What is the evidence tft.o nemf- c691fses,nl2 . poo:y ki2hat sound travels as a wave?

What is the evidence that sound -nb 595s unanfis a form of energy?

Children sometimes play with a homemaeobee5 v (4fs)de “telephone” by attaching a string to the bottoms of e o b4)(5esefvtwo 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 wat sbdipsr--n* j,xwyd2 f 9;b+her, do you expect the frequency or wavelength to ch2+ bh-s -;fsbp9*iy dj ndw,rxange?

What evidence can you give that the speed of sound in aiaf 9q5fov:r53 ptdce 1r does not depend significant5af vefo 59rpd: c1qt3ly on frequency?

The voice of a person whop48r(qoj9wkg8 uq* yg0 i f0xe has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p6f mr.,dz)nn gipes?

Explain how a tube might be usbht22bj5ei-h chmm j:.hoc8 + uf++sg ed as a filter to reduce the amplitude of sounds in v fijjs.hh+eh2+- tcg o c:+5mh2bb8mu arious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closp all i72rcqh175ys1wx/oc o*er together as you move up the fingerboard 7c/ox7a wp51l il y1och2 q*srtoward the bridge?

A noisy truck approaches you from behind a building. Initially you heau4jd t09jrz* f 71vrigr it but cannot see it. When it emerges and you do seejirf074zgt d v u9rj*1 it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats ni1k5589k ks5 rqkwzyvd9t ;ncan b5vkr9n5dyi w18zqn9 kkt;ks5 e said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speaky.zbqae oh h0j 0d+e m ua6uu0nn(;q51ers were lowered, would the points D and C (where destructive and constructive interference occur) move fartheu+hu.q6jnhzdeq0aa005 ;1ym (uebn or apart or closer together?

Traditional methods of protecting the hearing of people who work in areas witxz 2ep0+ (d fb+bml1avh very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it el+0zavmlb ( xfd21e+bp ectronically, 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 emre9 /-xma5i0 wkdk. can be thought of as a superp-5xe /w km. kea90dmriosition 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.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction,w5(sq3ni + 8)vha mzco with the same vezn+wsav 8i(5qhco)3 mlocity? Explain.

If a wind is blowing, will th1ydd bt7h r85cq,nmn4uo(ad ;is alter the frequency of the sound heard by a person at rest with respect to toq,nn d 4d7b51( a;myht8udc rhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positio bbh1p-mg 9(rvfv-,ycns 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 frequenmrh(b-1v c-9 gvbf py,cy for the sound of the whistle? Explain your reasoning.

  A hiker determines th2 amnxj :fnyx6gcmw.9j+u+ d4e length of a lake by listening for the echo of her shout reflected by a c:mn 9.xux4 6 wjcmyfjna2d++gliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidepkc .xcnydr1xp(l/dak4q:i p75/6 q s of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Tabl c1k qcpxxl 4k6i.nds:(/ady 5r pp/q7e 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aimm o4e,9 xr2wrr 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 foggy dayu( flsm/ 1jkg9. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backf( mgs f1lku/9jire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fromu (x(l xk/a.kz the top of a cliff. The splash it makes when striking the water below is heard 3.5 s llxk k/(x u(z.aater. How high is the cliff?    m

  A person, with his ear f n ;r+do a6cghd ic 5w8068x25kaocydto the ground, sees a huge stone strike the concrete pavement. A moment later two sounds arcy g5 o nf cw85ad+0x6di;8k6acd2hroe heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made overw;fp85)z3vcn yh-u/ si.x sip 6 jv+yu one mile of distance by the “5-second rule” for estimating the distance from a lightnin5i vpjsih )y+-xpw8 czf6yu;vs.3n /ug strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity h4e0n4szvq*ls;uz bpq / uq1or(l (7 fof a sound 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 soundnufs7c 0ax*g)o zz2k3-b fas. whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultlm*)ijol*4 y9+qwl cvc ey2k0l-/hbj aneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB /-yejm9ohlbjk0*ivcl+4 2l w ly* c)q’s.]    dB

  A person standing a certain distance from an airplannk2.h2j2l ka)w8 a. xti/u2pgg fmp 0ge with four equally noisy jet engines is expep.knxg/8fmpg l j2.huwa 2t)i kg202 ariencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have)uwrj,h *)r; y(jdrap si7kr ; a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sig;d,jp s(iwyjhr 7*r ukar); r)nal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sou 4xkp o6ud,/jfnd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads ropo6u4/x fjd ,kughly 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 0pwinhufd a)cs.p 9+9y;yp(v 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 r/hfbpbd8 0+rplw07bet 4m2tlated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect 0l 4tp2dtwbrebm b0/8 l 7hp+fat 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 meter registered 130 dB when pliw6g s5mmk5o ,aced 2.8 m in front of a loudspeakerm56 oi skm,5gw 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 ps*l/6m q-((cr an;o7qpb dgt a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by t-gqcqsp n7lab (td*; r o(p6/mhis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatl ;8kmg qn4rmw59x9k u factor will the intensity increase? Incre5gwm9;qn 4rkx8l m9kuase 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 frpgf5cayk6t w dy,5*a- equency of the other. What is the ratio of their intdyck fw56 -a 5g*y,tpaensities?   

  What would be the sound level (in dB) of a sound wave in, 8dzpmgzcq)n)ur21ex01 fz d air that corresponds to a displacement amplitudeg)z8 d n),q1 cfmduzr xpe21z0 of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what av1 i 8m oielofq/,9c6sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6li vi/a9oc81qf eom,6.)    dB

What are the lowest and highest h8q 94my8v ghpfrequencies that an ear can detect when the sound levqy98pg 8hh 4vmel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodateek :h6a* iwvbm3l urgt0 2fn3* a huge range of sound levels. What is the rati*k0*6ewg3ntlb um3v a :rfi2ho of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengt 5rybizqm;uo76 5ya*ph of the vibrating portion is 32 cm, oyzr5iy57 ;6q*p mbuaand it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threqt3qmg 2iqa4a 8 g9 0d8w: hrgp* jdvnnp3)-cze audible overtojgdqh4 td8-i pzngqn *9p3 aqv:ag 20)r8w3mcnes 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 blowin,rp rxaxch0db q9mo272h5 zl. g across the top of an empty soda bottle that is 18 cm deep, bq hxr2pl95mo.,70a2dr cx zh if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe o7d xu3nh29a rgod yujx54u8:nrgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of theo xj9un d4u8ha g7ny3:x25ud r lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenc90b0vk 6rwvoy y of 540 Hz as its third harmonic. What will be its fundamental frequency if0v0rw kyv 96ob it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lon r9q 80njqr.qm/z hq9u9kg+ zag and is tuned to play E above middle Ckqhnqq9/ 8 rm.zg jr9zq0+a9 u (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 openj6 bg r *knez6(j*i2;bldj .rv organ pipe that emits middle C (262 Hz) when the temperature is 21 62 k.jvzb( rbe*nd;*g l rj6ji$^{\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 atnb*x)z+a p(;/uyulvf 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthp 3u6:cnvubgn 47 ejwge0y ;n3viece of the flute in Example 12–10 should the hole be that must be uncovered to play D ab47 u63gev3nn n:wvu0b gjyec;ove 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 Hzp0ba r;t7u7ae ;,u ifqiya kdq/7:o ,x, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this i,qu btiqdxaa;777/,ka : r0i ;eoufyps 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. Ir iq)o+la.x rgqml:./t resonates at two successive harmonics of f.qgiqla+x/ mr: )lro.requencies 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 o :ml 761g,xrce6nl cw$^{\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 f/b db5a m-yr8cor a 2.14-m-long organ pipe atdyb8mb 5 /a-cr 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to c+ 1j5txs ajv,the outside and is closed at the other end by the eardrum. Estimate the freqj+51j xatcv,s uencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to a my70bkqk -u.adjust two strings, one of which is sounding 440 Hz. How far off in frequencuq 7.yakk0-mb y is the other string? ±    Hz

  What is the beat frequenam,mf 2m r7+vxwmn)w/cy 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 another (brand X) operk: eg0v-cm 0uhates at an unknown frequene0-:kvmuc 0ghcy. 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 4 beats +u7b0/sq udd*mc9kgsug-p 6m-w x7 ib/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with76wgkc 7*g/9 b -pbuiu d0-duqmms+ sx a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T0 yl * cuh4 fvux1:fxw4a,c1b lnhan*0he tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are b*c,0h*4h 4 ylx1uwnff0nau 1 v lcax:played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flss7ume vos: a p7ms,5)utes each try to play middle C (262 Hz), but one is at 5.0°C ):mvss,7s e asum57p oand the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441bkfhkdl- z /b71z*it6 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? Whhl /tb* k zi6b1d-7kzfat 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 standk:yj *sj:a5j +7gerops 3.00 m from one speaker and 3.50 m from the other. sjo5r7 a+yp:j:eg k*j
(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 i6 ,hquce 6sy3be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrathey,6uc 6sq3 iing 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 h5o v+6)kgstq2.64 m and 2.76 m in air. How many beats per second will bet)k qvho65gs+ heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whenog zzt:k /n+ y/splvhmuc:c85e ) w4t+ at rest. What frequency do you detect if you move with +/m: vk zz5/wto 8pcns hcl:y4ug)t+ea 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 fire engine whose sirer9 9u03;2e6uxpc ttpzptgsk ( gct6spp tzer0 u 2p99u(x3;t kn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift i6it:2x nv+xxl r.+jstwn9g e+n frequency 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 frnjt xtw2+6xex i.n:9s+l gv +requencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one 2 k+8;3h 3.lrjjk fsmxw vjv.- ars+lfis at rest and the other is moving towa3rkr-k8 +jwsl jav j s2ffmhlvx.. 3;+rd 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 ultrasoni6cgxff5 463wvhb nas8d 4pso 8c sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received 8 pw6sf xhovgc4b4n85da3f6s sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emf;g j )sh.n)xl/q odut k29rsjlat.+*its an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat 2s*otxfgt.; +h aq9njkujdr)). lls/ hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flade-(q*,*uiijlk ho2s t 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 freqjk*sh-2,(lu*di e iqouency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavesj5k/9llrzg ) p 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 )lpzl/9g k5 rjin large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves oz):i0d j:rp okp4xj/r f 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. xm 2qbgf-y)9- -wrtl;miaf; -ut xxr;When the wind velocity is 12 m/sblf9m-)ixu -;a ; ft-2rg yw;-rmxxt q from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed x)bbo4k;2f o cat 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whonku .p7xtmzi-p09y z wm0, j0at is the angle the shock wave makes with the z- 0.07j9 mp0y ,nozutikwxmpdirection 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 th q8c 25 kg(yeckh 7qq gxz8u3p7:i3hrve thin atmosphere of a planet where the speed of sound is only about 35 guxk:5hg(2cr7p zv cq8qqik3e8y 37hm/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 858zrxxq:a v a3y))6vu o00 m/s strikes the ocean. Determine the shock wave angleq a3o6 r:8ayzxvxv) u) it 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 bcmaqe 0ajg 24fzb) ftph;,i6 doc /,-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anerjbxy8,, /a yd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you j 8re,ybax y,/hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz se iyx*42 zl:atound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is dax:*tzl eyi4 2esigned 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 range? esqsyva73 l 75j8vkq. $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a se6vv )5epdcrro+uhg:oa x4 6s(wer pipe symphony. It consists of many plastic pipes of various lengths, which ( v)pu6e 4g rdovhx+sao5r6c :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 s .-rwa e:qydg3ound close to the threshold of human hearing (0 dB). What will be the sound.ygred-wa : 3q level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an k(uw+*biz3 70 yctzmb82-dB sound and an 87-dB sound are heard simultaneously? tkuybz3* bz+7 (0iwcm   dB

  The sound level 12.0 m from a loudspeaker, placed in the open8q**krb f- lvi, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dik fqi- bvlr*8*rections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpuo sc5 );db4c,wer i9our47uwrt drops by 10 dB at 15 kHz. What is the power output in watts at 15 ur;r4 ccwbu r,esi9o74)dw5okHz?    dB

  Workers around jet aircraft typically wear protective devices over t 6o *ed)2i5mq(jb lfon qn(vo.heir 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 rav)5nb (ofe lo*iq. 6mjdn2qo (dius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, dz.x27 p7lurbthe 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 ao lwygw+zc,h5,d*bw+jj0+ru 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 isonw qk36, ss)s 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per un)kn, 6oqss w3sit 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 vertip2gv)y(y84j1zcnv el cal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the c8gz1ej(n4) 2vyv lpy air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube tuqb9d:2a 7 htf3/t4ga(hsgl qhat is open at one end and also 75 cm long. How much tension should be in the stshl 7hauq a9b/23 qggd t4:t(fring if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lox3zmc m568iwbx9np:s 2ub ,fgop ($\frac{1}{2}\lambda$) 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–xg y*n5 3pboz/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 about and finds that the sound level is minimal at a point 0./by*pgn x3 oz534 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(/zvz 8y3p3-ofnb k mm stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train ap/8(vpb-z fomm3 knz3y proaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle1jbm4pdc7s,q g( k) ug as it approaches you is 538 Hz. After it passes you, its frequenc1gs4quj7,pgb(ckd ) my is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars ju0.n xmihqa* 3d+6eyikz y(nn qlmh4 wf0at639 st by listening to the difference in pitch of the engine noise between approachinqkaf+ a6z 34nmw9(tqnnxml6iihy.3d0 * e0 yhg 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, soundin 4 voi5,hs8v4gmphpd. g together, produce a beat frequency of 11 Hz. The shortoh,4 i.s pp5vv48ghmder one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of l;vq+x 3juafb0)s6p la 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 212lvu)3 +xpj0 6 ;lqfabs 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 the aorta is normally abor1(.0su0bx :ij fdr0b6i m yleh;*letut 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected jm bru i;0 yfrtl6e .(e01:lix0*dshbfrom 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 .fjfj* b h:hr2at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the 2b jfr* hfj:h.bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frvd slgd,+;e xkgy. ht,6(hvb;equency sound pulses 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 b6s;h,dv,;+ebgg x .y(dk hv tly the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usedgf:a/w n*(x lh tu,z6e to send signals from one Alpine village to another. Since lo f*/zguh:t6,e( aln wxwer 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 stereo lr/)+k4qdvmunwa;ax8 vv , 9e distening can be compromised by the presence of standin+q vx9du8av m, ) nr4/kawedv;g waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 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, c4xv) np. ng/wkalled “singing rods,” 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 rvxwn)n. 4pk/ god 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 thresholrr052r ei7 fobd of hearing for the human ear at a frequency of about 1000 Hz ir 75feirbr o20s $I_0$ = $1 \times10^{12 } W / m^2$ 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 onbmg f: /o6c1dr the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude /brco 1gm6fd:?    $ \times10^{4 }$ m

  The wake of a speedboat is )5vz,cif 9smt* nb1mo15 $^{\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