What is the evidence that stso/vd 5ip8b spn 3:,qound travels as a wave?

What is the evidence thitccrs+ ;w-qdn j -r,) ,tapn:at sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a si(v (-*n 4 5zzkx)irimfjfu 1pl f;+itimig 8-tring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound- 8(flugfx;5mf - i*)1imi+ vtp(r 4ijk nzzii 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,h2 s6-po b s)gm+azbv4by/ iq) do you expect the frequency or wavelen4) s-+mo2) hvzyb b g/qp6bsiagth to change?

What evidence can you give that t3.jb -pt 8ncxdu: io+.ivvyq0 he speed of sound in air does not depend significantl-n +uvt pdi:.ojx3c 8 ivyqb.0y on frequency?

The voice of a person who has inhaled helium sounds very high-pit q5e)b1-l4rgud *uctsched. Why?

How will the air temperat9h:ha. w 2+jvjffgc-sx 13w b+ungzh+ ure in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduxk.0r:6 : z +mae.rainm/jrdace the amplitude of sounds in varja+rm an .::/mzd.e0ixr 6r kaious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as yn1kc d- .c0 yd4t;p1 vdz yqsvu.t7te7ou move up the fingerboard 4edz .cq t s1vk- y.tpcndvt0 du77y;1toward the bridge?

A noisy truck approaches you from p ra8 s)ecof;tsyjv tji2()8 :behind a building. Initially you hear it but cannot see it2jy )p s:os);v it e8r8fact(j. When it emerges and you do see 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 tuno2ew -v3z 7e:zxj1 go be due to “interference in space,” whereas beats can be said to be due to “inter7xeg-w3zv 2:e1ozun j ference in time.” Explain.

In Fig. 12–16, if the frequency of t6q5v nr 5 mljcfy/ka6 o8:.tidhe speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fao:kvqmircyf6/ d 68.5lta5 j nrther apart or closer together?

Traditional methods of pro)fnwj bus 0s*l --zsq5tecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a devub5) f jw z0ss-*qn-lsice 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. 12–31. Each wave can be though-wx yf.c,/m .acjqes) t of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, ca ymsf/.w e). xqjc-,(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obseje2(cb 6jdul;81mzt0t x z5t crver move in the same direction, with the same v61tx ut(j 8jzlcd5t 2;bemzc0elocity? Explain.

If a wind is blowing, will tir96x5 xrm/n:o 0gnxf ok th6+his alter the frequency of the sound heard by a person at rest with respect to th k:69 o60x xx+nnh /mtgofrir5e source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swingty* -; t1hih,1 dikldz. 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 thhki1 ;t zh*id1ldty,-e whistle? Explain your reasoning.

  A hiker determines the length of l7h2r ;azsy r0a lake by listening for the echo of her shout refry sr0a;2lzh7 lected by a cliff 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 side of his ship just below the waterline. jdak:7taftn 9 a7 9h qu1k0ukq.68cxpHe 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 sp: q089cju 6qk.xn9haatda kf7p7tk1ueed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 28-+vwtlf q)5q7fpm5f (y u uok0 $^{\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 7sobhgz9*w(e,- dq:el fb q 4ddrifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 14 qed*zs f7wlq, e(gbb :9-ohd.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.ok7s 0l2xcpg/c 2.mlg The splash it makes when striking the water below is heard 3.5 s later. How high is thexc7lg. /o m0pkg2c2s l cliff?    m

  A person, with his ear to the ground, se4b0r yfb p2g3 z8.rffhes a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. H04f8rrzbb. p y2f3fghow 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-sefh5pxjle94clr7g.l(; m s - ffcond rule” for estimating the distance from a lightning l.j9g(lfrxc5lshm pf;f-4 e7strike 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 ov *kml*mfpin/ 5. sb7lf 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 whosu5m786t tv *bh/zzo6 g jyau4he intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lqj1*s7jun55 lpz.f egevel of 95 dB when fired simultaneously at a certain place, u1g5qpl7zn5e fj*sj. what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dist)46k)+*qcfkwu9 ,c t aufp gra7 e1ah3g )tbpaance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound leapgcc))wbkk ,ha t4uqar)atge+9 63fu 7*f 1pvel would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fz p/ 5dczxeb+h6/wtkr (9ok. zor a CDpr c/ ./wz9 khz(kdz5e6o btx+ player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a yv;l+4m h/l5snr 3ikec i8ba0wed5 m3 person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformm wlm5l3i+n; e/yrsi5vk 0d8ac e 3hb4ly 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 areabwa j )4h7;x(qxudq+i 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*v xti3t oru w; :rz/97q(cqqo, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each a7 * tt;/:q3zvqwc9iqoorr(xu mp.$I_{250}$ =    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 9(phnf;i sst7*m ;:qohg0n o 77sv gds130 dB when placed 2.8 m in front of a loudspeaker;ds foqho0i *hns ptsmgns97;v( 7g:7 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 dww zqiqq4mfh 9t0(3 8 lyhy8a. k.vi/dB. What is the ratio offqywi 8kyhw3 a49l.qh.d0t8qz(v im/ the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)6u 3pqt5nb 1+db+qf nh by what factor will the intensity in 3bhdu+1q ftnn5bq6+pcrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq0r3fe8 0dkm)iqgs6uwi. xh r( ual displacement amplitudes, but one has twice the frequency of the other. Wi6hrse) kfr i .(0 8u3m0gxwqdhat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound waved5fg8i4 n 7c:i d2qpjl in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?iig4 7j5ddp8f:n l2q c    dB

  A 6000-Hz tone must hawxvl4 *g*h;ipve what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)4v whgpix* ;*l    dB

What are the lowest and highest frehnw43jad3(:l k 8bsb5t ex6pzquencies that an ear can detect when the sound level is 30 dbpwd5ab(kx: 6 tnlsez4h 3j83B? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l1fh 0u9z mi0a nj;o0mlevels. What is the ratio of hju0imahf 009n 1zmlo;ighest 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 lewln(2t /1;tu(tuv*g+p c 1 ;egqipxawngth of thel+e; p t1 2uwg /uvxinpc;(1ga(twq t* vibrating portion is 32 cm, and 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 th0;fh6.xfa( irrf,y m8vp nim9 ree audible overtones if thefyhm f 8rr v90m(.nx;p 6ii,af 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 gftzfju 4k rad.n* 0;-from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? *;dfn 04j.ktg-fau zr   Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a y k)apx53 01kbfmu-rxpipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the xrkx5 3f1- ak ym0b)purange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freqq2j8 bg0qy8*a6 zoj,pr kzua,uency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of i8jr,jqa k2*bpg z6 ,az0oq y8uts original length?   Hz

  An unfingered guitar string is 0.73 m long and28l co28xo8gwpzm9w+hbc) 8 pdspt w6 is tuned to play E above middle C (330 Hz).tmw wxgd 8ocbs288 lp 2wzo+69hpp) 8c
(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 (2. hrbs(q+lake 0upw/n li72, q62 Hz) when b l7(wp0iqnk aru /2l,seh+.qthe temperature 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*(-ky ysrx /eaatuna.co8 58f /5meqi 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute l+ z)pr8g d/uyin Example 12–10 should the hole be that must be uncovered rz8)dug+py/l 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 resonat p14vss7s; uwbe at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is a;ssw sbp471uv n 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 :)h9urlxs) kn yfxw,) 9gu 8rcat both ends. It resonates at two successive harmo 9:gyhr)kx)9n)lr,fxsu ucw 8nics 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 c)tiw e1sol/ -o3(jlt$^{\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 wsx c3t3vh(3knztb:g b119quhithin the audible range for a 2.14-m-long organ pi(gsqz t:3n1 3u13htbxv9h cbk pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It issh1gkeuih.6-jj3(hhn)ztr i+t7/k i open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the informatiozns-i.k +h1j)e /t jh3ii6ghth(r 7u kn 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 adjust twolurp*a8alf9 v,xq2 t : strings, one of which is sounding 440 Hz. How far off in frequency is the other string?t ua,v2qa f8xr lp:9*l ±    Hz

  What is the beat frequency if middle C (26.4bm6.bi6wx e5 uhqk l2 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 o**sfyk;.fq wmucdsrf16lw -i,o*i d.perates at 23.5 kHz, 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 w*, 6y c.*sf-lo.kud*1ffsq imr;wi d5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whea z6wcd) e ,i.szr7 / 5an)gcihiy64psf.ig h(n sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 35fp n 466i cs/7)yz,.dhsai)a . i(whggezric55-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same si/g)oy e4gc7 frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pla)c/4gi og7 seyyed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flu :trlk(z;klnaueq;e2bscxxf m 4pg;/-s(3 1jtes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 kst4n /q(xl2 ;- (x; :pr1k ufceaeb ;js3lgzm$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequel(g fmbtjm 8mb14fbp :-f5s/tncy 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 frefbp-:l bfm( 4gj ttfb8sm/51 mquencies 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 ;1n+aj6e br wy8 vf *cs8,zddoperson stands 3.00 m from one speaker and 3ro6 n,v1wy 88+;zadecsj*dfb.50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supp xk-n0 ns9c2ezosed 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 is vibrating at 132 Hz, what must nk02 zcn9xes-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 beats h(mba qtppku a93.8h5 per second will be heard? (Assume T qa5p3hup.mt a8h9b k( = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh3vfcpj)f jy-+7zdo ;r6rcjre30 e/az en at rest. What frequency do you detect 3 ;d03)jj ceryfzvf6a+7pr o-/ezc rj 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 fire engine whose snq*/7l: ;k eu(o:4dnt wmbj ssiren emits at 1550 Hz mov/qkn b*:mueds4:jo s(;w l nt7es at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mo4 w;t 8gnbk. /si8cofdd8.yqaving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cloya 8oc wtd8 .qs4fgi8n/.d;kb se? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the samt 40v:q;8 )p0 wn3znphvgywyje single frequency horn. When one is at rest4 :)zyhwp ;j0vnpyn 0qv8t wg3 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 ultrar(k jt6r p7+3exej /fnsonic sound waves at 50.0 kHz and receives them returned from an jfrx k/+pet3r7j e(n6 object moving 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 baq 83- cpfiyl7j)hdex5t emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat head3)-ij lp5hye 8qxf7 cr in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experime 0l3lqnjs )*zents, a tuba was played on a moving flat train car at a frequency of 75 Hz,) q*slenz3lj 0 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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounephai1 lk,*q-d 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 ai-k*ep h,ql1 at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency on)5b osl l 6bpjn,yr,0, neu0nr-y-wzbhp4- $2.25 \times10^{ 6}$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.uz/ri)z ;io-suub x, frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear -u;izuzx/ ,os)ibr. uwho 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 m *r6coy bo) fhr*:5e 3*bk hj)pl3dtnmoving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/wz/r27f4zxu 5u,4frh ess4 wb s (a) What is the angle the shock wave makes with the direction of the afrw/ 4s7zwb uhxs2,4e fzr u45irplane’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 planae3n6xl lcb7 mol)f( 46nnx7net where the speed of sound is onlyn nx7xb7 nal o3)6ll 6m4efn(c about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Dete. 71y doz2x sv0qc(sxprmine the shock wave angle its.q7s2xdzpv(c y0x 1o 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 l2mqhhd3f lyv3gl /x*i w -31nhg6u6 n$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove 4k66o v7lcrt sio+q,vrhead and see a plane exactly 1.5 km above the ground flying faster th4tk,o 7vq6oc l+rv6sian the speed of sound. By the time you 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 s :jh zj3xrn:nqoxr z/eo7zw2y 0l)b9/8k8 wfsends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the ofnerkbn739w:y8)z sx lhzo j2 w0q/z/:jxr8minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humfg(b g)-tdqic fvs24/fvx7 6*4zw goian audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symp:nej4 a9bl;pchony. It consists of many plastic pipes of various lengths, which are open on both eba:enpj c4;9lnds.
(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 of5/qpixa:5tmv0dv70 w8o::zj ds w5zc-mf epd human hearing (0 m fvw 0v-e:a :z8j z5p7pdo/cd 0tmsdqi:5x5w dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound l9*dbhv wirfml ( 8k.hil2f*y22vks6kevel when an 82-dB sound and an 87-dB sound are heard simultanehbh98*lk.2(ifk*f dm l6vryk2 sw2 ivously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105oac 5:sb- (imjo4 dq,k dB. What is the acoustic power output (W) of the speaker, assuming bq5(joak,mci4ds :-o it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100l qh-7p)-/7d)8w oytmr+dm +lo t taac0 Hz. The power output drops by +h o7rm8-t qto)ltd+pc)ad-/ wly am710 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear ps3 k l3ihvbyk.0,e xa)rotective devices 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 distance of 30 mkyilxs3)eb 0a. ,k3h v from a jet airplane engine?    W

  In audio and communications systems, th0v; wy0o h c )tgn-xh+7f7yiope 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 q3rrf klao3v*+d y9c0 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 3a*limy w7 z ,bbnh.jxv9z.3 ois 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit lenb9*w,yo x 3j a 7zv.mlinz3h.bgth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tubwbh6(;zgma j7e filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What i6h ;a bwjzmg7(s the frequency of the tuning fork?   Hz

  A 75-cm-long guitar stdth*ghk +a84oring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string i+hdtgk4* 8 haof 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 onp9lfqh-kxq u) f6.p3lczc -2oe 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 500–1000-Hz range coming from two sourcih7y)-5ec 1thfw 2jbles. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequenc5c )ye 1hj7btw-ilh2fy of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conjhbb b:sv35i1l q+0 tmductor on the stationary train hears a 3.0-Hz beat frequency when the other train0:bbli s5hvm 3+jtbq1 approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538aie87cn*cr 4/; p6q ukb4vp yu Hz. After it passes you, its frequency is measured as 48kv* n i;c/7ae8 4b6qupp4cu yr6 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estim9:, 9n nmkrikhgqi1 2nate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and r9rkkn h2qi9nngim1 ,: eceding 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, produce a beat frequency of 7d-b +s-ve,13 hix;d g vetynx11 Hz. The shorter one isy-+1v,;n 3-e bv xt7seddxhg i 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a8dwng1peb81s(, :czg:itbbo0jaks)2eaj q : 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 the speakers after they have passed him,abg)tw1qs(,z2 ek s:pd8gic1 : :bba8je n o0j at C?

  If the velocity of blooi 5vbo 9e/b9ccd 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 from the red blood cells? Assumcbe ibv 99c/5oe 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 thml .7)b 7wac ubar9dh;3kb5jo-7t pjbe 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 kw uc37ap .)9b; bhj or-75ltdbam7jbthe bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenc3d3/ufff1 v- /+6evrnecou fhy sound pulses as it approaches a moth. The pulses are ad+h6on1f3u/ vfvcr/3 ue- ff epproximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpines j(. qsxqwq4ej*8az( village to another. Since lower frequen jx*( wse qzqa(8js.4qcy 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 listening can be compromised by the presence of rl gqm:)n)n9 jglf3ex;j9q*qstanding waves, which can cause acoustic “dead spots” at the lon)9jfjq 3 :q9x)genl;mqrg*lcations 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 rods,” involves a long, slender alumin2c*q 9yztb 8oyum 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, lo8yt9zcq*byo2 ud, 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 hep/-5/ +ahg+rvjyl c( f zzg1lkaring for the human ear at a frequency of about 1000 Hz isc/kyl+g5 / p (r-avz +zjh1glf $I_0$ = $1 \times10^{12 } W / m^2$ 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 hea fj35jv),k7 z bsji;jrr uq /u9)n/vtwrs the sonic boom 1.5 min after the plank)jn/;jsfub /9jizr5u7vwvq3 ),t r je passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isbncd1 5;k)lp0buvf5n zffp* , 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