What is the evidence that((u-w/regqk1*en pu g sound travels as a wave?

What is the evidence that soun9th: es*v,uh+nl3k) vg pk:aqd is a form of energy?

Children sometimes play with a homemade “telephone” by attaching wbthleyw 2,8fn*s )tqrq ;0j2a string to the bottoms of two paper cups. When )qs;t 0w *wn2ejyrl,h8q2tbf 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 fraoyq2kn z12*x om air into water, do you expect the frequency or wavelength t*yakn2 1ozq 2xo change?

What evidence can you give that the speed of sound in air does not de ,.dw bgmtli6z1 /famyz9*,r wpend significantly og. i,9al/byzmd,z*m6 r tw1wfn frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why? m-r* dr+jpr*l

How will the air temperature in a -:wx elqe:ow g /c ,c;roz/d,sroom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to ret( x9lqrr*l 7pjz ;u-sduce the amplitude of sounds in various frequency ranges. (An example is a calt-s *qz 9xlpjr(;ru7r muffler.)

Why are the frets on a guitar18 ghvf0d +ryrux e8 jrgi;v9+ (Fig. 12–30) spaced closer together as you move up the fing rfvdr;x+8ig he98vgu 1 +0ryjerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially yogr mo.54pqb 8h7)rul ou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brim5r.uglo8b4oq h)r p 7ghter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due tz98:(oclyp89sp ey lv o “interference in space,” whereas beats can be sv zlep 8l:s98 ocy(yp9aid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would th6ac y.bw )w agbmd-)h8e points D and C (where destructive and constructive interference occur) move fh )yc aw8b6b)da- m.gwarther apart or closer together?

Traditional methods of protectinnw6e)/na 2v*80jt oc(ddj.ty. gvx vrg 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 .an)*gcenv(t wr0/t.dvoxjdy j826v 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. Each w nr.ev,/ 7jo1nnnub2 )imv st.ave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (bu) tv onr, 7m1nbn i/v.njes.2), 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, sgcvfa/ :)(5qvx0dne3.xwl o with the v:g )lscax.0/qo(5x de fnv3wsame velocity? Explain.

If a wind is blowing, will this alter the frequency of ,4cyvq:,i eirjr +i f.,zr0 qothe sound heard by a person at rest with respect to the source? Is the wavelength or velocity changcqeyriji:qfrr4 ,o,.+i , z0ved?

Figure 12–32 shows various positions m610 qarrzbzv76 c* vyof a child in motion on a swing. A monitor is blowingy*6baq1vrc0m 7z vrz6 a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hrd:-;vn/qlojq65a jder shout reflected by a cliff aqv 6 -r;n:jd5 lodaqj/t 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 brb ,+:6yn8(: srh4ukd8mz c)mtbac skelow 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 1bm6rnz tucd 4rmk,b):8a +kcy(s:h 8s560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in- sollsx z3kul(o2 2-n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on (w+ 9d0dfc egt60tzbq a foggy day. Without warning, an 9g60bwtd (0t zq+de fcengine backfire occurs on another boat 1.0 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. The sp1iwn w o gx5na1dparc- m6-k)6lash it makes when striking the water below is heard 3.5 s-r6k1-wg1nxo d )anw p am65ic later. How high is the cliff?    m

  A person, with his ear to the gro fu/0ty no4b+mund, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othy/ufo4+bn0 tmer in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by t +t:997 qmtu-od dpa4zulrf1t he “5-second rule” for estimating the distance from a lightning strike if the temperat fl-u:z9+4qm pda r1ttt o79duure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t+ gc28(p yfqhehe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity i ht)bl u s5u kf5kv+wx(2v)lgpn frrz7/s:c:0s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sounimg372/q-w8xz:w(d +r bygw ui2dtrb d level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intwg78zr( tmxq +rddi3bb:ywg-2 2i/ uwensities, not dB’s.]    dB

  A person standing a certaytbtd -qr7c f2g35 q+hin distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person expe 7+hbr5fq2qcty gt3- drience 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 f+ f /5hjg zfc82 wuzv:rdxc(oh( z/d:ratio of 58 dB, whereas for a CD player it is 9vzfz ccuh (wjdz:g+d5/(f 2 f:/8 hxro5 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 person speakinsmpdv3;rtt1ze rkpmn /(xb6*9,r j f3g in normal conversation. Use Table 12–2. Assume the sound spreads roughr6pmjb;( t sp,*1 t/xvz k3e39mr drfnly 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 enkg p+ztd0nt g9;;p7gardrum 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 rated at 250 W, while the more modest amplifier B is rayho) ob6osv6ie,k76 gz/bb9 +kw5u ru ted at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in ,yk5zk i) 9gw+6b/b6 oooh7busv 6uer 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 ohh2 do6 7er*uplaced 2.8 m in front of a loudspeaker on the sdo*oe6uh7 r2 htage.
(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 detecql p1yx ukj1r;8rw6z kn1m5+r1 p(jzut a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose lewq1jl;uk p1( j8xzm rp r5n+y16rk1 zuvels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensiuv,vac wlhvg7,b w( 5;ty increase? Increase byba ,hv cvgul7;w5wv,( a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fr-bptk(.vi0d m2lljgm p zsb3q8v2+0wequency of the other. What is the ratio of t0sv dp t0(zl .m8w22mvpgqi+kj -b l3bheir intensities?   

  What would be the sound level (in dB) of a 7 duyrhkm a00:d2 +bqxa *.jqtsound wave in air that corresponds to a displacement amplitude of vibrating ai0h2x kjdmb0ay*7.:qrad + uqtr molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must ch9vkd:i hp/bu13,*gf rnp -mhave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound lever /icpf h uvbd9pg*mn1-:h ,3kl? (See Fig. 12–6.)    dB

What are the lowest and hib6 k().l33zd g)i erehm(uztxghest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–xe)mt)g b6e(iz(. 3 lr ukdh3z6.)

  Your auditory system can accommodate a huge range of sound levels. What is the-qs qs6t09x:pw0g,d z8v x1jjbvji m ) ratio jt0wbdvxg9v j xm18qs0jq 6-,zsi p):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 r4:bvk,-0937u * trsol hvn6t ckhjcnlength of the vibrating portion is 32 cm, and it has a massrsjr:-uh k3*n7,b0kncv 9ov cht4 6tl of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thhc078ob 42wgic t nmr:e fundamental and first three audible overtones if the phgb8t0no c2cm4w r 7i:ipe 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 wo8qf3 7lh::im oxn9 51paai 1 wc9gvdbculd you expect from blowing across the top of an empty soda bottle that is 18 cm deep, i8a 1a7vmhf ingq9bxco pwi:5:c91dl 3 f you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube piwr6 b )m.md2mv-jn5hrpes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of tb- m6n . m2rv)5dhjrwmhe lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 561mb svss 9ok540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at ab6 mso1ks59v s length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E aos8)5m v4d mqx;l;h hhuum6ntyp; , i)qv,2z above middle C 6q8 ahh;m4m)5 izvuxm,);h2n;v updsytqlo , (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 open organ pipe s6nm :ghehw:.)8 poelthat emits middle C (262 Hz) when the temperature is 21 nl6 h:ehmgo.pew: )s8 $^{\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 nbzlz vp y8z13682n, i5segnmat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be hm/*.cin,g ae that must be uncovered to play D above middle C at h,./ai*nmg e c294 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 c,m b)fg bjqe r;7xyw.+an resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe.;y mxbg.7 rwq+ bfj,)e ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open g z67o4 )mvsbeot4zdbb :13bk5ha j9iat both ends. It resonates at two successive harmonics of frequencies gozbijmoevbz b )ab3:4t5 9h4s61d7k275 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 fc). *1jmhmcs$^{\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 audiblthvazq8e 7jut 49kc;mt/ /.h ve range for a 2.14-m-long organ pipe ahzuh/acm tkvt .qv4etj79/;8t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.or;.x) gv*mi- +xvz zb5 cm long. It is open to the outside and is closed at the other end by tx)z-.v v*obix z+;rg mhe 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 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 whenr fo443kus. ze trying to adjust two strings, one of which is sounding 440 Hz4u4zfe 3s ro.k. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and goph. 9ma4 9 rtx+jr0g$C^＃$ (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) operates atkykkc2j0ao)vt* 2 vfrw e .l3: an unknown frequency. If neither whistle can be heard b2l av3r*2) k c0kt:yjwof.evky 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 beats4.6h g fyfdbxbp8.x bh-5a4 qp(3jlqv/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hfd.q blpa 6vbyhxpj-g .h(34q x4fb85z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to thnnc79fcwc +q;nh1gb 4e same 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 played together? [Hint: Recall Eqh;b fcc47ncn+9 1gnwq . 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play ku d-cn*-stm)middle C (262 Hz), but ouk)ndt -*c -smne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f02,bi*k s;1kkn ngkirx l1+bsj.gb. srequency of 441 Hz; when A and B are sounded together, sk1s nbgrx ;bg .kkl +insi,.j *10k2ba beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are 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 apartge ;(ks-hf uwb(b6 k e*j(,qux. A person stands 3.00 m from one speaker and 3.50 m from the other. b (e6fskbkx,u(uj*e; (ghqw-
(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 hy* 72h lviwc/qears three beats every 2.2* c lhv7wqiy/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 waveleng0i g rb cm-0p/m(n/yqhths 2.64 m and 2.76 m in air. How many beats per second wi -0 b( pmqmy0/ngr/chill be 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 H)5, q+ w,esyrdkp6abw z when at rest. abwdk,+r)sqe6y 5p ,w What frequency do you detect 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 fipj;- 2,i(bcg fgt g-f9y omi:uhx49ywre engine whose siren emits at 1550 Hz moves at a speed of 32 i4c go y 29fh-j;, 9tyip(gfxw b-umg:m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movinggyq0+mphl/ ec. e5+wpri2c2p toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenci cgp h5y/pr2p w0+l+.c m2ieqees 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 thes4pcdvz. onka 9 f*o/u6 5zie1 same single frequency horn. When one is at rest 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 eazu 4k*i /. zco6 915opfsdvnT = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives theavoy. lx;(s ;ahqxw7;m returned from an objec.x;yl ;voahw;sx a7q( t 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 oamk/1v1- vaqqf 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequ-q vqaa/m1vk1 ency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuhw+ -/k x8tpuzba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car appr p- /w+htxuz8koached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter u.ie(igjw.1kf1y w d g;ses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in h.1fw 1kw (i;g y.dijeguman 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 frequencdug neh-qe95xi -)ct6q((f zv yht )t3y $2.25 \times10^{ 6}$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 veloc2gvclwzwq92w9kk38 e ity is 12 m/s from the north, what frequencyk l2k9wgwvq9c8e 23wz 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 objectgm sz 2an(t6)mw+k ci4 moving 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 souns. s5 ,q bof;ghv)+wdud is 310 m/s (a) What is the angle the shock wave makes with the direction of the aqob d5,. ;gsuwf)h+vsirplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the un 6v3 (t1 wsic 5ytgw-nt.v1ispeed of sound is only abouttt u w g1wityvvin5.31 s-6(cn 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. Determine the shock wave qmka + e/ul.9i(ix5gz angle it p5( ax+u z9eiigkl /qm.roduces
(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 uq rc2*d3f(utw ou68y $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactl uts4 3*.eicdnox/eo1 y 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determ*otc/ee d1. i nu43soxine
(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 ab u-ke9 8btnp. sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detect e8ptn9k.b u-bs echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibletj17t n(w f-3 zzzmb-z range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manj(cs:7mhnu+u; wcwz4uw) *jl r4:yr sy plastic pipes of various lengths, which are open on bot)wy;mcu(w h7jnz:uu4:rr*c ws4js + lh ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold 4 6/xp5fnknu bof human hearing (0 dB). What wu/kx pb5n4n f6ill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dz8pv8 fyeq+s riz( +9uB sound are heard simultaneously?ez(s8fy9urq+ z vi+8p    dB

  The sound level 12.0 m fromuybo8,h kio j77c)a .e a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directi8yio)j.7kec7 u ,h aboons?    W

  A stereo amplifier is rated at 150 W outpd 540qqvnxprqp,) gztds k88, ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kH45rs),gqtkz80qdp n8d ,vpq xz?    dB

  Workers around jet aircraft typically wear protective devices ovmn/w98)8 gy/qg ky .faeg*vswnglz8-er their ears. Assume that the sound level of a jet9ve y*fk/ysal8qwmgn g z8g -g8.)w/n 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 systems, the g0os g (p 1e:xy6ogej;dain, $\beta$ 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 violrdozv 5b1)3a6imt6mn t:ikq +in is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixe 4plg5l0cw hr:,zjs 1n6i+fznd points with a fundamental fpi n4j: +wlgzlnch f0 z56s,r1requency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with water j/n. cll)t1zv/:ou4anot xm 8 (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the wzotln:u./8mta on1)c4j/ vl x ater 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 2.15i r x*v8hr q1epkt3 lfo+r-m50 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if i8vfrx+h-rt q*kl1ierm 55p3 ot 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 he d4jl1h ftvw6 6mgc20suh02loop ($\frac{1}{2}\lambda$) 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 500–1dzm5dsp7 +vz/ 000-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 7vzm pzd5+d /s0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stat;za/xu(t93kl 1yze /la; cynjs+mz. jionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What ic;na xuj/( 31 yyst+l9zz;/jm.z el aks the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After ikkn2/wa 57qaut passes you, its frequenk27aqu/ an w5kcy 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 just by listening toqbo5kr f+3b(hdp+ hg68- ygpl 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 halved) as it goes by on the straightaway. How fyq h(g+ hbk6pbd8+lfr3 -5ogpast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11gv9 2)drh4l+kiyj ( le Hz. The shorter one is 2.40 m long. How long is the othe(j4yi 2 llked9+v)rhg r?    m

Two loudspeakers are at opposite ends of a g6 o9m+wgezjo3x5hf8w5kn,a8xjq 7e railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears t3jf+zjhmeogkgne8w x 5x,ow98 76a q5he speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 md3og(2k n5t nh/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? Assume that the wavesnt(kh5og3n 2 d 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 wbhc+oc6q: 6o;8vfd,hnq dx z*hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave z,+oo86q * b;xdc nfh:vqc6dhof 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachts*e 2 cp6u*c5 .cluo ed2:rl88u lcenes a moth. The pulses are approximately 70.0 ms apart, and each orc*uuce.2pc2:l*lse t88l ecdun5 6is 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 fm 0,g5okjrzmqxt0ffc 9uzy* 9q /5o)orom one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and whicmfmtu fy oo9r5xkzq05g 0z o/,qc*9j)h overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compro2g6ion.u i r*amised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0.nraioig 2* u6 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 71/ xr-aaofgnzt3 n1yl :xvh,a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,xa,a:f7th1v3 /xoz n-y lr1ng” 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 thresholdzs 3d+ak:i 3suwj-p 0v of hearing for the human ear at a frequency of abv-zdpisu0 a:j3 kw s3+out 1000 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 heasnuih,ian3bo0,36 m s rs the sonic boom 1.5 min after the plane passes directly overhead. What is b o ua,n03s imn3s6,ihthe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is ey *va7lfgo09liope (e*e 1(t15 $^{\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