What is the evidence that sound travels as a wz53 m7bhg-z b.f 7shv yl3zp, 7c6kghpave?

What is the evidence th/ aah4nrmisxc7 j;f;8at sound is a form of energy?

Children sometimes play with a homemade “telepy6,lhowm2oa*z smy3u :nm: f (3r 3lvvhone” by attaching a string to the 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 othe:ouv6mmy 2lzlvsrn3(f y: h*33 wm,oar.

When a sound wave passes from air into water, do you expect the frequey- qswq( -u*tyncy or wavelength toq* tqyw(uy--s change?

What evidence can you give that the speed of sound in air doessa0zk)5 3,9tg brozpy.d1p etk-).3v vvvikn not depend significantly on frequency?) 3 k9 3tbt) vvna0,-1ir d govevpz.p.k5zsyk

The voice of a person who has inhaled helium sounds very high-pitched. Whtjt .cp n8 sibr fo7s8 e7ek*(0;lc; wl4vz9tyy?

How will the air tem ruz;end;,1v sperature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduh;jdybmnl 55u;q:n 4,4 fbm8+ dtalbh ce the amplitude of sounds in varioustb;h4,jqbbnl+ luf:m4hym58 ; a 5 ndd frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as /gxtgw u *5,,o o3uj:xu i68-fyossjmyou move up the fingerboard toward the35mowf ,uogjj- uo s6/gusx, :y8 ixt* bridge?

A noisy truck approaches you from behind a bu fyl2 nf(k+eps 7aj-h(ilding. Initially you hear it but cannot see it. Whe+ lepj-yasf2 k7 nf((hn it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space(s (xepg)g5h ;v c*u.irmqrx u,kwj;;,” whereas beats can be said to be due to “interference in time.” Explurjh s)wmc, q(5;(p xr;g;*i egk.v xuain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin6/aevl f; ipwf2crr8m (a/ 0pots D and C (where destruc e mflf2i8ar p/ r6;(/wcovap0tive and constructive interference occur) move farther apart or closer together?

Traditional methods of proteyudsaa1d4:;v5kc6 tjh tyv +*cting 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, h*s;vdadv hua t46 :1 jtcyyk+5eadphones 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. Each wave can ad h2a8t5rvcbww5u4 *be thought of as a superposition of two sound waves with slightly differenthb2a5 wv*4 ac dr8tw5u 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 i; ;qhwln1r;wif the source and observer move in the same direction, with the same velocity? ;w q;l1whn;riExplain.

If a wind is blowing, will this alter the frequency of the sound he7h mbk di+ ;uudj:.ptmb oz25(.r4eddard by a person at rest with respect to the source? Is the wavelenj 5obmuk 2e+dtub ;dz7 ir.m d(4dph.:gth or velocity changed?

Figure 12–32 shows various pogpmt)zi oc:o v1;fbvf.;w)s5 sitions of a child in motion on a swing. A monitor is blowing a whistle in fronpz i.tcvw1:s 5fbofg)om ) ;v;t 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 lisrvuby ,u(0ry;iv4( hdtening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afty uhdi u4yb;v(,0v( rrer shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below zwe7phr -p *d0the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How przw7dp-eh0 *deep is the ocean at this 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 wavelengths in air at 20 zmmmh v76 v8 *zmgv.s:zqe78d $^{\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 justs/d,;e9rm 4con,/kbf 0j7 xwke8kh wu above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothec8,u/e0wr7/dn9 kkjs 4ob ek;hwf ,xmr 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 splash it makes when strikinglp2rg4 :or;s1s7 dt h ne9x,ch the water below is heard 3.5 s later. How high is the cliff?n2tr;ds1l,h rcx opse7 :g9 h4    m

  A person, with his ear to the gr7ro. ptv.t 57 oyqh z:9me3r24i tgelkound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one zkoei gp95 4 q mh7y7t:tr3tr 2vo.le.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 disti. :+i,mye o1haildk( ance by the “5-second rule” for estimating the distance from a lightningkhl i mi1,:d(oei+a .y 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 levelepjt+zoc0 ffp c2 8 jbin),hmr5(i5 j4 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+. ;eoh c/8yn kdugnw wg..(eg sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9t jw,x;7v +/ mtyxv a)2cdv2pv5 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensi2td vpjym xa tcw;+7x)v2vv,/ties, not dB’s.]    dB

  A person standing a certain distance from an airp r+-+ zuiz-ofwa3g/qtlane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not-ot zrg 3z /uia-+w+qf dB’s.]    dB

  A cassette player is said to have a signal-to-noise 2jbexqsl uqe44l.c 02ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ea20qb 4.luqj2 l4eesxcch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound 9x z5j30vphp,ds+k6;ozplz0 (x- fgrirfq:i from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere +poz -:q, r6ji;0vpf9riz(ps0zlx3kh5x dfgcentered 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 eardruva4 b*qqz ra2kt v+(mhf -e*o5m 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, whioan 6i5g.s0d- 0y4 zmcxhh j3ile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expe4h ny5x0-j s6ghm3ac 0. oziidct 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 pl3zw. /5q v(g6w0l nt:y kfpxpbaced 2.8 m in front of a loudspeakfxzyptw bwk3n5 v (glp0:q./6er 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 differeqxn))l7nrfc0e2s*d5: ie 4we )kqmajy,1 na ence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounne dkerl wxnqj)esma efia*c2)7 5 q40:n,) y1ds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave 4z5jio us6;wyis tripled, (a) by what factor will the intensity incr6o ;iswjz4 yu5ease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onee(sza,mj :gjgn :6 w;l has twice the frequency of the other. Wha;s6gje:njzl a ( :w,mgt is the ratio of their intensities?   

  What would be the sou yx.sc,tcjr 27nd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of sr27t cyc ,.xjvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whuv tnh,v*qej 25aq 6-rat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1 q,au n*th52vre6- jqv2–6.)    dB

What are the lowest and highest frequencies that ani 7 ykhq4k,ie -va,3jx3 xkzb cgs17w8 ear can detect when the sound level is 30 dB? 4k, qhb7,vsxayii73kjgx 1w-ez 38ck(See Fig. 12–6.)

  Your auditory system can accommodate a2: w 5 h mowumm8mzjs/a5um2r3 huge range of sound levels. What is the ratimz5 ums:5mm/ 2m3rj 8auo hww2o 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 9*ah(h/lzn vn has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has /9 nahn*z( lvha mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first rysrwa(5p1cegt8:tfs 7( 1 km three audible overtones if the pipe(fc(rtm t1s ar8w :1ksypg5e7 is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect vvl.h/t*k kg 0from blowing across the top of an empty soda bottle that is 18 cm deep, g v*lt/0vkh.k if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tubeisd6 r+aolz3- pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the zo-6lid 3sra +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 harmoc2vuf8es +8n8sh yjjy m79o0bnic. What will be its fundamental frequency if it is fingered at a length of ons8+jshf c0yvn2o8um b 8j ey79ly 60% of its original length?   Hz

  An unfingered guitar string is 0.jsm.a 8 /ofmy+73 m long and is tuned to play E above middle C (3 amo+mjs8/.f y30 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 pipewrt aa;d2pqu/ebe4xt)6h h24 +px+b z that emits middle C (262 Hz) when the temperab)edp tae bxzx6; hah/++u244tr 2 pwqture 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 bgb9g*rw61ly9oh3ib/9zgo f 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 m(z *k 6v)kgtb)ac j*sshould the hole be that must be uncovered to play D above middle C ** sb jta )6(vmzc)kgkat 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 Hz, 440 Hz, and 616 Hz, but not at aw(s5ctgf kv- w8/5/obs+aw gany other frequencies in between. (a) Shwtv 8/ws o5b sc/(g5f+k-gaa wow 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 1.80 m long is open at bot+ f pel5t.q1 ck.ny 5 ,q(srtv9*diussh ends. It resonates at two successive harmonics of frequencies 2u5ect q+1y.(v,dk t*s9qr s n s.ilf5p75 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 fjbgsf )v-eds v5 l1c/2(l do-$^{\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 pre h5 ey8y:4kcuwsent within the audible range for a 2.14-m-long organ pipe y4khu5 yw 8:ecat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longdckmu5tx9 )ptp- 9 t8m. 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 waves in the ear canal. What is the relationship of your answer to the informat-c59mm )8utktppdx t9ion 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 tid- ujx5pbzaqt//wj y;n:u t/+o ;dr, o adjust two strings, one of which is sounding 440 Hz. Ho,;t d/b:r jdouiajp-+n;/5w y/xztqu w far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C ++s*bufrq eji0;n- 6bqfn ff2(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 opt8ed ie4 ;h((chky:heep2r1apqqe*zf * ;t; ierates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sepytzii8d1h e:c*;e fkq;tp2q*(4(phe ;eh r eaarately, 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 with a 350-Hz tuningu to 8kb0g:cg0/9bi; n+pu.nnv to)r e t(lhm4 fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Exklt :9 0p(umt8c;) +n rbeoubn ti/ n.ghog0v4plain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tf4fxd; * r ymk6;qih5cension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toget; 5q4dr x fiyk6cf*;hmher? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hear.2gx:nb ulcb )qq,6dq4b1/ei x zsbq: d if two identical flutes each try to play middle C (262 Hz), b6bq)q:bgicq:sxnu2d.x 1/ z4lb ,qe but one 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 frequency of 441 Hz; )des*yd3ai5 8- iqfu0aj.fmswhen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are s daq-i 0s3ie8fa5um.jd*) y sfounded 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 apart. A person stands 3.00 m frohs j8cp .qal:y:q+o x7m one speaker and 3.50 m from the oth::q87c.plxojysq + aher.
(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 H fem 4bvlf;-94bnd be)mna s(,-2y diaz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frn 4aydbmndb9fsel m i--befa2;(4),vequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ha b/8fkv/a,8e,lv fed*l q:6lvfv* dn ow many beats per sefvql8:/8v f d/fe,,*el6vb ak*valdn cond will 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 Hz when attfq o n j9,q+l+7e*erb rest. What frequency do you detect if yotoqlr9 e7*fe+jn+ ,bqu move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. W;4aw1*-h; w1p jafb-5mo9o g08rphv techocdhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speedb5h*w4orch-9cm p0pgdo8-weato a;v;j1 1hf of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sour;nr8.4sx (vchy5ehrj ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly t ;8chejnryr5h(sv4x . he same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is8;o ( 2eu)(f4 etptem3sstabo2dw7c p at rest and the other isst4m(f b)e pso2aeu82wp d7e(;ot c3t moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicja::wbq ;tw; +4tp ;f680l whz /9kns veohstt sound waves at 50.0 kHz and receives them returned from an object moving directly away from it tat h0wh:;6 stljeb ;94tpfwnvosk/:8 q;wz+ at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a2lkgn3k :c*xyx-eij8 speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ix xnke8: -c ljky32g*in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was p2ftb ckng* a1z)mjz38layed 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 tra *fg b81ajmk)3 zn2tczin car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow /121; jtuzvye jq6yyk speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s 1eyy/u;z j2qjt 6yk v1directly away from the sound source?   Hz

  The Doppler effect using ultrasonicpnqn8 vw.yiq*, 1tn 4d waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emitsl,,ebqny41i88x cmz a sound of frequency 570 Hz. When the wind velocity is 12 m/s from the norziy8,q48ec bxan, l1mth, 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 mo:5rto t7ydc6l g( lu7.wc4+zmu(rs kmving 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/s7qxc3 smw 6wzyrcm-09sk2d o3,h9axi (a) What is the angle the shock wave makes with the direction of tmzd hr92 mkiscx3, sy oxw 67-wq0c39ahe 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 a planet wh sk6ifk*dn2t ket05i5hzf-h4laqf -- ere the speed of sound is only about 35 m/sf2tfn55-d-lifkh4* zhi6e 0qkts -ak
(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 strikenn;jph 1-y3eog 0.z lcs the ocean. Determine the shock wave angle itn 13yelhz.pgj 0;con- 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 pj x d fqds9g3s1s(+8d$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove4xr5 as:mhfhamxzqk8wik00wz95v( 9 rhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By th hkmm05(iz f:sh98aqa9 xw0xz4 wvr5k e time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fro;,ycmn eacd+6,7 e ghgm the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work , ehc67d,geyncga+m ; is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves 9 5/kp:)kca,mcgnc cz-7utb5*3dntgj .hwhsare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal6()hmz y g+g nxgs)7chled a sewer pipe symphony. It consists of many plastic pipes of various lengghh)s)7z (g x+ 6cygnmths, 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 person makes a sound close to/xz,(lp ap5h k the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoep( ,xz kpah5l/s?    dB

  What is the resultanvcfxt8r,1vp*)/w/wif m t, lv5gmzl5t sound level when an 82-dB sound and an 87-dB sound are heard/,8v t,)5/plf vcvm 5zwx1tlgfri* mw simultaneously?    dB

  The sound level 12.0 m from a loudsp5*3 dlx*4ffw4g * gzmbm66fb+ mdhnnaeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equallf 6f6nmlzng4a4f5dbgmmhx* bw 3* +*dy in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpujy r 6jvej7/b-0 8sosnpu*u.o t drops by 10 dB at 15 kHz. What is the power output in wa0s-os78 .upb rynovj6ej* /jutts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their efk d3tv4 :jp.bars. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m frof.pj:t 3dvb4km a jet airplane engine?    W

  In audio and communications systems, t(k id9h;/m c:t swpk4yex9.f vhe 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 freque3p4tn0-lif(b:(ilx .akyxc y ncy 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 poin0j32o g84 n1gd qfxy feusgligt17 k,4ts with a fundamental frequency of jey427x,gsg01gff3l1uqik8o dt 4g n 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 fiq7)e hxh ail);lled 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 fexq hl ))ia;h7ork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at ond3q b6)oh5qw ue end and also 75 cm long. How much tension should be in the string if it is to produ3) 5 bdwqhuoq6ce 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 loop (qg*.audz 02 tj 3*k 5xkxvsv)b$\frac{1}{2}\lambda$) 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 edtc1vl8y:3 ./ht ecgqz yl2b5* oet1 in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than tvtce3et2.c8:tzyl15l qd/*1 g eoh byhe other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stajl9*u l ryqdxw8q881t tionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro y qjxd1q*l8w t9r88ulaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yoy,o xoeczovy h4x9x(( 0 u08wqu is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving(x08x0 uo,wxo(c 9eyvz 4oy qh (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by limt92* d 3) eehyr5caene(-h zpstening 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 hazp3m*(5 d2hatnee9-yer c)e hlved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produeo m;whd r. dg36y5mmb. m9gs2ce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How los;gmwdd 6h.re3 bo.9 mm5m2ygng is the other?    m

Two loudspeakers are at opposite ends of a railrw1/crf s0a7f.kkos/tv8k k b(oad 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 8f7bwk f o(vks0. ck/1 rtk/safrom the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s *:zkoq x(n v;l ;msx1mu5i:thwhat beat frequency would you expect if 5.ms: n*5zxx;uh ioqv(; 1:mktl50-MHz ultrasound 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 6.5 m/s while the moth is flying +is4qcsm-hz.toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wz-i sc.m+4hqs hat 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 f8u9 ;vidr 8j,ciwl2t erequency sound pulses as it approaches a moth. The pulses are approximately 70.eru8dict;8j ,wi2 9lv0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpin4hy+l9wcg lh7 e village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. +hl 7glw 9hy4cWhen played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromiz (twoe xq1 k7e.*abc)sed 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 m wide, and 2.8 m high. Calculate the fundamental frequencies q . )kbz*o(txcw7aee1 for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a ofiw+ k 4bj(6klong, slender aluminum r6k4ko+wj( bif od held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, 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 thrk bkmeb ;:j n8w.dt)w)eshold of hearing for the human ear at a frequency of about 100kt:mb)8 .d)new;jk w b0 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 jdmqn24/sp7 nobserver on the ground hears the sonic boom 1.5 m /p74d2n jmqnsin after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ipzjc2k8iw ek( +vo(:o s 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