What is the evidence that sound travels 1ba + 3g0 z3,j ,t r30trk7xyqwcmagiyas a wave?

What is the evidence that sound is a form of emfmbs6*p 2v t 7riqj:1i pf:0knergy?

Children sometimes play with a homemade “telephone” by attaching a strin9ur 6ns 8fhp0. lbey5sg to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the soun5bhnf9 ysu.6 ep8s0r ld 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 passe1h qrpx/k:jo5; rq h9+ilyh. nthg:b2vg x1 j:s from air into water, do you expect the frequency or wavelk; :rhx xt2hhqig hjo.+jnv:p l59:/q1 g1y brength to change?

What evidence can you give that the spf61 ;6+ vyz-)av:emrtw vycvcs(nt q- eed of sound in air does not depend significantl c+t(e ;:a- ny6v6vc -swmzr1vvfqty) y on frequency?

The voice of a person who has inhalef2m:gb41n ca sd helium sounds very high-pitched. Why?

How will the air temperature in a room aff. ctn6+ ytcn4 ;(v0ewfvht m+x*ujje*ect the pitch of organ pipes?

Explain how a tube might be used as a filter mnkc-w52hde 6 to reduce the amplitude of sounds in various frequency ranges. (cwh6 en k2m5d-An example is a car muffler.)

Why are the frets on a guitar (a;b h e6h.a4mvrajy21za,it s40mb u,Fig. 12–30) spaced closer together as you move up the fiy .abh4,4arz1u 0vm a6as2 i, bmhjt;engerboard toward the bridge?

A noisy truck approaches you from behindyk 8-)q2p1u9 yjza evd a building. Initially you hear it but cannot see it. kd)-vy2aypje q1u z98 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 “inter5j d*cdox*vitgk88/g 6afd u9ference in space,” whereas beats can be said to be due to “interference in time.” Expltigd *6gdj *5ac8 9/8dufoxvk ain.

In Fig. 12–16, if the frequency of the speakers were lowered, would t+-:inoa*ib4v sq6sk uhe points D and C (where destructive and constructive interference occur) move farther apart or closer togethaksbuoi i6s +*q4v :n-er?

Traditional methods of protecting the hearing of people who work in z, eb02y)yuc,+khhcw areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Insteadk),y02h hcbcw,zeu+ y, 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 canpxrkurr0exv/, y7(/f ho+ 6gd be thought of as a superposition of two sound waves with slrx0rp/6kxdvu gf7 + y,r /oh(eightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in t7/y noc qg rcaa2 .9)c*m)pnqnhe same direction, with the same velocity? c9.rgnmapqn /qc*2)o7y) c an Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a peretluz 7m mvt(8euv3epp 14 2l(son at rest with respect ulept1 pmt3ulez7 em(8v 42( vto the source? Is the wavelength or velocity changed?

Figure 12–32 shows various posindcdo nvyvr/ ,ssf9m063 7/ a* wwbs-c+6upbf tions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A tmrn 9+n/do6,cy6dbvsw -b 03aswp u/*ffsv7chrough 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 listeningpa lpb.gpe /8ugfu zl;99:4hb for the echo of her shout reflected by a cliff at the far end of the lake. She hears the .gluafplgb 48h;9b p:/uz9peecho 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.; im q no73n7c+r.uesf He hears the echo of the sound reflected from n.s7u+ r;e7iocqm3 nfthe 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 wavene1mxe+wm p9-lengths 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 (x fp98eemp c4gafp 0pj0m:g)fm+2yy above a school of tuna on a foggy day. Without warning, an engine +40 cmea:yfy2mf 0(fp e)j8pggppxm 9backfire 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 from5/ i3oqx9p kgeu 5bxk4 the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is5/kb qg4u9xo53exip k the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pb*cz33 ghvc3phowj-9 y .+s6urpn s*navement. +* y3o*vwsh nc3nb9z-cs .6 hprgp j3uA 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 far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rl. 3;c, kuiv efh f4e) mw7pcvtt3oo0*ule” for estimating the distance from a lightning s0m oc )tlife4v tk3.*h7 3cp v;oufe,wtrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soum-c wt(q5tp7o s4uy ;und at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound lel wy/nme-:b(aqh1z v9 vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when tg9; j3xtbur; fired simultaneously at a certain place, what will be the s; rj t3txgu;9bound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cert ; 61pcalux4jgid71llain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would tdacj1l4 p6x7;iugl1 lhis 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 of4w7kn/gvvm. te 1f a7s iym9w* 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 54yn/v wm7* 9kaeg sm 7wt.fiv18 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spe*gsdfq;:*cu3 xjy)p1floz oh2h*zz 8 aking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlz 1jd8 gyco :)ls*2uxh fh 3fzz;o**pqy 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 an eardr5 qj hyuj p*ze)q, 0mv(fz);jnum 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 modest amplt:h9ug/6n sodifier B is rated at 40 W. (a) Estimate the sound level in decibels you would edo/:uth n9s g6xpect 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 p le)k-.yarsz r*9,xvmeter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ,)zr*xpevka.l- 9sy r
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level ofl0)( d)zu1de 6;ieoh lxg qm4b 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this zug i)dx0b1 lol de );4h6m(qeamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wi9yz2h+ hrdw1xx.sq b4ll the intensity increase? Increase by a factor 4+hq2s hw91ry db xzx.of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplilq-,oe .2ycnztudes, but one has twice the frequency of the other. What is the ratio of their intensities? l oy-.2znc,q e  

  What would be the sound level (in dB) of a sound wave in air thae d7jp1jimo8+. 9szvx:j lavc v:k.g0t corresponds to a displacement amplitude of vibrating air molecules 8 v7po0s1zim:vlvg.:cjx d+jk. a j9e 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 tonesoq ( q2:jiy,j that has a 50-dB sound level(: joq2si y,qj? (See Fig. 12–6.)    dB

What are the lowest and highest frequenciesb1a 4no3 +cwdq that an ear can detect when the souno14a3q nc wbd+d level is 30 dB? (See Fig. 12–6.)

  Your auditory system can acv9, fswh 6u3vtcommodate a huge range of sound levels. What is the ratio of highest to lowest 9shwu,f3 tvv6intensity 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 Hoyot*dv4;n71h, rph e z. The length of the vibrating portion is 32 cm, and it has a m 7od41t;ny pv,ehro h*ass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm ls* 8d6 wi(c+ akl)xma d( mco6fclx0)long. What are the fundamental and first three audible ovd sam(l *0+ x6om(l6 )liacdc )cxwk8fertones 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 wouleiep+4e j4jxg7o-i 1b d you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you a b441ij 7eop+exje ig-ssumed 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 opekgnj /1+25 .ufd*7 ymbkho smfn-tube pipes spanning the range of human heari /u m* 1kbh+ o7smfd2jnk.fg5yng (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-z40: gm t kok,ynu.ta of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onlku.,40 g:ttk-myz ao ny 60% of its original length?   Hz

  An unfingered guitar string is 0.cz f v2;kt5,g8tx,umn +aqlt; 73 m long and is tuned to play E above middle C (33f;,mlcx5ta v utt2;gz,8kq +n0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middleu+(p)kgqex j )+;tant C (262 Hz) when qg;+ p(jeaxtntk) u)+ the 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 at 2fbb33naxq5( r3vx98kxpzq* b 0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12 9sechp gb/t.yi0j2 xb;g22ej–10 should the hole be that must be i 0gteg9hsye2j2 .b/ x;jbcp2uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 H-8*evqjn 4:j mx 6mirnz, but not at any other frequencies in between. (a) * jm :4i8j-nqrm6nexvShow 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 lo :(hs6unx xep0ng is open at both ends. It resonates at two successive harmonics of frequencies xnh0p :xe6s( u275 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 ue3jm -oz31,g 6mh psi$^{\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 th-w jvp.(g pep/e audible range for a 2.14-m-long organ pip.p j/vg-(p wpee at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm0noieh39e4:g *k hk8v/o eolsabs1t- long. It is open to the outside and is closed at the other end by the earde / ebl *os:i hk13gvohe9t-oksn 480arum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears og1+n19f vwuknvhz (e, s+ybo.j(*ud cp-: hbjne beat every 2.0 s when trying to adjust two strings, one of which is soundiy zuuhwcbn,-v( khogf1 e.(v+dp:* b+n js91j ng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and i udh9pjx7-yaa ta.gb/p0(i 4 qw0e4c $C^＃$ (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 (brand z5 p5umr1iq4uqoj+bu.o3;ne*wu f o 6X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill woi.nb;mfuoe65 rw5 j1uqq3+o4 *pzuuhine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded 0we;*17yg ga jleham1with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrationa;ewa01y*amg he 71jlgl frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to thy6*rsll:d5b guvq42t e same frequency, 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 tog5t s:g lru6yb*dlvq4 2ether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identip uck; .dw2r7bcal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.;c k7 .dbup2rw0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequengl.1bm c kxj/(+urif6cy of 441 Hz; when A and B are sounded together, a beat frequency of 3 H+ lr .jx/bc ufm6(1kgiz is heard. When B and 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 stands 3.00hq+t f1k7,frwy/jay) m from one speaker and 3.50 m fr7yrfw1t+,qfjya h) k/om 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 vibrf *smk9h;pw 8iating 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 132 Hz, what must be the frequefswh*k9 im8 p;ncy 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 wavelengbbzf*;t-y((,rd *syx od-es2v 1qikz ths 2.64 m and 2.76 m in air. How many beats per second will be heary*;,z f szr-o2(sdkvt(xbbe*y 1iq d- d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequxf52tg;6zxqf bs)3w k ency of a certain fire engine’s siren is 1550 Hz when at rest. Whak z6f23x gbx;t)sf5 wqt frequency 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. What fre8z5f )l,8qif/d ejb tkquency do you detect if a fire engine whose siren emikl/di b8t 8, )qeffjz5ts 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 source is mn8-hap8gzo0yjn r 32nx)z2a e oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close2)njazz h88y0n3gxra- peno 2 ? $f'_{source\,movine}$    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 f3t 6 6tsxgvl,rrequency horn. 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. g xt663r,lst vWhat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends or ywy5gz e-v;8ut ultrasonic sound waves at 50.0 kHz and receives them returned from an obj5w -ey;rvgz 8yect moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward ae1b it oj:t5 rkxu-5+l wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.015 u-ko:xit+ rtlbe5 j kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp h* g8xnh0qah(ler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached thnh( 80q*haxghe station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wa /pa +66bxbglrves 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 flowing in large leg arteries at 2 cm/s directly away from the r6l /+gbpb x6asound source?   Hz

  The Doppler effect using ultrasonic waves of -e5msh.*hw(e kx z:s xvc 4pj*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 frequency 570 Hz. When the wind velpzuk*vq4 )3ri-i4xaa ; f ma4;bleva4ocity is 12 m/s from the no4*mrzkeli a;xb p; uav-)q 4f3 a4via4rth, 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:y+27 j qkxy9be fw;yadu6,z n 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/ gt7l/i mxq 65p:r2zxrs (a) What is the angle the shock wave makes with the directiozi 5lxg2:/6mrr7xp tq n 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 spti7/pk : yp 2mc0ha id-o/(rbzeed of sound is d0c /p m7-p/ itba:i rh(yokz2only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine -a*bwpw1sj4.n- l zbethe shock wave angle it produces-j 4z slb. e1ap-*nwwb
(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 /f xwm b +76wklrw-z)8yce;y t$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhnqkg3 e rqk;+7ead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. Seq;ge37r +k qnke 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 sou 9dd(rq9*; djg qexu,wnd pulses downward from the bottom of the boat, and then detects echoes. If t re9qu,(dqjw 9d*;xgdhe 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 octaves are there in the human audibq k ec*fqvz7jr+9h, -ile range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called 7* :u1zgzf3hzktr hz2a sewer pipe symphony. It consists of many plastic pipes of various lengthkhz:1tu 3rgz * 2zhz7fs, 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 m:9 bsi bbkz47)uu0 lc4hn(l afakes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? zb7ilb:( l 9achbuu0ks4f )4n    dB

  What is the resultant scra9 hlc;o* q:ound level when an 82-dB sound and an 87-dB sound are hea c;r*9qa:oc lhrd simultaneously?    dB

  The sound level 12.0 m from7rn/npz +i)cxd)) hx u a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all zxnux7+ p) )chrin/d)directions?    W

  A stereo amplifier is rated at 150 W output at 100hznn 9afo.0py( .*nar0 Hz. The power output drops by 10 dB at 15 kHz.y9n o0a(zp an. hfn*r. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices lnfew 2l-*g.x* n7w8mjnb ,pvover 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 interceptedw2x*-el,*8v n7. mnp gfbwljn by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communi i*qcb./ jr+w(;j myrkcations 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 freque osklmi9 8zy12ncy 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 betwd8/jjq1/jn loeen fixed points with a fundamental frequency of j18j qnd/l /jo440 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 vibra/ s:5gu-iv25zaj*/wffy u yixtion above a vertical 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 yu/ 5 wvf:*aszxuiyg/if2j5- 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 string of mass 2.10 g is near a tube that x0+/ o4tj9d v8fgzqoq is open at one end and also 75 cm long. How much tension s /o9x tqdgf 840qzvoj+hould 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 observed to resonate as 01h23:8hbs ym ditzvy6 -arxs 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 from hskea 3apnr;z1o8( 019 2qn nrdt/cis two sources. The sound is loudest at points equidistant from the two sources. s ne83 rc/s11inkzh(r0p;92aotdqan To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is sq) vnu deqlrtqb31c t9 -;hc6*tationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. bt 3v)9qt*;ed-r qcqnlchu61What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approacheus ycm )r:g7el*ionyr . c3;6is you is 538 Hz. After it passes y ru.li7*y;oy 3neg:ci 6rms) cou, 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 spe72r 6 ybunpw6 yqa*se bia16:zed 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 drops by a full ocb:a61ryywe7iusb2 n 6 pa*z6qtave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency osla.;;o a7ta)tc;cpbs 6yh;kamo ,;nf 11 Hz. The shorter one il oasm;7 b);s, ;kca.6ac nat;hot;pys 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroadq7tzbpfma3 0y 7 7jr )zh:eia, car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of t77fhmeaz q 7a:b j3yi0)p,zr212 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 normall9zqv2cn 6o;d hp. jx7 edf0jk;y about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cel;0o;2vhe6 dxd. jq9 p7nfkcz jls? 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 mothlssm8t0g-a4 d is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. sgmas t -d0l84What 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 frequency soueef*cguu:v,6u8 zdh3d s )q,kb2 x6zh nd 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 from one chirp returns befo2z6uh*)hds86u qcevd3u,b f,kzge:xre the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used t )gztw vt7)gkd.8j-mbo 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 overtone is close to wj.m d7)gtgt z -vk)b8F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be cr .vqbm2 o)x.gz cs.-hompromised 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 standing soqxbz)r-gm .. h 2cv.waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, c ,jnwoh )y:+pzalled “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. Wijoh:+znp y,)wth 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 ofj.h - eq4kmhgy :t9ic7 hearing for the human ear at a frequency of about 100hm-9kg4. j7:ehctq i y0 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 vml, :nnu6ny0fx;iv . at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alti;nn,imnxy. 6:fuv0l vtude?    $ \times10^{4 }$ m

  The wake of a speedboa gz22 :ifg6svlt 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