What is the evidence that sound traveljajgyf,q1 x4yy.jx(:s as a wave?

What is the evidence that siaj np( .vpe1rkh-(b .ound is a form of energy?

Children sometimes play with a h8(,w7vt qq m y.djh7rjomemade “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 travels fromdm8vq 7ytr wj.hqj(7, one cup to the other.

When a sound wave passes from air into water, do you expect th0q.un0 t) t xcbavk 4ro fz:6dh0n:xhq0e1 ld9e frequency or wavelength to change? xl a 1q :46r ne0xzn.)0bhvkhttoudf09q 0:dc

What evidence can you give that the speed of sound in air does not de oz zcm/;izxv)j;7y 8gsgw 4q,pend significantly onoz ;js)7c gmqx,ig/wyvz;z 48 frequency?

The voice of a person who ha64k(esr,pr3r(jz7+ p nr pmy ys inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgas(9- eboiqzcw(lte gaur:js6q:f1f4mx-6c * n pipes?

Explain how a tube might be used as a filter to red vjq q:2s eibv4q(rs8 mqz;*,wuce the amplitude of sounds in various frequency ranges. (An exampzjw v:qi2rb8qq*mqs 4;e ,v s(le is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move hy (u8ky,e:ivup the fingerboard toward theukiy (8vh,ye: bridge?

A noisy truck approa 2nvii;mwf: l:.s mp.jches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddejniw:.sml2 mi:p.f v; nly “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,” where rh.q 34p dqrj,wevl(3as beats can be said to be dv,e 33r wj4phrqqdl. (ue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thej;wbd8vem s:a +4l)-nj9 uh jg points D and C (where destructive and constructive interference occur) move jjgde lba)hv:jm 9nw+ u8;4-sfarther apart or closer together?

Traditional methods of protectingx5ddmi9c3o5d 3 gukc . the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block5ccdmio 3xd3.g5d9 ku or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which 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 of as prk; dn,44gje a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (4nj;d 4rkegp ,b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the saqc2qm4bp k/m -me direction, wi2kpbcq4qm /m -th the same velocity? Explain.

If a wind is blowing, wi ;kx/ * i5t,z+boaczasll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the waveleng /tz+ax*sk5cz ia;o ,bth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.puwvwp jyg1(ryk63m7 /gs g 2, A monitor is blowing a whistle in fronj 3p(ugsgkpy1w2 wvg/m r7 6y,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 listening for the ecb27( a a67evat9n op;azwrwd7k , o8moho of her shout reflected by a cliff at the far 67 onzaaavr7pokw ;2o8 dm(b9at 7,ew 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 sd2)t;ghm ev e5 uw+3eaide of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table )m5d2;hutw 3ee+aev g 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air -5b)8 r2kjpc q cr7dlet+py0mat 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 ju,q1pw:x2z; . zz(52riaghx hk aejbq1st above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another bo a5;p h2zqh:z(21,biwg1 qjxkrae.zxat 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 cliffjd ta*ueei. ,qj -5/qy. The splash it makes when striking the water below is heard 3.5 s later. How high is the cjq- u*.5 qaj,/ityeedliff?    m

  A person, with his ear to the ground, sees a huge stone strike the c,q lu/ jiu/8hboncrete pavement. A moment later two sounds a qbi/uju h/,l8re heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of disqk dgh7l;j: m7stu+m ;tance by the “5-second rule” for estimating the distance from a lightning strike if the temperature tdu mk hsl;g7m+;7:jqis (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at p1.ccfrijc9 qj9 (q+dthe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ofri5t h oi6nw)h q)uz:, a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired:c*t/ icrh aqmhv6(i s*4:(;snl a xck simultaneously at a (lsn/a4*ikhsrcqm : ( 6axc t:;h*v iccertain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista8pgd95y4 jle u *gvfu0n /7jzgnce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on gf jgd7zg* jp/540e luuyvn89pain, 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-noise ratio of 58 dB, whereas9-)vmxty 3 :whecxjb , for a CD player it is 95 dB. What is the ratio of intensities of the signalh-9y:),wvxc mxt bej 3 and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou hp)9mljigv/ )tput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound sprj )hl/v) p9mgieads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes av5-(bf,g k m.lb,acc/9 ksskhashw - -n eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W/xz.dec cy+yf: p.,h64a hzdo, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m f :cd +o aczxe4.fh .p,z6/dyyhrom 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 registeredhfi ta(: vjd4cw- 5yv3 130 dB when placed 2.8 m in front of a loudspeaker on -t: w (hvi35jya f4vcdthe 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 typicallxu; hjloz mq:* mtx8*;y detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffmq th ozl:;ux8*mxj;* er by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the i lx(umr 7rm8;kntensity increase? Increase by a fac mr;r l(k7um8xtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twshwbv wm zzg+;- dp0 sk.ywa7/eu8e2/ice the frequency of the other. What is the ratio of their inta wp02w. +ge mhbz;kvse/ud8-y7sw/ zensities?   

  What would be the sound level (in dB) of a sou e3/qczyew 9 qzosb-5*nd wave in air that corresponds to a displacement amp*5ce-3 /z9zybqq ew solitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz ton wkex*1ok*4f xe that has a 50-dB sound level? (See Fig. 12–6.*fxex41k*o kw)    dB

What are the lowest and highest frequencies thaz *skpzt1w6x; ezfv2/t an ear can detect when the sound le6v k/w 2zftzs;zx*e1p vel is 30 dB? (See Fig. 12–6.)

  Your auditory system cao7i04 kayxkt; zx48jde8l g 5ln accommodate a huge range of sound levels. What is the ratio of highxd8goje a7yzki5x4 l l;0t48 kest 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 frequen9, i;xgddy 1 t6cu+mgocy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what t d ,9;tmgduy6cogx +i1ension must the string be placed?    N

  An organ pipe is 112 cm long. What are f5vifv5i :s, 6d dx,f5*ixgkcthe fundamental and first three audible overto,*d6 ,5i vdf:if5fcxg sx5 kivnes 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 from blowing across the top of amgkjo1ur g557m0v;bt n empty soda bottle that is 18 cm deepgjm1b;7 gmo0u5tkrv5 , 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 oplxl nh/e4 p6) rsqb14ul (unk7en-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes rel1)k4 6lup n7x(ner ubshq4l/quired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third 6f2 j:3lakroj harmonic. What will be its fundamental frequency if it is 26okarjjl3 :f fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mid0d ( ol5ce+8zmzrf7k8 g2 zlpydle C (330 Hz). e+zg8ocykdl5 278 0zrpz(l mf
(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 emi rawa *rz xnz323dza4/ts middle C (262 Hz) when the temperatureznz33*4 d/rzraw xaa2 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 20tbu0gnaw -cab;k2u( *ya,w))fk .aq z $^{\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 5v;znse. ( kmh12–10 should the hole be that must be uncovered to play D above mv nme( z.shk5;iddle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, bux8 soy )nhor5irjou o f951-jcd*35bdt not at any other frequencies in between. (a) Show why this is an open or a closed pod9)j* u8b-s5rfnoo 5jr51xcd3yo ih ipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 7r jwyfo99nmj7 xda::m long is open at both ends. It resonates at two successive harmonics of frequencies 275 H997w jyn::rjfd7 amxo z 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 2ko1r 9+m nlaeaqeuw7v :oy3o t- xu31$^{\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 lhstg8.-,hk9 vcv9un range for a 2.14-m-long organ pipe a, nkvhlvcu -9sh.tg89t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a1)zfmm x +:ryu b87gvspproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies b)vmx187rz mgfs+y:u (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, o0qk:z6aq /tm6ksvo ko( svq 8+ne of which is sounding 440 Hz. How far ak :( q8zq/q6skvvm6t k0s+oooff in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and m*jno.3lk-l rwff wj);ecn (+zsf: w2$C^＃$ (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 whistlews z:f,0dgyead8 daq .s l14j7 operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency ,a1sq:j4dw d lge8.afd 0s7 yzof brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork anojnt/ /p 9i z1q,yr:jmd 9 beats/s whenq:/i j9j pznym,ot/r1 sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension idbug)w x+* j sp hxe5p(/f2r+ )gonfw)n one string is then decreased by 2.0%. What will be ther/n( f* we) f)j+xg godpu52bhwpsx )+ beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h bo-s ioalpm93ghz 39-eard if two identical flutes each try to play middle C (2 g-mio-33obs9hl9paz 62 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninrm ;u9d(8eh yvg forks, 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 ;v em98h( rduyand 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. A person standslihmbj m/* 8* gopb9)d 3.00 m from one speaker and 3.50 mi98 m/p*mjg dhbb *o)l 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 vaped -zk bez** e p/31of;;yube vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when-pz eadv*keboyu e;*z1p;3/f they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelen4micu :u(gm dfv3t1 0ogths 2.64 m and 2.76 m in air. How many beats per second wi:m 3movug t0ci d(1fu4ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certai u6yp(ocpymfg v5)1 h*n fire engine’s siren is 1550 Hz when at rest. What frequency dom(p56upy f gh 1yv)o*c you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whos*fy3glawxs 2t -y4 )t6tu gyq(e siren emits at qu( ts-xtt g fy4)lag*y3wy26 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencygus ;l9j- ye:vt.jom+,nd3 eh if a 2000-Hz source is moving toward you at 15 m/sen ;m-h 9v: ojet.dg3u+,ljy s versus you moving toward it at 15 m/s Are 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 single frequency ho4o6+ie*wvx *jc u cf;crn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What wc c* +xoceu;*jvi46fis the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kH8ux:gedem(xp: eo c) f0t426bw5z jmdz and receives them returned from an (d e::08z6mgxu2 b4xe mw 5jctp)oefd object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emi +i *uz*jkp;kg/kr.p sts an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear*pkz pg.sku*+i jk /r; in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movi8oq bzw3ze2; bng flat train car at a frequency of 75 Hz, and a 3e;wbb8 oz2qz second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to r y-,b9 981q- 0:lkc2u vltflmgodlj imeasure blood-flow speeds. Suppose the deviro 9b yljv,8t 90c1i2luflq: m -glkd-ce emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso9x d:rk r0utvn)r,gz1nic 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 sound of frequ6xzgnl1 ai7se82b.lkjo5 l 1 eency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hnge1 l5. 2lokijz l6xas1 e7b8ear 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 objeckd,ex: odn7m) t moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (7v7nrq 0e,sl za) What is the angle the shock wave makes with the direction of th0r,lzev n7s7q e 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 t8m p83 4m:grne3wn.gkh gv :-y/zshosf.msf,he speed of sound is only about 35 m/s r hgno48smf3s8,-s:/gz .yv.ngw3phm:k ef m
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the oce wgo b.u2bae; 9fsacr 5i1(-tyan. Determine the shock wave angle it bg5a(y-1ibcu f 2aewo9st ;r.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 2dpe37)gss cs. yy: ns$/theta$ 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 1p pantd(ecc0c42r78 g .5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizonta8 p2pt0cad7ge c4(nrc l 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 kk6nc c ,-(;nag,z mansonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, wha( g -amn ack,kzc;6,nnt is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are therp4jyl /pv(a 16gij0wme in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called 1g :gcxx7 /g.k quhn-ba sewer pipe symphony. It consists of many plastic pipes of various lengths, wgckh .b q-:u7g/1nxgxhich 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 soqk mw1vat2:k(icm3 qv dl,99wund close to the threshold of human hearing (0 wmi9,vv(k 2 qdwm 3c9q1k ta:ldB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound andmtty9+ap)ttw/ .: pd (x4fzvd an 87-dB sound are heard simultpty/p (xwdzvf:)+.ma t4t td9aneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. 1 mq2ub6hh8 osWhat is the acoustic power output (W 1uh6ombhsq2 8) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated 6lkc-; mkceauclhky4f391x,at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHzmccl3 ha, ly14k6ku 9k;fc -ex?    dB

  Workers around jet aircraft typically wear protectivrh *07wsp1gnp;k vr)pe devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has a*wg;rhr7 npppv1s0)kn effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatoij-pyr1ds: d5k-e m; ions 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 tuned to a frepu+:vqn+ 7m v,ald4.gz8tc uqquency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with9xjv 5uozt, ;,2fss gvldi2(d a fundamental frequency of 440 Hz and a massi22 9vxf,v5 t,dd sl(;gsozuj per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wit8ebce18xy+/a i 97d/nfeu ywzh water (Fig. 12–35)8wizn/9 8fdxb/e+yu c 7e1aye. 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 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 strin) okjf8b7ltur:i8,y xg of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should yitu8)jof r 8 x7,kb:lbe 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 observed to resonatu81hurbnq e2(b v,,nne 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 ran fg8z/i(zs v+/bg;:tlai k/ dwge 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 othe:l/tiz ba(/ wv/;gkgsdifz +8 r. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train iu suh.x6cjp7s4 9; wnrs stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appcsn9 x w4psuurj.;6h7roaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hzmv io54y,gj2q . After it passes 2vojq i4m,y5gyou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to 8 uh e:1)hswlt,u:)o- o vos/b(omstn the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound ob:- he,u )(o)twu s sohmtosn/1o8lv :f a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, poa +/v.p7aa frroduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. /+fv.o7paara How long is the other?    m

Two loudspeakers are a csdcw: t/a t,8eo*4hat opposite ends of a railroad car as it moves past a statiact8a/ ch:4*wtdos e,onary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.2ak* ahcf9- qsgn;ttl;zx mgz:9j.-r32 m/s what beat fre 2: hzggscmf* 9tq-a-; j;9t l.arkzxnquency would 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 whivyd.(fad )6 fdx9;nwele the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectey); .9wnf(ax ddd v6efd by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high freqgisxfc:,wpg h*y9s/ 3)ab92v 9nsdrmuency 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 fro3/9sa *fg,y) dmvhw2: r b99 sxgcsnpim one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ot uhj v a j6ks83y6+-sm+ ;k3bhr3mjmyne 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 tb-a3umtj +h633j +mhsyrm k v;jyk s86he 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 compromiseu03kcr d2dd1 xd 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 for the standingx2d d3rk1 ud0c waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long ,tuq pr6:7dhz x2;uu-rv+ gfj, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other han hu:u6u2- ;pxzqrj ,v ftd7gr+d. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the hum.t wsw 3 zc0x1qhxy+cj+ -h6rlan ear at a frequency of abohxt-q x3chcy+ 0sj61zw + .rlwut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer onpntqq(u 2 l91v the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What vp1 qn9q 2u(tlis the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo(c f+p2ko) dtaat is 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