8hr5/:e).
(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 (lz 7s+ b,(npj3.s:ke tz hqah(262 Hz) when the tem3bhjt(eap:qshzs+, ( kz .ln7perature 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 */a0cnkh vdm f-.:f zz20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flmn3:zwa9 ng6cute in Example 12–10 should the hole be that must be uncoveren:g3n c6amzw 9d 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 264 Hz,/c**qm nmu2tm 440 Hz, and 616 Hz, but not at ac*mn2 qumt/ *mny other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at twugci.2jhx i2 9.b6njko successive harmonics of fre2ig.ukjcn 6x2j9 b.i hquencies 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 pucju,:+g gw8$^{\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 g,h c,2j/pdyzha n2-q present within the audible range for a 2.14-m-long organ pi,/ nq2 hhcg jp,zy2-dape at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximat8npf3ul/0 al sely 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 a3flsnu/ 08plrange) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0ozii o7r4 -*jb+05xnygwstv1 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otherrx 5o1 j*zty wsg-74 ii0vno+b string? ±    Hz

  What is the beat freqe:r,y(vk8:u pvo u; eauency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while c+v0ox3l d.llur 3*nhhwj50,2clnh2 zx,ivdanother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a sh*5cr,d n32l+wjivhvcxz.0u02 ldlh,l o 3nh xrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 31ou +l*jrg6ngc vd74g50-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. *o+ vgdlg u6r1g7 cjn4What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency,qy32fl h7z56 qeb3jps. fcx /n 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 together? [Hint: Recall Eq. 11–13.2h l5.bjzfy qpesc/3763q nfx ]    Hz

  How many beats will be heard if two identical flutes each try to nm)-6-k l(qjp)yaihr play middle C (262 Hz), but one is ay-ik-arj)n)lhq mp6 ( t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Co xwzv 8gd*,lb2mp9u wbc, o60. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are popwcgld0 xoz b*b6u8owv9,2, mssible 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 aremc zc:t d6l+z4 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m frl c md4c:t+zz6om 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 wo/ vp1a -zs-gtuner hears three beats every 2.0 s when they are played together. (a) If one is vibratin- z pas-ogw1/vg 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 2.76 m in air. How many bea zd:.yatcalmr4u3 f.8ts per second will be heard? (Assume.yal 3furc datzm 48:. T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency o(l 33da8pteule.g8oj ,8p p daf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you dete8p pl a e3a3eud, t8.gdjpo(l8ct 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 fxf/.ij0j*p6 /ce ye 73mwqz rsire engine whose siren emits at 1550e3wc e iy6fx0j . qzp*/s/7mjr Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequef88nchw3q p1 + pvov2qncy if 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? A2 p 1nfwqvqvho38c +p8re 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. Whe8 y5nm yfed hkiw j5.*m,mf1)un one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequeny*1emd) 8imyum 5hj ,f w.5fkncy 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 receives them rebi9()f 3rb:qxpn 7g0 k5elvraturned from an object moxkv()g blp5a9 3ie q :r7frbn0ving 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, the bat emits an ultrninvk+ on ug7fv,34r ,asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in nvv3 4n,,7ork +nigfuthe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, au8 c3tpudyky 2i hh9/fh 8s(8a tuba was 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. Whd8 fht asyyki8 c(pu3hh2/8u9at beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spef138y4qqkj sp b 0g k)rg5s6wseds. Suppose the device emits sound at 3.5 MHz, and the speed of soundfsq04yjk gg 5p)rk6ss w1b 3q8 in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavey 9,u:d:opufa/qti/g s 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 winojlgcgrj j2ml+ 2); 9dd velocity is 12 m/s from the north, what frequency will observers hear who are loca;lld9om+ gj)cg 2r j2jted, 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 lan/, v9ocnbf)nr d 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 spub( x7hcz ed9,lais3(eed of sound is 310 m/s (a) What is the z9 cil( deh(saux73b, angle the shock wave makes with 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 ofu*u+x yem.2 ev sound is only about 35u*2mx. v+u eye 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 8xze4i-(mj5 x mkbe+)k500 m/s strikes the ocean. Determine the shock wave angle it prod) i emkzxk+j(m5 -b4xeuces
(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 dt m+)x hai/+f$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see ai hwlv z)m.e35 plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.5lv 3 zihm.e)w0 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 )5ja( z cwo)ldcv72eq20,000-Hz sound pulses downward from tj (dcv5qw))eo2 za7lc he 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 water)?    s

  Approximately how many octaves are there in the human audible rangi8sh(m47bh qf:j oqx 9e? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cons j )n8zq6bv9 km2. i+wlc.qkr .;)rvwkol*bqeists of many plastic pipes of various lengths, which are open oqwv j+czbqvqnli8. 9k;. m)k w ).6kl err2*bon 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 sound close to the threshold of hy69i5 e5sl:u/asun w guman hearing (0 dB). What will be the sound level of 1000 :5sy6gsu /9ln5ia u ewsuch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-r4 khrdj1.g 034x:nn rwcq*c n4los,qdB sound are heard si h*xg4qdo s1 ,rjlr4nck .rw:n 4q03ncmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open,- (yzdbpj *bs8 is 105 dB. What is the acoustic power output (W) of dz*- p(bjys8bthe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at(l::*szfxfqyz k;9l vk i8va 0 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power o zaqfy x8k*v(kz::vis ;ll90futput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear g8p0e8j c;ravprotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of jpv0re 88ga; c30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communir78aq.jsw: vq cations systems, 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 violin is tuned to a frequencu+wxak.bse1e vw1 : e+y 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 fundamentalwn9mx4 y bi5j4k lt63g8*xdcr frequency of 4*ctljxyb8nwrx k9i m4 5 6dg4340 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical opf ebp ghs9(q57en 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 hear7g(ps9bh qef 5d 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 tube that is ix ,g:raqfidq3ru m2lfw /2o *7)8lncopen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundf*2i a )rcgwfrm2qd: 7, uxlloni q/38amental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to re1b(cf jtm pam-g41 eu+sonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in tho: i)j hnv/i,ke 500–1000-Hz range coming from two sources. The sound is loudest at pointsiji:,/vo)hn k 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 the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on the.v5; ;n3 b:tlc9tqxxpge c* lj stationary train hears a 3.0-Hz beat frequency when the other train approaches. tc;.c*;3 5vx9jn eq b: xtllpgWhat is the speed of the moving train?   m/s

  The frequency of a steam train whistl8 vn3 t.knnd2hifc1b-1jtv7v e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocithnf 82cknjd.1v 7tv1-tniv 3by)?    m/s

  At a race track, you can estimat2lkc y10. u9f+krby tne the speed of cars just by listening to the difference in pitch of the engi uy lcn k+kb9.y1rt2f0ne 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 fast is it going?    m/s

  Two open organ pipes, sounding together, produ ei8a60 3balxdce a beat frequency of 11 Hz. The shorter one is 2.40 m long. 8b3xeda al 60iHow long is the other?    m

Two loudspeakers are at oppositfq8k02m 1nzjm l3ipd: e 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) he is between the speakers, at B, and (c) he hears theki m:1qd0 8mfj nl32zp speakers after they have passed him, at C?

  If the velocity of blazr :f1ne7:xzs ipj6:i; 3 lqfood flow in the aorta 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 1zplaij e iq: fs6;z:f37x r:nfrom the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying t*qh nqr 234xg0ap4ep yoward the b4 2 n *q0ph3y4qxageprat 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it ab5b,act rxd*c b:1xmf cqy9zh,h, :h-pproaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detecbbcd:b c1htz5hq,y -mc, xh*, raf:x9 ted by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1smws, 0tiahesz4 (7,b2–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtonew ,40thie(7b sasm zs, is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised c /.2:tmsxt pv+uq(wk;xqfk 9 by the presence of standing waves, which can cause acoustic “dv2 t+m;(k .pxq /:x qukt9fwscead 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 demonstration, called “singing rodswk 5 mps3i;0 bnb9oq)q,” involves 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 rod can be made to “sing,” or emit a clear, loud, ringing sound. Fo;n) bq3qw9o 0kbp5simr a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequengwack li6k.)dq f,-sq92el ; z +gug3ecy of about 1000 Hz is- ; wqzee)2 9c sq i3gguk6flkg.l+da, $I_0$ = $1 \times10^{12 } W / m^2$ 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 sonic boo exz8zja h38d6m 1.5 min after the plane passx3j z8e zah6d8es directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ist-mglram1t5q 9 wq 1uwo7j.+w 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