What is the evidence that sound travelso,z-xys 3- wcpl,8 jpx as a wave?

What is the evidence the 9 mcwg/.+tfhat sound is a form of energy?

Children sometimes play withcl kwt s 78hxpz6b60mu sbqp-,;w.c-m a homemade “telephone” 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 travelsx-; clt66- whk zsqpbb,87m0c.swm pu from one cup to the other.

When a sound wave passes from air into water, do you expect the frequencya2:g7 v*c8xy zeqcssu:o bb 7+ or waveloe8u2gqsz: 7c : +*vax7ycbbsength to change?

What evidence can you l+yo;e fdi 7 0dxzq 0wny9:5 h;tvzm6igive that the speed of sound in air does not depend signifevdiz:w7niytx5 dl;06h omq9fy;0z+icantly on frequency?

The voice of a person who has inhaled helium sounds very high-pit9.cxv7lo 7l acched. Why?

How will the air temperature in a room affect the +t l(k4-vpo6gqlj3 hrc 4:z6 qfuuic0pitch of organ pipes?

Explain how a tube might be used as a fdej (gcy,p u79cbm;.gilter to reduce the amplitude of sounds in various frequency ranges. (An examplee,g9gcm( jcy.dp u7 b; is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov 5e(b0,d5rm j, tapfbme up thp0afm t, b,5e(b5drj me fingerboard toward the bridge?

A noisy truck approaches you from b xg.4sdf(kle* geum;5ehind a building. Initially you hear it but can mu *;k.lxgsef4 e(dg5not see it. When 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,” whereasyru)p4y) op nm+y9vn . beats can be said to be due to “interferencep4vyyruym)9 np).+n o in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wereo m+.kpu3y /z mry,e6mymb -r2 lowered, would the points D and ey b2u3,+rp6k.mrzmyo mm -y /C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people w *j,6ubk +cjwx ads.m;ho work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new techdwm*k;.jsx +cu a j,b6nology, 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 oa 2g 6u wclkw8*u,dr)v f0 p/o/f;blgjf as a superposition of two sound waves with slightly different frequencies, as in *w2g)p/a0 c6 k,lb/djfu8;g vwr lof uFig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thebx9ylw b18 2fo source and observer move in the same direction, with the same velocity19ox2 bywfbl8? Explain.

If a wind is blowing, wilkjor5bupj*t gso)4d* 7i :k-mm 1 lhb(l this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changgpod)k-b*k7: tjl bij(* mohmur5s1 4ed?

Figure 12–32 shows various positions of a child in motp.(1ql nsv qywapx)b 30 b-d1nion on a swing. A monitor is blowing a whistle in front of the child on the groundwb( q3y0 n.ld-vn1qb ap x)s1p. 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 las z*c7zr z: iq4*g8s07viliq istening 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 shouting. Estiml7 q8*rsg*v7sz0:c q ai4ziziate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship ei:t :+t9h ;ja6imtqrjust below the waterline. He hears the echa9 q r+: eth;ttmji6i:o 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aio h j))2jqn18xv7 mbppr 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 drif-qhfu8 vg p(m5g t3w.tting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before53tfuqvmw g-8h tg(p. the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from theg )ky 1t7p+f1+qfo h0g+qdppo top of a cliff. The splash it makes when striking the water below gpkty7pof+o d+p1qf1 )gh+q 0 is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees aj.eeqnsi 7q+ti1* r :v huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How fai.t v*i+ qrqesje:n71 r 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 757no;omh krdxhf83l “5-second rule” for estimating the distance 7dho okxf3nl5mr ;7h 8from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level76qxo)er54cwd+yb 5 eh1d)jhax p g 0y 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.7;gfmr5 / bpn / j:z1qexjoxj of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundf2t2v i2996mvo5ogp 7 rt bhon 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,vto 2n75i2pf9t6ogo r9b2 m vh not dB’s.]    dB

  A person standing a certai,5l0vm cg 4nnyn distance from an airplane with four equally noisy jet engines is experiencing a sound level m4yvc g ln5n,0bordering 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-nqcdw(jx78a+ ioise ratio of 58 dB, whereas for a cixjd+wa 8(q7 CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal cojpb +/rao -l 7zthz;t.nversation. Use Table 12–2. Assume the sound spreads roughly uniformly ove /;pzz- hta7 .trojb+lr a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eard/ib t8 lw;eo6nrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modesl- t0tc t1 2+2kkuy 1kiaa63uop(qrk;w nmr +nt amplifier B is rated at 40 W. nmk13twk- t;u ka 62y n2 ripar1+tlku+qco0((a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB met;nprow5i5 c,e er registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ,nwr ipo 5c;5e
(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 dgf u 1h(xy/utm :9ci(la4xow 0etect a difference in sound level of 2.0 dB. What is the ratio of the amplitud4oxw/( (19hlf x0mc:iatu yg ues of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a shj+/ b(w;*fgbhs nuw,p( t se4ound wave is tripled, (a) by what factor will the intensity increase? Increase h(b/* s+j; utnewb(pfs hw,4gby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampl(p ,j,.-d4zgixlv cu;a+j sr lhk57oiitudes, but one has twice the frequency of the other. What is the rr4pjol;,l7v gs(.h+xjz,da k uii5c - atio of their intensities?   

  What would be the sound level (in dB) gjnu6np frdb 8be(7 (,of a sound wave in air that corresponds to a j (g(6epud,78 fb nrbndisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what s8jh:kybzpb +a (y2zm:y0 v 9wcound level to seem as loud as a 100-Hz tone that ha(p2mkz8 wbzhy j::cyy+b v 9a0s a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and hig*,8v3)x6w-e pq qikbd0vbk s yhest frequencies that an ear can detect when the sound l, pkq3qbydv-6 v0 )b k8xeisw*evel is 30 dB? (See Fig. 12–6.)

  Your auditory system can lg*gyhzn7lso-). 6ty accommodate a huge range of sound levels. What is the ratio of l7zsgg y-o*nl6t) hy. 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 violiezuwnl5; 1n1hl 0+cgln has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string blc 0h;+1gnnu w1zl el5e placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fir2.5/csh) ywzclf 8fs ;qqj.7bad3 cgfst three audible overtones h82sb.fcd;)c 3zlw.yfsc7 a5g/qjq fif 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 from bls90+k 3xede;xa i .beqowing across the top of an empty soda bottle that is e;qdeai e.0 k9b+3xsx18 cm deep, 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-tube9zsqt: meiexn-/4 r8ka um+0y+phx 1*v 1 xebi pipes spanning the range of human hearrsx/-yke u1 z8en:x+ 4 1 mbt i+epxaqmv*9h0iing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What w3 y9 ;+;v. )om- yfxrcm)uk salq5nrbaill be fna+u;vysr .r)k5 xc3oa);mbyl9qm -its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long bj (qn-f7e-jyand is tuned to play E above middle C (330 Hzj b( -7y-fnqje).
(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 emitaun.+av8g,zzi2 - wfacjdh* 9s middle C (262 Hz) when the g9 ,ah w+d-zaj28uv acif.n*z 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 afmahu2 y46vcucq 4+9o6af )g zt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the q6bl4m g /swd, qgkmop )v n/thj+;v38flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? hnj,8)/ k dmt;wsqvop/q3lbv+6ggm 4    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 gh yybx6e97;unzn6w k /ky2:kHz, but not at any other frequencies in between. (a) Showkxu;b :e yw 976z/nkyn6gy2hk 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 both ends. It resonateqko j,sv( m),cs at two successive harmonics of frequencies 275 Hz and 330 Hz. What iso,,k v) m(cqsj
(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 o mr9s: (i+wu,e lt*hx$^{\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 ar: lsz.ccamvr uc2209qe present within the audible range for a 2.14-m-long organ pipe at 2:z2v.9c src2 u alqcm00 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsid(6tr95 :a sbwoft1eyte 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 tof a yrs(twt: 596b1eanswer 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 tw9+3fv dgdw1 - 0:+ 8q2 tk3vf: ewxqdajujmfqko strings, one of which is sounding 440 Hz. How far off in frequency is the otf3u j 2d3ev-fv 8tgmqw0k a+f+qdj 19wqdx: :kher string? ±    Hz

  What is the beat frequency if middle C q74p7v fm 8emu(262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (bc hd9 gq61zcxyws*j6(rand 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 w*c6c(j6yz d1qhs9w g xhen 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 tuning fork and 9 +pqo3 xlnh4c2 beats/s when sounded with a 355-Hz tuning fork. What is the vibrati2pox +hq nc43lonal frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frejad3 4*)pdztj(epwpi+ j0v(bquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toget (d+p0j *vbj)iejpaptd 3w(4z her? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle b-e5onj:j *jbs (zdw5C (262 Hz), but one is at 5.0°C and the other at 25.5 b boenz5*-wj(jd: sj0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bo+( 6 /mwija3ofdfwidphh7 k:64 gvg 5 has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B an5f /a(+jimh k6gv h7di :3gow6ofpwd4d C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. Ail j hlc7afs /za6xe3 x3(*m:j person stands 3.00 m from one speaker and 3.5eix7falas (hjj:*63xmcl 3 z/ 0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vsi - k,j0br*hdb-t w4oibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 13rjbh -dtob-4w*, ik0s 2 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bem-00kmt(y m 4sz 6aoevats per se00a4k(sotmez 6my-v mcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firlyu *msyd ,q-7e engine’s siren is 1550 Hz when at rest. What frel,*y -sd7uqmyquency 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 39tf6q::6di ny5nt b,eeqooshat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves ao9 3std:y6 i6bqon5: fene,qtt 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 sourc;upx.m:l3 o e wr8noz(e is moving toward you at 15 m/s versus you moving toward it at 15 m/s :em3.;8( pn loruo zwxAre the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same s1cuz.jn; rq2aingle frequency horn. When one is at rest and the otru 21; qz.cnajher is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounoo* c6y(zxq wot,gu9os6-x2qd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What ist,oz 6(gq wyxsco*ou62 q 9-xo the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As itqs z a-u4-whw mw0u-v: flies, the bat emits an ultrasonic sound wave with frequency 30.0 kw--vw zsqawu 0h4um- :Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,73x qxw1w)0 dxl3 /gvmbk4j kg 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. Wha) /x lg3gxmk 7w4wb3vkxq d01jt beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrcjr5mb)x/(lv 1ol zlwc9m+s9 asound waves to measure blood-flow 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 flj lc9zobxmc9m(v 1 l+)5swl/rowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrason ji4svn/ qfg, rif(mn3w9tz01ic 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 emits s77ug7p lvbc ,hound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are gvl7uph 7c7b ,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 spe sh4 3dbu(nsh8ed 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 2.3n*9mm bsn bbv6d-+ 2wj where the speed of sound is 310 m/s (a) What is n b+m*jnbws v-29mb6dthe 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 a planet where the speed of bh tb y)nu.t,8isno7: +p1wee8kpp(rf; jkk 8sound is only about 3.eowtp7n8tr pyf;k kkn(hu1,pe8 bib: s +j )85 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 strpc j bmgjsx*w:z (6f-9ikes the ocean. Determine the shock wave angle izj x6(csjpbw9 f*g m-:t 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 sb:6w )q z4j fgozjr1:$/theta$ 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 exactly 8i: ubw:q:cohy8h 1 is1.5 km above the ground flying faster than the speed of sound. By the time you hear the son ui8chq :8:1si hbo:ywic 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-l2c xkdyfasbygts/ort2egq3/33b . 9j 7d0:aHz 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 ms9b/2s:fct7yjd. ekg/a3y tqb3o 2dagl r x03, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there ilm2 9pm i:d8bbq2off. n the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a di6o.tnir/ue:kohs pqy6( *3imsplay called a sewer pipe symphony. It consists of many plastu3k6pnist*m h/qo r:6 e.(yoiic pipes of various lengths, 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 5.0q3p/ng, ;m*it zv)s lr m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 si,vm;rt )g* n lq3pz/such mosquitoes?    dB

  What is the resultant sound levi 6gji(h u9qq89xz qfq)y(jpx ).bz0qel when an 82-dB sound and an 87-dB sound are heard s9u q 8zjq9yhx)j((.p6igq)0 fbq ziq ximultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in .k-vspp e+ d/pthe open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equal- vd/pskp e+.ply in all directions?    W

  A stereo amplifier is,1kwnow16 ngq rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Whatgkw1w q,6no n1 is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective 7l nmvjjic 7e1/a-.ihdevices 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 cm. What would be the power intercepted by an unprotecl7je .i-i7/v ch mjan1ted ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicua)gad+q)p+x eiek 6/ations systems, 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 tune w 4:0x;(he+wwqb gezhd to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is- m5seo yau4i:t-cu- x 32 cm long between fixed points with a fundamental frequency of 5x-t :4yae s-omuuic-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 vertq;629j1p+xc xxochkd bizv 9; ical 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 th +hozbxvp16 ciq9;c;kdxj2 x 9e 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 mas,-hif8zwj r egp/c 53ws 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube? grze-8i3pj/w5hf, cw    $ \times10^{ 2}$ N

A highway overpass was observed toa,k fua+p95/jkz 0sk2mc3j u r 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 3ez /q **( teas+lzddtrange 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 the other. What /tezdd+a *3 (lste*zq is the frequency of the sound?   Hz

  Two trains emit 424-Hz wv 5:bvntty9lt1 *:lu lhistles. One train is stationary. The conductor on the stationary tryv5 n1t9*::tv lt bullain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you06c5cs36yao x kkege) is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Howe 0s6cayke)o kcx3g65 fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate t (:rdlqjwlm.meze i;q*/g+6 v he speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car droplm.+ eeqz ( wglr/v: qmid*;j6s 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, produc/bcjk( lj t7g2e a beat frequency of 11 Hz. The shorter one is 2.40 m lljg2k cb(7 /tjong. How long is the other?    m

Two loudspeakers are at opposite ends ofrzfn0( rh)8az4udy-+ l0jq d y a railroad car as it moves past a stationary observer at 10 m/s as shown i+r udy zl-4) aqhzn j(0y08frdn Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears 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 what8mj1a 8ihlqg. nl4ex32msj 5 a beat frequency would you expect if 5.50-MHz ultrasound waves were directed almjanaxg2mlq hsi1 l8e. 5j843 ong 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 mo qswkuf ko483 +jioow,k d3t67th 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 the bat after tho 7duwi63kt, +q3fw84okj sko at wave reflects off the moth?    kHz

  A bat emits a series of high freq sf.:t)e)s(pzfz ) mhjuency 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 that the echo ff.ms sz:e)hft)z(pj )rom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was o05jo 6y(89 d(lbct4g e puttrhnce 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 fundamental frequency of this horn, and which overt (god4l br6 5phu(9tte8cyt j0one is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be k3 2,r9 wbk:gn2y zrogo8het0compromised by the presence of standing wave:y nw, kt k9bgzh22830ooe rrgs, 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 the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratio2lvmzgc4. o*a, 56dih t+nvs mn, called “singing rods,” involves 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 2msg6vlc.zv5 + m4t,dio anh* 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 hw i;lo c280osiearing for the human ear at a frequency of about 1000 H 0oi slo28;ciwz 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 obb ,ac:up(;zd rserver on the ground hears the sonic boom 1.5 min after the plane passe b; uc,rad(:pzs directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ea3w9 ,*z2jhhltxnjxl.mi /5 bv*r8g$^{\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