What is the evidence that sound travels aszf /)0ojdm2 js a wave?

What is the evidence that sound is a form of en.g +q+bv:in *)htaseiergy?

Children sometimes play with a homemade * v3rd1o 7*lj)s 8tnmqiqh3iy “telephone” by attaching a string to the bottoms of two paper cu n )q71jd 3oiim*3hy8ls*qrtvps. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fr(s7kz(bqnxb8 1 qn4lvch v4 x;equency or wavelength to chaqk4 (n8;vsxchxbqb n4 7z(1 lvnge?

What evidence can you give that the speed of sound in air does not depe .p2 v9 -*q7tvztgbltlh4cp4- ye mduz((1aelnd significantly o-lp.49 dm47vz(l(g-pebyh1 qctt2 t alv z *uen frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?66j ve 5slklt km6.3ff

How will the air temperature in a room affect 00r r8dy(kjo 5cpvn0h;e*g xmthe pitch of organ pipes?

Explain how a tube might be usede,/ss/g)m70 a ht chuw as a filter to reduce the amplitude of sounds in various frequehgah/tsu ,m7 0 cs)e/wncy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) s+o 6c9-bmucdp n)u4+8; n3lurq dfgo cpaced closer together as you move up the fingerboard o rdcl+3dqfmn8ncbpg +;o u9c-)4 6uutoward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it bu ;dc e*p y,uhus ,jfp;3xkfvtg::(+ vvt cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. h y:v:usx,; vf;k, +t(pp fdv c*3uejg[Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferenc /u fltybno.+qougg .f-13u+v e in space,” whereas beats can be said to be due to “intero+ vfn1y-uftqug+l .. 3/ ubogference in time.” Explain.

In Fig. 12–16, if the freqz93gk8c0b vs+zmov, fuency of the speakers were lowered, would the points D and C (where destrucg,z0 3bzvvos8+ c9f mktive and constructive interference occur) move farther apart or closer together?

Traditional methods of protec :xz1 vdma, qbhgyub45jjz/8+ ting 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 device is used which detect,48 ah5udjbzv/+x ygm b qzj:1s 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. E+(pf5l07a wnqt l.bbzach wave 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 (b), are the two component frequencies farpz wlblfa(+q0t7 n .b5ther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dc/ uev*da xr lc2mt,-df5n5e -irection, with the same velocity? Expla-x2/dv*edr, 5nta5uflecm c-in.

If a wind is blowing, will this alter the frequency of the sound heard by a perzk5 z /:ojybw( x61qsmson at rest with respjbw: q s6ok(1yzmz/5 xect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child m/*3qug:p mura2a7+pp dx)k e in motion on a swing. A monitor is blowip7/3u2 prapad)+u:xmmkqe*g ng 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 lak;hcxpur;t9 ,k e by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shour ;uhk;p ,xc9tting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the way zrcte4u/nxqz/uyl1;j*a c7 hk) 2x, terline. 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 12 ,hjcyyr*xzqu4k)/ x;lnct aeu/7z 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 vn u.wznwre0e)0)62jo+ njj nair 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 boatg): lhh3p2e4chw)s c+tu 4wlg is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on ano g4 +t luwh)hcch4g )s:e2wpl3ther 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 to wmqf0 9rtp;h9xexc /.f ru0f. 7hkl d3aoh5.ip of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hhhu t5/rp 39df l7q90.owi.h rkxce0xaf f; m.igh is the cliff?    m

  A person, with his ear to the ground, sees a huge stocf 2 qerjtx;ndj;h/g vi,2 ;3ane strike the concrete pavement. A moment later two sounds ad ; 3hic;2 e2qnjg vjar,/f;xtre heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “)bs4uc1q,mf( i um zr*5-second rule” for estimating the distance from a lightning strike if th)umcz su*1 rfqb(,4mie temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of o6 x8r *,rnrn o( lt(v:bgt:ona sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inteno7s w.orz+hs( :fl pu3sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 97- d;:8jjfp/+lud m u,y- ytbkmamth05 dB when fired simultaneously at a certain place, what will ah k ujmty+/;d 8y7 bf,p-lmu0j d:-mtbe 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 0kyf; t+6nk9a, mz:oz :wl eupfour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound levu ztkolkezw 0,ypn+;a:9f :6mel 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, whereasr/*u0s zu2* p /uo 3a+w7)zrufykqymg for a CD player it is 95 dB. What is the ratio of intensitipk+rw oz*ga yq/ m*uuy/su2zf)7 r3u 0es 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 normal conversdzy1 3an iad2-d4sx/ /jxke 0sation. Use Table 12–2. Assume the sound sprad1jy2 d dn/ ki-x0xzsa3 /4eseads 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 so vamdp20)1 mn xra+g:trikes an eardrum 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 thec+sd m bl4d+1e more modest amplifier B is rated at 40 W. (a) Estimate the sou+s dl1d e+cm4bnd 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 registered 130 dB when placed j sqi2ndzk5z3 i(,mf)bd4kp92.8 m in front of a loudspeaker on the st)dfk3 i(b259jz qd,sn m4z pikage.
(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 dci0pbti64ao2 t x6tu63 )xpdhB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See0o)6ti 2tp d6 bahtx3p4xcu i6 Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fact / w(6.t29 sw.nn8zgjt+qny i 8bjwnzjor will the intensity increase? Increase6+jnwqn2. w(b. s/8jnyjt t z8wgizn9 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 frequf9+ a.-bxiddny t9:h vency of the other.da- b9: +xn9tyh.vi fd What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave xw.+qsx e+ox2in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H xq s+2.woxxe+z?    dB

  A 6000-Hz tone must have wz5dqodypnx+v, b *2*pcx3tna -r5-irhat sound level to seem as loud as a 100-Hz tone that has a 50-dBxtncqnyb55d*2rz -p-rox+3 d*ipv , a sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect -4vbv 9d56d gnb3 shwvwhen the sound level is 30vsg6h w4bdb-53 9vdnv dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rtjcmyv 1u8.h )ange of sound levels. What is the ratio of highest y .cth 1v8uj)mto 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 length of:o+qks3wm .qzjk(/ g d the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be+ qz. g(s:oqm3kjkw/d placed?    N

  An organ pipe is 112 cm long. What are the fundamental xwten9,w +a5(pw zfqdd :72yhand first three audible overtones if the pipe is +w 9 dwa7ey df,w5z:txq2h(np
(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 yo- t3 uwmkxh(v0u expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a k(-x0vu3wmht closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of n.acj1 aee972wx j doad26in0human hearing (20 Hz to 20 kHz), what wou. 7dweaji9ne0 d2cjx 12 naa6old 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 its third harmonic. What wiep8c b-gqs+ y+fd0 l4,aca: ppll be its fundamental frequency if it is fingere+ e spa:8lp+cp,bdycfg0a- q4d at a length of only 60% of its original length?   Hz

  An unfingered guitar strir7l7ncw d+o5a1h b o:qng is 0.73 m long and is tuned to play E above middle C (7 honl d:ar+5oq 1cbw7330 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 that emits middle C (262 Hz) y: s-pb y9kku1when 9uk1sp: k- yybthe 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 aq*kv x p 6jyzt256zv8at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of 0bv n4b6 lpii80x gji)the flute in Example 12–10 should the hole be that must be uncovex6 j )i40vinblb8gpi0red 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 csh5kmb it65 k*an resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is ak 6bimh*k5ts5 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 qcb4wn.d, 1 he14oihqis open at both ends. It resonates at two successive harmonics of frequencies 275 d1ic 414owh.qb,n h qeHz 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 :qsp zq 42avip zae /l2u8n4cm *)kb*n$^{\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 prgn (ixsc;dqpa56 p k;e7 is1i7esent within the audible range for a 2.14-m-long organ pipxas pe6(n qd17k5cii ;7ig;spe 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 is ope2*.xwf8 erkd)es+qr pn to the outside and is closed at th*wpexr 2ks r.)e+8 fdqe 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 information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tw 2 i8bb-:rfg8vnuqr h,o strings, one of which is sounding 440 Hz. How far off in frequency8r,gi8 bhn vf: qu-b2r is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anda2m5q -ab wi rn;hhbq-.(xoj/ $C^＃$ (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,r+ , cc-vue8ty while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when tercucv + ,-8tyhey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sd* vt o8fcwjutv75j82ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whjv8t5ctuow8d j* 2f 7vat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencokx0m9 n -ravdjc/c0 +tcd)n(y, 294 Hz. The tension in one strid mr)j0(9dt0o vx-c+/c kcnan ng is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if ta -n6b6zt: u0ksk*f mxwo identical flutes each try to play middle C (262 Hz), but one is atn*:tx mb kzuf-as606k 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fo gn,l)cy 4 ovu/mxkd51rk 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 arelo g4/yx,m ) nu5kv1dc 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 q: 1o+ok:1umuck jd3h d(6 iwuapart. A person stands 3.00 m from one speaker and 3.50 m from the othekwi :du1u 6ok(oq+c3hj:1u mdr.
(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 gfld 6jh w/4gdl0lb asoof6(b))qo:+ hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, whatw 6qd l 6)fas)0:flobgj / b(+do4holg 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 mpqzu0 1f(jj 19p /v4 +ejtfadvep-wz( and 2.76 m in air. How many beats per second will be heard? (Assumevv tje1f1 /9f+zz(ed p 4(pj w0pa-qju T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at revlnnf.60vb+ n thm as3g nyni: 7-n+5est. What fre-nmnngh3l + s n67nn t.ye:fa 5+vbvi0quency 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. W fj)3tlw4/33 fnpes yshat frequency do you detect if a fire engine whose siren emits at 15w f/ey4 3 fl)3ts3jpns50 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movin7gosgkzb9 07w7 khp:1 nhj 8ldg toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactl9jblp01ng8 dho :khw k g77sz7y the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whec31c5lb gc5f vn 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 horc5fl ccv1b5g3 ns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz ae5w n4zk5t6m(cwi ( spnd receives them returned from an object moving di(z5 pmw e4( it5n6kwcsrectly 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 iup*qzp)mum(u3z7l 5gc oh/-rt flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecguuc)p7(mqz ou-/pm5lz * rh 3ted wave?    $ \times10^{4}$ Hz

  In one of the original t5f 1*c*lwgnfDoppler experiments, a tuba 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 approached the station at ag *cwffl1*t n5 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds.yj)qt: u acw5cz7odz -.q+mjs8+ /xce Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound so c) z8qscc :dy+xja/-qztj 5.7uow+m eurce?   Hz

  The Doppler effect using ultrasonic waves of frequen0kt;a sw e/.grgh0qs +aftzwxn50: 4icy $2.25 \times10^{ 6}$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 iw - 8 , *tip7hd7i/h7fwlfndkbrgswy) a7iw5-s 12 m/s from the north, what frequency will observers hear who are located,7wkisr/5i)b7p hiwdf* 7- lnf y w7tg,8 adwh- 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 movingy (giul, a3mga7 5spa1 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/s (abo6/5wv v+jrq ) What is the5j v/qwro6+bv angle the shock wave makes with the 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 thin atmosphere of a4;kclnt0 dza-/ )iwta planet where the speed of sound is )i/0ta tdwc-a ;zl4 nkonly 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. Determine the shock wavep ;/ cz/g2. )u*az6ado2c pu1zjcxv mp angle it produczvacz*m/)pga xp1.2o cu6; jc dzp2u/es
(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 ktg0 i*:bk1 iy$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhee60a8dml 0hto3o+rx 6c)g hjuchx 3q, ad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the s6 03ro3c+jo, ahe gmh d)tlx8hx0uq6c onic 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 devic sclsd1w07o+ g6 pesm.e that sends 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 minim sml ce.71d6o+s0gw spum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audiblegxb+5j yg, (pz lj3-w osjq(3m range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a s7x/ (pg1naw1o vn7pfqk-e+ ysuyji7 0ewer pipe symphony. It consists of many plastic pipes of various lengths, whia g-pxj/77 nus1niop f+qwk1v (y e7y0ch 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.f9u b*ryjcs9bj9x4wi (v-:o x 0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 suchb -9u jxsy9jf vi (4xo*brw:9c mosquitoes?    dB

  What is the resultant sound level when an 82-dB y;( 14ndsbngv 4m+o lzsound and an 87-dB sound are heard yn+d1nob svz(g;4 lm4 simultaneously?    dB

  The sound level 12.0 m fromj,or.a9 ubia+ qfuxl+ 0/bdesqc)3(d a loudspeaker, placed in the open, is 105 dB. What is the acole/su+ q9+duar 0ba)cf(b., qjx 3iodustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power out6jei;g 4e rjh2*ori8f put drops by 10 dB at 15 kHz. What is the power output in watts at 158426ioiejhr r f;eg*j kHz?    dB

  Workers around jet aircraft typically wear protectiu -:zsw.(8 (aoq 9vpnzgr-c 5, psvdshve 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 radiuv-, h dpcusvzs.p:-n r5((8wszqg9 ao s 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 s .jxjuhec:2b ,7/fnpuystems, 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 frequencb3c upc.*/ : hc/(ae2 ggqp;x-vjstl ly 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with -rozjjc96ss m8 e+)p aa fundamental frequency of 440 Hz and a mass p-8)ajjem6r9os z +cp ser 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 tzlta +gmx8 -y0ube 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 llx0 -gy m8t+azevel 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 is open at one endqlc1)1gjzbj9 qft4k * and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thir9 lftqcgbj )1k41z*qjd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full looptftf 5kjjr. 2ohec )+gywk2 5n;2gu (7mca7ry ($\frac{1}{2}\lambda$) 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 source sci9l 9pzmd6 9s65v+c-zwrvws. The sound is loudest at points equidistant from the two-cl di9zvcw9rs+z 6 w5vp6s 9m 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condg r;ljg8av jy0:)ij o 1*q8kguuctor on the stationary train hears a 3.0-Hz beat frequency when the other train apr8gojiq 1y0;)8 jjk:gl vga*uproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approach (buyrm00 .gtyes you is 538 Hz. After it passes you, its frequency is measurer btym y(0ug.0d 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 justj 5;t9lte5zb x by listening to the difference in pitch of the engine noise between approaching and receding x5 ;ztte9b lj5cars. 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 11 Hz. cc s)musx n63;The shorter one is 2.uns3cxm;6s) c 40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sthjysagya75 bh0s8s 7) ationary 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 betwee7haag ys 80ss75hy )bjn the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood ffd.y4 7r:my qwpt 6ik/oou*9c86 msu slow 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? Assume that 6itqc*7wr :uf/ 4uys9o 8syk6 pmmd.othe waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed ty;fqfle*z( 2 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by th lt2f(ezq*yf;e bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a ;0gadscw:gu/ 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 0wgc: us;/ga dnext chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wasr c6 nsm) 6b2u*cdk-jpaul5a, once used to send signals from 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 sc,a p lb r ad*nuku5cm)2s6j6-uch 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 presence8ldx: ynkk*2q 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 m wide, and 2.8 m high. Calculate the fundamental frequencies for tnqkly d x*:8k2he standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, c530 ,kcb6h7ajr)hxn yq j.e(; ,wfsehxx j) vialled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The(x5b qan;ys 6 jhh0iw,)ex3.k7 rxh jc)f,ejv rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing7b80dea +xcw7 /dz2y:ut,xhp-t ls h q for the human ear at a frequency of about 1000 Hz is t/uazls- te 07:xq7y p +wcdhb,8xd2 h$I_0$ = $1 \times10^{12 } W / m^2$ 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 th:5yltgk k1c hk-h:;m se sonic boom 1.5 min after the plane passes directly overhead. What iss-1t:;k:lhmhc 5 gkky the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 trs(*hdo08bm $^{\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