What is the evidence that sound travels ag-hung;(n s6s s a wave?

What is the evidence that sound is a form off j7g z/,d; +s(h0)alrug odtv energy?

Children sometimes play with a homemade “telephoy-at7 f*tht+k97;xadmj7 dtpne” by attaching a string to the bfjpa-7 y +*tt9ak;ddx7hmt7 tottoms 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 other.

When a sound wave passes from air into water, do lc wrf.c(8ka:you expect the frequency or wavelength to changfr( l. k8:acwce?

What evidence can you give that the speed of sound in air does not dep z,7c12 fa,*ffcgonh v(tr p9eend significan 7*nco9htrcpf,ge 1v,f z (fa2tly on frequency?

The voice of a person who has inhaled helium so fng,g q,0rqo(mgd6 rb56a c+uqs/ k3om: ;sehunds very high-pitched. Why?

How will the air temperatuyhd0uuzya:u5t2(6 l n1 our6mkk-v n(re in a room affect the pitch of organ pipes?

Explain how a tube migy-gsd*a*t mw +ht be used as a filter to reduce the amplitude of sounds in variog y*stwa -*md+us frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar g4 vutexz8xj5c.r.tkx+qv-. (Fig. 12–30) spaced closer together as you move up the fingerboard toward the br q rjz8tt5+.xxux .v-gkve .c4idge?

A noisy truck approaches you from behind a bui +nqmft5zx03 wlding. Initially you hear it but cannot see it. When it emerges anq+m5z wnf x0t3d 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,” whereas b -e rjey s:6m1q,v t.f jkwk-nh3/cg,leats can be said to be due to “interference in time.” Exnl cgtj .,jrhwf1/km3e6-: - vysqek, plain.

In Fig. 12–16, if the frequency of the speakers were lowered, would8ni ,7 vlqezy2sm6h* t the points D and C (where destructive and constructzst e*v8hli,2m76 qynive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearinghx 1/i0mo ym6vh-b4 5vf unuf: of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce n m fyhm-:x04ofh /bu61ui n5vvoise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought oi yv ((d tu f7ufezw g0/fzy;ou9ae)+6f 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 farther apart? Explain. 6gef /av;y7+zew(zyo0i( t)d uff 9 uu
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same lyjx q80ejhb++:cms726o9f ffexq6edirection, with the s j6y8eo 9fjclbxx+ fq e7+6e2 f:hmq0same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by adcdr4 e2z 8f:a*jay-6v j8:m)zmov gb person at rest with respect to the source? Is the wavelength or velocif8 -6 mdarjm2oevb:j4a g8: cz*zy) vdty changed?

Figure 12–32 shows various posiw jqli4q6;vw. tions of a child in motion on a swing. A monitor is ;4iwlv w6 q.qjblowing 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 lexz ./u6va ,wxake by listening for the echo of her shout reflected by a cliff at the wxz/. x aev6,ufar end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echalx)8o-y;ibze4 y u/ xo 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 1560 m/s (Table 12–1) and does not vary sig;ay ozix8l/be-x)yu4 nificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavb5pdu/0 0etzc elengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just aboz. 1p 8tfi5knnve a school of tuna on a foggy day. Without warning, an engin8 5znp1ki ft.ne 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. T/)fle mozbi 7ww***r dhe splash it makes when striking the water below is heard 3.5 s me/w 7)*fbwro z*lid* later. How high is the cliff?    m

  A person, with his ear to the ground, sees b-nffg+1ev5w cp 7 t:xa huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels inxfgv +5e:f71t wp-bnc 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 errn jf;p 6ghc01zor made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 10phc gf6;zj n30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain x0s+ i gin.ss72ded1ka7zo,s 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 ism7e p*-0k w2pm(ecc ny $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pb9c-aargfvq 3bih ,iz*s4 c -9roduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB, cb9vf q4hisb*-a3igz- r9ca’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy je+mr(0iu s aaz eqrg+f;-7b4spt engines is experiefmrqz bue7 p0+s( +4;gasira-ncing 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 dB’s.]    dB

  A cassette player is said to have a signal-to-nois)hetdjuq 7gint+nf8a+d0 8 g 1e ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the ba8nuhgg 1)adj++ 0ie 8df qnt7tckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pdspnu*5qh v6 sc, : xe9zy y10syth2v+erson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over nt+vz5ph9*s y6, du:yq0yhscex12v sa 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 ajniy(8npk( - 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 i8ok .g gp+1paes rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3+8pke 1.gapgo .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 registi,-/pd2,rne x (1 awjlux h5e+uoel1rered 130 dB when placed 2.8 m in front of a loudspeaker on t(r-p1e2a 1 l ,nr+elx5uhe d oxu,/ijwhe 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 det wwx*nmrm:zac :,8 ;ukect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this n,; :urwkz*:wmc8mxa amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of x 9vg;-a2lvzl ;p; elca sound wave is tripled, (a) by what factor will the intensity in-l;ep;2lzc;v g9vla x crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equa,1/w :e no)cc6bcig bpl displacement amplitudes, but one has twice the frequenp 6g):bc wcei/,ocnb 1cy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wb/f + nahr;k;*/8+h7nlmvd +a mmtderave in air that corresponds to a nb/m;l+7 r tfr ah hk+vam/dne+;*d 8mdisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must kz 5hhsp- c1c4(hre -dhave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Seeecchs1h 4-ph ( z-5krd Fig. 12–6.)    dB

What are the lowest and highest frequencies thar;/(a +ir zl,8c rxuift an ear can detect when the sound leic /r8ir,x;rzl uf+a(vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge raa(nc)et:c -k(qhezg:k.a) ocrf +te1nge of sound levels. What is the ratio of+zet e:.-aotnk:)c )chq( k1 r(eafcg 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 lenp n/q oy1:lfah3dn3,d lp68y vgth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the str llpfo68: /y ,naqd hdnvpy313ing be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first+ 42 zlb(dzwtsnsima isic:4+8o+g8f three audible ovezcgwti: o ++4bln(ii 8f2ss8ms +da4zrtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect t*y(n3jzagy,:d fb5 3xw:tyefrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assume 5(ye:j ,x*bdfta zt:3wyg3ny d 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 op 9 zc ads 2in/k.6ebf3fqv9rl 9)xlh5fen-tube pipes spanning the range of human hearing (20 Hzfdf3a)99bf 5 lk6/2n.e qlizh v csx9r to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonijmz(,vtr bp+ q s4oupdfgu8;/ +/o j1ec. What will be its fundamental frequency if it is fingered at a length of only 60% of its o/vfr,m upd1bqpgsz4jt8 oo/+u (ej;+ riginal length?   Hz

  An unfingered guitar string mzedz 9yz ;em6v2+jv (k,wsq;is 0.73 m long and is tuned to play E above middle C (3306m2z;wk ;z(mv, yjzsq de+v9e 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 lenncugk0*s+zz ;gth of an open organ pipe that emits middle C (262 Hz) when the temperatur znzguksc 0*;+e 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 atvl u8yi s8+ i.c-lj5jj 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thzche5z7i gdg/i 1) a(te flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz1ch(td/7ie5z g) gz ia?    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 68 szge.gxize;1c(pi* /ho,x vt fb)s*16 Hz, but not at any other frequencies in between. (a) Show why this is an open oe)i oz(1v8 s x.,f/eg*ixs*b gtpz;hcr a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube:ihfnpml y36 6p jl82d 1.80 m long is open at both ends. It resonates at two successive harmonics of nhpfp 6im:2 86lyd3ljfrequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 otb23z ipy. 8-xkn jh:$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long op +:s57)ptueetqkyd-u+kyr , rgan ) +-r eu y:pudq5+y ,7teptskkpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.bf mp3;6 -gsnr5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate tpgs3 ;fr6nbm -he 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 ev 6rf5 z1q no4jguct5w d9g,,dfery 2.0 s when trying to adjust two strings, one of which is soundinngd6oj15r wqgtcz u 49d,,f5fg 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262z9tfy0kw7y .dn- 87;se vejpq,kzin: Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (br :12b6o.s kowyw kf-,a/jptjp and X) operates at an unknown frequency. If neither whistle can be heard by humans when kpjb.2oo:k t waf,jwp16 sy-/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 beat/xq y5gs *lgjm e (wr0*0m;pcynl8ts 0s/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your rearsyyx ; cgmq0*5pt m(0e w8s*gl0nj l/soning.    Hz

  Two violin strings are tune2wz * )o 0rvqzov,( (2ln+vi 1zrrmqned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.12( l(rq+rv zr)zweon vv*q 2mzin,o0 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 xhee/+uz 4w p 2m+tf;h/5bondtwo identical flutes each try to play middle C (262 Hz), but omzhefxe n+ hd+/b4 2;to5wpu/ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks50*r3ciyw 7ajnq r p4m, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. Whatrr0myp57aiwc3 4 jqn* 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 a2) r+evida*y,b gw7e1.80 m apart. A person stands 3.00 m from one speaker and 3.5gyr*e7waebd 2i +v)a, 0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppoqrx b)nrz4ftz /4h0; wsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) Ifnf tzxr;w)/ h044rbqz 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 wavele4.:dvj5g m0j ezc+fgkrxsu 9-ngths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Ajgmv+gcszr -05fk 9x4: dej.ussume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginebu2x81zws yuqze/2hr+ 2gi3o yr /g5z’s siren is 1550 Hz when at rest. What frequency do you detect if/uzru2y /i besozqh 1w2gxyzg85+ 2r3 you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still..dx*x3dcmyxkh ez5 :5 What frequency do you detect if a fire engine whose siren emcx5 3xdz5k. xyh:* demits at 1550 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 sourba /da+;+ rulbhqjz: rha2 oro/3o8 u4ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s A4b / aruo;lbz8+h+j32aaoq hdrr:/ oure the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are ee7hsp qln2t, gmt4*i8quipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s eim7 n482, tgsh*qtlp 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 ultrau dp2;8e97lpp7 tlegs* uldr-sonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? ;7g 2lrlp7 t*u-d 8dpeeplsu 9   $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 mqjrc ;zydkra0m4 vu/ 1n(+y1 n/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequenc1yqukcrajz+mvr0; 4 yn1 n(d/y does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played o;pufkm12ke -7:m x jikn 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 1kmip7x-k2ju:;fk me at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses m/ qi de70ld:0l :ntmjultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is takn0jl:q0/m l d :7tdmeien 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 wavrlc sf;*let(fi-7m0 y es 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 emits d3 yo0*i3 j)e/ wfvut;xuchy/sound of frequency 570 Hz. When the wind velocity is 12 m/s from the nortu u/ieh*w)vc ojd / 3ty0yfx3;h, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed ao0j rj 5/dh,5foz7 ru,vo 4srkt 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 whe6wapx/m2za x ;re the speed of sound is 310 m/s (a) What is the angle the shock wavex pm2/xaw;a6 z 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 a planet where the speed of sound is7(g .cew v r.b02xapvp only about 35 m/sc(. .vxp 2 br0vegwp7a
(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 sorn0 ct1i c4mvy; 5iad1xg95 qtrikes the ocean. Determine the shock wave angletd 4 ymnxoca95qcrg;15iv1 i0 it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle j0 r9(wreoaa5 no z67 j8e7wii$/theta$ 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 exactc :m/k. oktpv9ly 1.5 km above the ground flying faster than the speed of sound. By the time you hear tok.k m:v/9c pthe 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 .5o n- mm/ldr-a yf6(eifl 9zysound pulses downward from the bottom of the boat, and then detecnd(m.y-fyeof-azl/m 95 lr6 its 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 oyx)d vqr z*g(.ctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disp0jua*p 0 9qrgjqzgj-3 lay called a sewer pipe symphony. It consists of many plastic pipes of various lengtr900gajgzju *qj 3qp-hs, 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 closey07uus;si hxjg gu5,zk8l5 y0 to the threshold of human hearj8gslu uy0kug;7s0z 55,yi hxing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dBb36((m. q ukiwsm3dyu sound and an 87-dB sound are heard simultaneousu3. qmk(w6d yib3(ms uly?    dB

  The sound level 12.0 m from a loudspeaker, placez vnnp k5k7ip0ac5d4(d in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal 0c a7vi5kpn d(npz45kly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000.og5u0h(ufj:v5yv:ws 0 v my e Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? :vums0 hj u(yvf0v weo.y5:5g   dB

  Workers around jet aircraft typically wear protective device-g )tbx; cnek :sbj7g2s over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cmgt g-k)7:ns2j bx; bce. 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 ga*ow9) uwalur w-(jj/u in, $\beta$ 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 frequeg1sm2jb3 o( aincy 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 32adigr koe 9u zy3;:+r0 cm long between fixed points with a fundamental frequency of 440 +0 rke3d; z ayiguo9:rHz 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 verticyhjk*xr x xma,43n /*zal open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water le*x x3*n,/jz 4m ayrkxhvel 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 yyi/t914,y7jy,ao8 bbyk fgq )vv(nr is open at one end and also 75 cnqva ygy/fi(4)1vk7by jy 9oryt8 ,,bm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observep(+ *ji(+- mmf n+uajwi9r eqgq/kpf+d to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming r. v7i ca,pgh;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 the other. What is theai .p, hgrc;v7 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on jc6 ,rly,ke44c 4ocovthe stationary train hears a 3.0-Hz beat frequency when the c4cok v,,y46l ocr4j eother train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 548h2f mtlm h03jsm f5fa*jl g+38 Hz. After it passes you, its frequejffh+mj 23a 58hm0mlt4 f*g lsncy 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 cars09xp/nmw:gn92 ba ehq just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by b0nmag2w:q 9hxn/e p9a 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(rvdd ku i+,*ddse2s w b38djr: 8a0nn frequency of 11 Hz. The shorter one is 2.40 m long. How long suad wb: n0+28i,nr8jv* 3d(kds rd edis the other?    m

Two loudspeakers are at pjb8g p(62sxt opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speaker8pgs( tj6xp2 bs have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow xx ig2,e ch1n+;a1cdo in the aorta is normally about 0.32 m/s what beat frequency w xo1cc e+;,d2n1hxaigould you expect if 5.50-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 ix/qrws fz d;u37p )/xds flying toward the bat at qd /x /7zd)p;sruxw3f speed 5 m/s The bat emits a sound wave of 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 frequen ny5zzi*t 6q7w4+nchcdc4 k) syp:tm-cy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so thai56swc c- :+zt4z )nk c 7hqy4ntydm*pt the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wasl1al1 xi9e.ilr: 2bj y3zy b5m 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 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 fundameab115 .lzbxry2i:i9y j3 mllental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stef5e ked rr g6x)h3+mj1qw;ixx t15nc:reo listening can be compromised by the presence of standing waves, which can cause acorc) ;i1+6e3fn 5wgdxtx he1j :5kmxrqustic “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 the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” c .va/yj eln(1involves 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,” or emit a clear, loud, ringing soun e1ln./cyvaj(d. 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 trwnwsf jt7.c:(y*jo2 hreshold of hearing for the human ear at a frequency of about 1000 Hzn2wt*w( jcr7f j sy:.o 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 ar.8zu0 v07s awsj n3*dr ccad-oxi v0mz*0o2y t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. *xnc *dra0joocsw 7r 008u zv im.ays3-2zv0dWhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is a-ma55 t 14ws ibjiozxd8da 6;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