What is the evidence that sound travels as a wave? 6uwa3 outu.v4xm+ zh-9 y ih.0ki7ewy

What is the evidence q2.mfc adgwpty8/nf (2 nw6 j9 b6zae(b-f9 asthat sound is a form of energy?

Children sometimes play with a homemade “telephone”68;6vknes1jow: f;eyxvp d o0 by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cupwys;d1o6v; e:xp8f 6 v0ekjn o, 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 exp)oy 5lgjm;x an b222csect the frequency or wavemca 52yjs2gbxl2 o);nlength to change?

What evidence can you7pumhj+h e(7 7b; lqob give that the speed of sound in air does not depend significantly on frequencybpm;7ehl+obh7 uj (7q?

The voice of a person who has inhaled helium sounds very high-pitched. Why?ycucmang3li1 i ipf 9g) -2o80

How will the air temperature in a room afxzjot5( qd 5)sfect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce s)wzgy9eeiko n wcj/o214;n 2the amplitude of sounds in various frequency ranges. (An exage)4 9ynes/2kow o 2win cj1;zmple is a car muffler.)

Why are the frets on a guitar (Fig. .ehe9ki+ /fh- ao.zsenb9b3 g12–30) spaced closer together as you move up the fingerboe+sfhh-b.. n9kze 3 ob9geia /ard toward the bridge?

A noisy truck approaches you from behind a building. Inijm9 fgcq(hy 1)tially 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 noise. Explain. [Hint: See Sec(g q)jhm 19fyction 11–15 on diffraction.]

Standing waves can be said towx48ms.lf . a.dsfyp/ be due to “interference in space,” whereas beats can be said to be due to “interfe a..wss.x/8p4 l dfmyfrence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points(9n1h )d p eu.biotj*z D and C (where destructive and constructive interference occur) movp).9dnz b(u j*o1it hee farther apart or closer together?

Traditional methods of protecting the h 8; um smpv-xh3ioy5s*earing of people who work in areas with very high noise - 8ssy *um h35vm;xipolevels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, 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.i.7c u 8di+xst 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In x7.tsii8du +c 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 soslwh9x62a/ ,pfo .0q bnnh)ii urce and observer move in the same direction, with the sa0 oq)n9bp,wih2i.6s n/ axhlfme velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bye9,mgon59font-d h6f 98u47 elwiruz a person at rest with respect to the source? Is the wavelength or v5697 el -n9 r, eo4z9 ftmihfugow8dunelocity changed?

Figure 12–32 shows various posit: dphs5dd lo 0/mu2m1qujws,c ,bp2c6ions of a child in motion 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 0,,62cwsmsql mc1bou5d/judd2 p:h p frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the ts e4o 7/zzzg1length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake/gzs z ozet741. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echb46rt7p.l ptos l:.neo of the sound reflected from the ocean floor dir.ter bnlo tpp. :6sl47ectly 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 wavelengths irw**ml9 b eog+n 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 school of tuna on a fogg2cdtoc (f7(sclce6wa ; 56gxk y day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsewoc2tl; gaesc6fcd( (56x c 7ks 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 splash ivizdykg+)m-)j1a6 wf t makes when striking the water below is heard 3.5 s later. How high1im)k af)zv gw y6dj-+ is the cliff?    m

  A person, with his ear to the grounv +q z55q:obm0;xestgd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels i: 5vzq+s5;g0 xte bmqon 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 errorfqn0 :o,itn ual2a3q 6w zc-g4 made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is0c3un,fwaz2 64ag-o q: qtlin (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sou1)sod0yf+m g jnd at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intelts8njojik .sk +qs0l:auz62 2bba08nsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultav)pa y+wj, qpp1+h,yxneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiey)p+p , h+a1p,jyxq wvs, not dB’s.]    dB

  A person standing a certain distance from asywtlautg h 3mge1t/-t +c(4-n airplane with four equally noisy jet engines is experiencing a sound level bort w-gm-l tutges(/a th1 y4+c3dering 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-iar.w/v r( u/tq2( sw (kahax8noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each deviatx k a qswa//r28v rhu(.(wi(ce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convezakc8n(b6h )e-2i jkgc-fqa+cl*1br rsaghbajc c8n i lr- b2+a(f*6q)-z1kkce tion. Use Table 12–2. Assume the 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 eardrum whose area is4sld h:hefv*.qbx c6ak6wi79g p0pz : $5 \times10^{ -5} m^2$ (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 W6st01 kn o rynbs4d4h39vq-jv , while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibedjh y bnrv9no-v s6144t0qsk 3ls 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 dB meter722fqv,elf)z 0 axh:s2c n ovu registered 130 dB when placed 2.8 m in front of a loudspeake,a x l0nou2hv e2zs7)fvcq2:fr 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 of 2.0 duwta )bo;: rx f9oo*+(q t1irmB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: ft wi+;(rooqo:m*9b aru)x1t See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fad8sbye .5qa5g ctor will the intensity incr8b . syq5dg5eaease? 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 fr i1c*. o76gh0kxueiz vequency of the other. What is the ratio of eucv1.hx 6*k ogizi 70their intensities?   

  What would be the sound level (in dB) of a sound wave in aeik60ai bn sxsml7-;ev-y6 5air that corresponds to a displacement amplitudenasbl s ex-iv66-7aki0 m;y 5e 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 100 i931ktv7 yuq*z;t nfk-Hz tone that has a 50-dB sound level? (See Fig. 12–kfktqzi97 v1 u;3*tyn 6.)    dB

What are the lowest and highest frezw (r ,ikoov +c;sw7i*quencies that an ear can detect when the sound level+ *k,v;i woiszr ocw(7 is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate 8 bw.vsj8it u r ,ws::4qe*eywod1q:ua huge range of sound levels. What is the ratio of highest to lowest intensyv:w,e8*bu r dw41.ejqsw8:o:us iqt ity 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 l ,o9 xr+g0fu (k9cie.ng sdg+jrhwn;)ength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placogdu e9 r,f+nk(r +g j0xcgw;i)h.n9 sed?    N

  An organ pipe is 112 cm long. What are the funpj+/ bhqe9wbr: 1x(+d q9xgg o/taan4damental and first three audible overtones if th a 9r t+q(ae/ :xp/4dggjb+h x1qwnb9oe 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 blo do0i4 ,atu h0 hw10)sx:ubzeewing across the top of an empty soda bottle that is 18 cm deep, if ew ,a oui0hs db:041zthue0 x)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 i,6z(.4a3 dsreec t 43j dq)l uyub9vrspanning the range of human hearing (20 Hz to 20 kHz), what would be the ranqz336d 4byed,ria4c9vl u.) rej us( tge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frexlf9f d.q-a2 qquency of 540 Hz as its third harmonic. What will be its fundamental frequ ffla-qdq2x9 .ency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tu* xgk d:ol;8f*1 hqwolned to play E above middle C :w hld8lko1o*q *;gxf (330 Hz).
(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 6mj-nnqm3tv u ,fdt4/s)e4y 5c ;vtnjopen organ pipe that emits middle C (262 Hz) when the temperaty4t-/etj,; sq5d mvnu4v ) 6mnfnj3cture 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 ah a0px2g+z ,6 +i 4sravwj4kdat 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 ls7x+w gb uu)u(nw-(fyai lw khc04*912–10 should the hole be that must be uncovered to plyu(iuk bsw *7uxl(lag-f0 w+9 n)c4hway 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 Hz5rw5)xl --vtpaly qp(, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cq5v- (l p -5prywtxl)alosed 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 se l5wdbt859ay:7zjb huccessive harmon9by b :h5 l8za5djwet7ics 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 pssdu n8i*o,c 9if 7s2$^{\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 vjja1ohv6e0a jo(jj u.g3l2j6f3 fz /audible range for a 2.14-m-long organ pipe vu/v33j faj6fzo2 l06 oj 1gja.j(hej at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appr;b7ma 57 kfkh1uc ld,toximately 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 ufbtm 1l7kd5k7ac,h ; waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryingj 2mr8nu(f ke5 to adjust two strings, one of which is sounding 440 Hz. How fa(m2e k j58rufnr off in frequency is the other string? ±    Hz

  What is the beat frequency if middle o 4 k1ocq (rfo3n0rtr5C (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 k 6zddvp0x4f*jlm6i 5qHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating freq6zm i fpxdl04q5jdv*6uency of brand X.    kHz

  A guitar string produces 4 beats/s ;v0 qluwl:1w6nsf rc5 when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What iwlc; 0f1wvlurqn: 5s 6s the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned t4w3 gerph8,tl3o* qcno the same frequency, 294 Hz. The tension in one string is n,q lr owth383*p4g cethen decreased by 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 identical flutes each try tobei+,1g /ycvuo0b2 i p play middle C (262 Hz), but one is at 5.0°C anv02biyp bc1o,gi/u + ed the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fopu2zuin:e v m2,e l:5irks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C u:2 zi,evn5m le:piu2are 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 apart. A person stands 3.00 m from one speaker g63 k,sqackwtp4y10m and 3.,q w k04g31m yc6ktspa50 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 suf-2ns0ii94b6fs :g)jwp jfbu pposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one 2p9bbisff)ij n0w g s6-fuj4: 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 2.64 m and 2.76 m in air. How mjs ij4.f+v(hb 8d-l xtg;/gw/npro 5vany beats per second will be heard? (Assume T =d(pft r 4xv;iwg-b./sonl 5jj /ghv+8 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550yf+o c8qj)pi 0 Hz when at rest. What frequency do you detect if you move with a speed of)ypj8cfo i0q+ 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fl kfh ,fkrkabgak.,*+: h,um6atn1( crequency do you detect if a fire engine whose siren emits at 1r a k hk6f*g1mn( kautk.,cah,lf: b+,550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if *5kqr bn1 rf:/b4rpxda 2000-Hz source is moving toward you at 15 m/s versus yof/1b pb* rn5rqkr:x4 du moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whe3/ pyrsifem3 75m blx3dc 5u,:pj pej.n one is at ree 7x3cmp5 3lfjp,35ed/um:bsyipr.jst and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out hb/-gp 7c:q4gurp4pjclvpj+a 9w u-. ultrasonic sound waves at 50.0 kHz and receives them returned from an object mog/-pbuwj 9l 4c h-:vju pgac7r4p+ .pqving 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 rb8f7xe1gx zl ,j lndd0 c;l+)flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHzndxxf1 g)j8elz0blc, +;drl7. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatbk;b0xy jp3uymhz03 4 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 frequency was heard if the train car approached the station at a speed ou3m40j;x3 yh0zb pkb yf 10 m/s ?   Hz

  A Doppler flow meter u(ndn fdv 9cq5wu587n 5sgohr 6ses 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 is flowing in large leg arteries at 2 cm/s directly away from the sounhn5g5u6nfcv9 w o sd drn5(78qd source?   Hz

  The Doppler effect using u.yme l sxgewb m2;*pj+8nje96ltrasonic 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 frequency2dtlbu)5 0ota 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear wh)50ob2ltda t uo 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 lazvb;:.rn2 k en7 rdwp-nd 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 sound is 310 mge qhud:f4 259nl2deo /s (a) What is the angle the shock wave makes with the dildefnuhq59g 2e 4d:o2rection 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 atmosumbhma zv( 8 9.-rnmn ly)0gn.phere of a planet where the speed of sound is only about 35 m.n z8nmugb.r(l-9 yh m vma)0n/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. Determaai2; d2ochg u)m9f dzb81al9ine the shock wave angle aam2;2oufbadl )gc8hi 9 9dz1it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle oxx /f8x6c ta,u ,yop-a8cu6m$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the gp6zuh)m d9u;xd(.4 4yf yyce;rvko2nround flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveleuo2fr y.p;xykhmu(; v6 ye4 nzd9)cd 4d 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.dj y na(v/ne8 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(aj ny /dn.ve8 is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humaqnzr4z1cv6. a n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer prq ,f-ntf(io(rk +* c2-ifiksipe symphony. It consists of many plastic pipes of varq2on(f,fskc(i ikr -+rt- if *ious lengths, 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 sound close tz v6tp:.pg8lyo the threshold of human hearing (0 dB). What will be the sounppyzg8:. 6ltv d level of 1000 such mosquitoes?    dB

  What is the resultant sound level when0b q, 01p6ld03cd 4gaxzgwutg an 82-dB sound and an 87-dB sound are heard simg14 q,gdt0glzdcu6x3 p0w a0 bultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in ttg0zys8a;xske p.l: , he open, is 105 dB. What isexz0gy:t ;,kaps8 l. s the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated 9r2db wfr7d 5 h:pyqi:4llx +fat 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHq5 fdyhx4 d wp27+fl 9:i:rblrz?    dB

  Workers around jet aircraft typically wear protective devzj6 rksn ;k; /5oqz+ yw3um*lju7*mpc ices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distanl 63yc5zw ;u krn jq7*;+jmmsp kouz*/ce of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gai * 9 0vjsm1;yfzjet apb d)9.q,vxqoz6n, $\beta$ 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 t 8pcfi+ p:-n7j7o udub8dtpv ig4+gr7 uned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wf +tr;wuj65g jkr9ma )ith a fundamental frequency of 440 Hz and a mass per unit length of g 96 tr)+fjj;u mw5ark$6.1 \times10^{-4 }$ 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 vibra2 8f8u ;retqa. z,zhwp2bb 4jgtion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, thej2 rbptqbuz84;h. , aeg z28fw air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of masb+r40xcc; kff3zt is6 s 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 (in its fundamental mode) with the third harmonci tkxrf4cf6+b3; sz0ic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observedqw h1a g0us3s+ to resonate 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 the 5*k,dh.6yjk roe 796seq)pk zg00–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves a gk)q7sp6kk9j. y ,z*deeh r6obout 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.c eu8 r.3q5us.zhdn9 l The conductor on the stationary train hears a 3.0-Hz beat frequency wuu lqd5 c38ns.ze.9rhhen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Af 6x2f52h qgibogxm s6(y 9khz3ter it passes you, its frequency is measured as 486 Hz. How fast was the train mov6xzhh2k(gx6 bo2sgqy i5 93mfing (assume constant velocity)?    m/s

  At a race track, you can estimate the speedw1sovgl. 6.w wa+b* jkpqu /2r of cars just by listening to the difference in pitch of the engine noise between approaching and recedin1 w*p.2 agqk +rbvjw6lsouw/.g 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, e 9bfj6 ,vk*qf. zx:y ciaw ay4/s4tu3produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is t fsvij /y,kfy3b :tu.ce4q 4awxz6*a9he other?    m

Two loudspeakers are at ojpys o)j 7e1a9* bco-fpposite ends of a railroad car as it moves past a stationary observer at 10 m/s as1* sy7pfa-e)j ojo9cb 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 the speakers after they have passed him, at C?

  If the velocity of blood flow in h.vzbtawdo3pd 2 o/*2 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 fro bt2ho2a* oddzvw/ 3.pm 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 flyizg+;2ffg4/:c t ev l lvfw;9cwng 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 2vl/fc4:ftglw;w9ev;cgz f+by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulse b6yeqg-d5:ihs as it approaches 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 detected by ehbiq5y gd-:6the 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 signals from one Al+g1 4zj7twtuxvo 6*vrmj ,6rxpine village to another. Since lruvtg ,4 j1+6x7oxr*zvmt w6jower 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 overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for ster5*13vzi nmu)hj wj6m ueo listening can be compromised by the presence of standing waves, which can unj16i3 v5) m j*huzwmcause 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 demonstration, c soi.s ltzd,g.;a)9cralled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked withad ,o gzcs9t)r.s; li. the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequem 5 d4xq39i jdqnnb5b0ncy of about 1bxm55q0n3nj qd i d9b4000 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 hears the sonic boomb asbj/+6nq bgnrq3( u j(fi.1 1.5 min after the si6+jb qn3ng brj b(/(qufa1. plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat vvg-1q ,5 csr*.do3r2wrjc u o vx-9)iiya4vu 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