What is the evidence thatbqkg6tx: xs4 : sound travels as a wave?

What is the evidence that sound is a form of energy?hvbw4 7y :u*61:*fvrkz is3, lu lllgw

Children sometimes play with a homemade “telephone” by attaching a string to qq b/1o te2wv v+8r5mlthe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the v+tbq8e/ vm ro21qlw 5other.

When a sound wave passes from air into wq - nqi, d;z 9l7ocetp;mu) 7bmi+im4mater, do you expect the frequency or wavelength to chang)mn,7itbzmqo4cq;m ;i e u+ldmi79- pe?

What evidence can you give that the speed of sound in)c91 d 0n+t;43nl7yv6muv i vjmjkjbx air does not depend significanv 4blj6c0dxn; 19 )u k+ji3ymjvtvn7 mtly on frequency?

The voice of a person who has inhaled heliua h. yb2(p)jas(nv)j tm sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organt5/4(uttj o/vzzstqjodf 7t 2x:t2r( pipes?

Explain how a tube might be used as a filter to reduc4pt:nfov bbhi2/p r4i 4 84hcim .oi-le the amplitude of sounds in various frequency ranges. (An example is a car mu ptim4ofhcb/no4li4iiv8 4 r-:pb .2hffler.)

Why are the frets on a guitar (Fig. 12–30) spaa pza- pz),k5wced closer together as you move up the zaw -)p,kp5zafingerboard toward the bridge?

A noisy truck approaches you from behind a buil8-)tyi))wnjanr yht5bt w q1 8ding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-fb a tt-18nq8t)w 5n) r)iywhjyrequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas j;p7umo:hed*cdikzo ebl6w0 7(:6 v mbeats can be said to be due to “interference in time.” Exjl7 u0em:com k 6w*dpb6zhei7dv(o: ;plain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thde x9fkp ojr)04x6x7.uszp9r e points D and C (where destructive and constructive interference occur) move farther apar9.4 790o x spj6pedxu kzfrx)rt or closer together?

Traditional methods of protecting jo-2t4lf4tao66; sfzf cjv 9 ythe 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 relativj at4s9;vf6-lt4c2 zo fy6j foely 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. 12–31 c m.+ y3r z4lylb8v,;obsd(md. Each wave can be thought of as a superposition of two sound ,;lmrb+8blsv cdo d.34 yy z(mwaves 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 observejylccy3o82ym5: htu l.y-xz1 r move in the same direction, with the2h5zyxou8yctlm c 1y j3:l-.y same velocity? Explain.

If a wind is blowing, will this a2boqz g(vr17xlter the frequency of the sound heard by a person zqvg712or(x b at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on aeemq g6x hl.p-pn7w;n,u 7 -:8niyqap swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency f-g 7 p:mnleaei86xn;.n qp7p-h y,wquor the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of m wqp o0o3vm-6her shout reflected by a cliff at 3o0 qvmomp -6wthe 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 bei ;: g5ghx,7jn .1- aioipbkdclow 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 thijchpgi:ika;db.71n 5 ,ix- gos 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 wavelength*ah mzrm( 09lts in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just asd s6 0nf)q)8sqitbx *bove a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 1isdtsxns6 )qb) *fq802–33). 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 -juoq i+azn6*c ,lh6 ia cliff. The splash it makes when striking the water below is *-+i6,h iqo cj6lunazheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pavk/.0nef )deai c* u5yiement. 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. Hoafee)5* iy/idc 0uk .nw far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mi );7x)scc)5upk za xsjxqnq) a57b* vwle of distance by the “5-second rule” for estim asj)7; qwsc))) p*7vn5qzc5bukaxxxating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 18yr2 ,z.zf0 ouwyir0y20 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 intensitagnr 6wo+ jw4s41w,cfy jvq+:y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoogm2)zo)w/ e busly at a certain place, what will bez)2eoom/)g bw the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy 9pau0vb y5s,5ot 8ga*c vv/ee jet engines is experiencing a sound level bordes5 8 a5v */ba9evgcv,0t ypouering 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-noise ratio of 58 dB, whereasf0sc,dc th. 8c for a CD player it is 95 dB. What is the ratio of intensic cs0h 8.dct,fties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nr4 a(-pktz/nml,h:h u0iwn ; kormal conversation. Use Table 12–2. Assume the sounapk:rinu;t hhlzm( - 0/kn,w4d 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 :0ewi yi8o1 arewb40 barea 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 isizeqi/t6a) 1lch w1 /x(e+xvhf p0lt+ rated at 250 W, while the more modest amplifier B is rated at 40 W. ( ih+l6l/ 0tfxzaq) t/ iw(ep+1vecx1ha) Estimate the sound level in decibels 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 meter regisgjlw.,j+g) ac+-,fwf v j8fqotered 130 dB when placed 2.8 m in front of a loudspeakejfa+f,8jwo j)q,- wlvg f+. gcr 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 dif jza)-,njwz w.k/+jlxference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9- jx. wzjljw a)kn/,z+.]$\approx$   

  If the amplitude of a sound 4k78ix2cp8rl-oln u) xy j21orsl+p a wave is tripled, (a) by what factor will the intensity increase? Increase pr+olsjpk2 xr7n8l y-iolc)x4a1u2 8 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 fry7)aus n;ff5 tu5jye2equency of the other. What is thfnufuj 5; y5)7eay2 ste ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thaxbq6ss8vd kdpf+.y fbs6 /1n9o 0ji6w t corresponds to a displacement am sf 9x /d6pvk y608bwfq6s1+j.oinsbdplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level tou er;edf9bj 4n+(unxvbl53+x seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 124;nre5 nj3bef(v+9udxxl +ub–6.)    dB

What are the lowest and highest frequencies that an ear) bnnpge(sy4y7;ocb7z(er , q can detect when the sound level is 30 dB? (See Fig. 12–6.) (4s)7 n( cb;pnq,gr 7oeyezyb

  Your auditory system can accommodate a huge range of sound levelsw; z2ua,6s5:r a shsbs. What is the rat2ba,s6sz5;u r hwas: sio 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 d1 t2+eoj (iryt1yavgr:k)g3n-z( d ifrequency of 440 Hz. The length of thezerdir: 3o(1t(2gtv i)1yjangy -kd+ 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 v mv;4,,+ vwucs*l peacm long. What are the fundamental and first three audible overtones if the pipe is p ,uvmw4vsevl,;+ac*
(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;hjzo/xgm8 z/qq6m n) blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wa /mxj 6zozqh n/)m;8qgs a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to buildxkwh(,ctag2 xxw 9f 2+ a pipe organ with open-tube pipes spanning the range of human hearin tx,kc2(w fh2xa xgw+9g (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itjlkx iis-7oq) 3ur1 .rs third harmonic. What will be its fundamental frequency if it is fingered a q) jk7isrrol-.i1xu3t a length of only 60% of its original length?   Hz

  An unfingered guitar stringd,7sjz i ;9h2gksdp6 uwle.y-id n.n ( is 0.73 m long and is tuned to play E above middle C (330 Hz)gn-pnwjyd ;usih d296ksled7,i.z. (.
(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 mi -2 bk6mj8wllir*v0ui ddle C (262 Hz) when the tej-u8rkbw* 6i20ivl l mmperature 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 20 sbsrp3m (5vc nlkr4 1:r o3z/y$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sh04 jc*+mforkzj - 5nd ffi4yq*/p ll;oould the hole be that must be uncovered to fd f;nop*f*5 qlc yom+zl4/4-ij k0 rjplay 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 H i;:omcurvj.+e3f,qd z, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Shoq.fr mj: 3v ud,e+ic;ow why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.8jdjqr3)p8m *k0 m long is open at both ends. It resonates at two successive harmonics of frequencies 2jp rd jk38q)*m75 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 p ux kam*54 vzg nqaf0*cq1q18z;-r sl$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long o e7ph9u n2a3mk75a obbrgan pipe 59a3pu mnk2aboh 7be7at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxi;b53av8lkos g me (0pgmately 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 gl sbv ao8ke3g 5(p;0mwaves 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 everux+u*j4 jmpv 42dg fdjm wg8ou+my179y 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is+p7mj*+d8d u uyoj42m jmgxvu4wf1 9g the other string? ±    Hz

  What is the beat frequency if middlea7r lr jms3pkjv8j(pr59+dq 4 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 a t53k1nvsl) kwt 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard1 sk5k)v wnl3t 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/s when sounded witypce(u9)/o uk3srjd,x hua 7 4h a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the (y p3xusurj7,e9k /ao4hudc )vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same di cg:eu5*p9qz 2-ymm8ib7 o afrequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1cog92 a7u:z m8 dpm-e5biyiq* 3.]    Hz

  How many beats will be heard if two identical fluteuna w.z(9-m0;ysm gkl s each try to play middle C (262 Hz), but one is at 5.0°C and thegk nma0lum9 z.-y(; ws other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.pp83aort ) ko :* oyjelwgk*5:af/b:g Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequenck:: b8/wg)o 3jal5op*yeota :g *kfrpies 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 s5uobcr7phwep./)d ar9 z( otzxc0 2c5tands 3.00 m from one speaker and 3.5(eac2dor. w c9bpzz0rtho cupx5/7)5 0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner l/b (cm3)a+z7,yb -cf ywsetvhears eybws-m/ ctc3 lbav yf)z7(,+three beats every 2.0 s when they are played together. (a) If one 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 2.7hi- crl6)gar. 04ookh 6 m in air. How many beats per second will broor g0l 4kha)6ic.-h e heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certa- (hq/qyv w7ms .p-j*hadws7sfax 95oin fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you qhoysw -xs*v w/dq7(.-957jsm hpfa amove 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 engius-1+5h:enko hv zyb (ne whose siren emits at 1550 H :u+bh(vyzkon- es1 5hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200e8v67l vbe b0s0-Hz source is moving toward you at 15 8bbsv0 e76lvem/s versus you 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 frequ0my 6 kc9f2pe.2dov hk1m tr-fency horn. When one is at rest and the other is moving towf12dmc9k rvk tpmeyh0o-6.f2ard 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 ultrasonic sound waves at 50.0 kHz and rec*s1 lenjyd ybyv(0e9 :eives them returned from an object moving directly away from it at 25 m/s What is the received soundj v(l y:*e1n0edbys9y frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an usbpq0r2pbj;x+ j/ hi -v3s g4nltrasonic sound wave with frequency 30.0 kHz. What frequency does the +bqgpvhbxrn/ps23; s 0 -jj4ibat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat td lo:ew0dvb;zr joh* 2km(8 .xjwq 63lrain car at a z dm;0wjqrv hb(:2xdkow . el86*3lj ofrequency 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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wave;fl2o l u4g, sxbwcr;p epg52rj3k qlg+/y.-hs to measure blood-flow speeds. Suppose the device emits sound at 3.5f3 g;cjg x5y+wrg lq-rl2o./p ;h4 lbu2, ksep 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 sound source?   Hz

  The Doppler effect using ultrasonic waves of freqff.d0 gfpmv 5lc7yj:7opo7 5w uency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity b54 ftpz pui83zvgar2 te;27bq :2 hixis 12 m/s from the qbi3hrzuz2p :g8 b752pe axt4i; t2fvnorth, 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 h+auxtd:7 e,.m zx3pkland 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*wg) ctxc3 -af)np /xlyq7 rv6.kz r)j speed of sound is 310 m/s (a) What is the angle the shock wave makes with t)af7)tyglr p.qw x*jc6z) -vckr /3 xnhe direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thi. en)ix/yzw 0*) x4rzjrhqf2an atmosphere of a planet where the speed of sound is only abouw0yn)hj zxif/ar z 2*x4. )erqt 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/sj7o+ r-lxx9 9s1bhjj w strikes the ocean. Determine the shock wave angle 9bwxj jjhsl197xr - o+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 9cd9 69juseq zpb3t o0$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove9fa9v j6 t8wosb,r rs-rhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the son9bs -rtfjaow vsr,98 6ic 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 sound puffia+ bd01wjch2g-f*k 7qh p6h z2vy8lses 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 mini i fq6wjh0za vyg2*-2dbf 18kh7fchp+mum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?h9 r hixjtw;9wa mz0;6 $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ofng e x9avc ;z.8hw+kb+ many plastic pipes of various lvbzc.8kh ;+ng+ex 9a wengths, 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 pea fh)2.w iu4unrson makes a sound close to the threshold of human hearing (0 dB). W4.) iau wnuhf2hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a0s *6qg. yu4im+q nf/pce:7jp2yju esn 82-dB sound and an 87-dB sound are heard simult* 64/ . cyqmgu2:ey0q+ fsujp7sijpneaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opestp2x uq)5i u5n, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in xqit usp2 55)uall directions?    W

  A stereo amplifier is rated at 150 W output/c72)equ:4mpvdug e b at 1000 Hz. The power output drops by 10 dB at 15ve:ebucg2) duq4 /7pm kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their e 0l lysz.py**tars. Assume tha0yl.tslz **pyt 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 m from a jet airplane engine?    W

  In audio and communications systetn r6f1j 94jjdms, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequenlu+n*q c1nkj+cy 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 isme*a)dxk 9rm2tn4,c;b z 0ufb 32 cm long between fixed points with a fundamental frequency of 4ud t0k;)*rc bm,zb9mfa24 xen40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertica7r q h2 s*a-zbhi(d3tnl open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from tb tad-nr7h(q2*izsh 3 he tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that k u.lei0qbn9rf2;c (ris 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 fundamentarc 9bil0;.e( qrf2n ukl mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full 0dq1cs3/ bya xgn u8a2loop ($\frac{1}{2}\lambda$) 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 500–1000v:r/jnxt(1f-v dz w p:-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly xv-z(dfj t 1: /wp:vrnwhat the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whis2g w2wgj4d8h0bp ipqh 3+ 3bentles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the othebq p3 0h834+b dngw p2g2wijehr 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 Hz5x gn+d, 0q4jyd cvl9y. After it passes you, its frequency is measured as 486 Hz. How fast was the 54g0q9nvdyxdj y,+c ltrain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bybs5fp x+ .na/t listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency+ fnax5.btsp / halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce .r 6 tsay1ka:va beat frequency of 11 Hz. The shorter one is 2.40 m lrv1 : tkysa6.aong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pap;o )s6s5gdnrm 2me; p g1l;pnst a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, whs;dn gges; r 1;6onm5m )lpp2pat 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 0j7odu-fhg-r flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ulthu-d gfj0 r7-orasound waves were directed along the flow and reflected from 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 6.5i3bvl+y.hhktdwq6 9 ; 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 frequdh+l 36 9vbh.y;tiwkqency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sb )py2emsepg6 ;owx ;7ound 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 by the bat so that the echo from one chirp returns before the next c6;) 2yeepw;m gosbx7phirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one f.gc3 ixu1fm.eae0i m ,h np4o19l,prAlpine village to another. Since lower freq 4p0rhp x9,uag o1.m3mi feei1.,ncfluency 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 bhnd 9(iywec - voj.n90e compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure n9v.hn j9-i e c0w(yondodes. 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,” iq g9d qi .x/cm8kr(bd+sg/l,dnvolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. Wit(kg 8 .xg/dls/q dm9cq rbi,d+h 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 :x1qe1o 7d beo,f kd8rfor the human ear at a frequency of about 10of71:edx,8d rq1bkeo00 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 s7m+ypiq, w9t1vulo:a u kd1o7*d6fg wonic boom 1.5 min after thekdt*pq17 f6+ m owi1:oavdl7,guuw9y plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboacw pj/ gopj1:1+pkrc+ ye;w( it 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