What is the evidence that sound trave(at1h5lyy vh4gx( c;pls as a wave?

What is the evidence that sound)jf/2 j psjjvlg1az q;:w33gm is a form of energy?

Children sometimes play +r sknb3d7hlrx9 -*ly with 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 travels from one cupn 9*sdh7yrl xblk+ 3-r to the other.

When a sound wave passes from air into water, do you expect the frequencdig+j(7w5 ci uy or wavelength to chang g +c5ijiwd7u(e?

What evidence can you give that thewys ,v7/-b y(3js tkck speed of sound in air does not depend significantly(v,7j k-b3 swsyyt ck/ on frequency?

The voice of a person who has inhaled helium souzm sadw9:t (u(nds very high-pitched. Why?

How will the air temperature in 61atq3h0htw0 z*nq d ba room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce tbi4mv1 i 1)oky0h+pra he amplitude of sounds in various frequency ranges. (An kyhp+ai10 oir) v 1bm4example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a9vygd j4.n8ka0ij0x5*ue o8 b wik5 aas you move up the fingerboard tow4o9 a ani8*y5ve j8k d0gk x0ubjw.5iaard the bridge?

A noisy truck approaches you from behind a building. Inixm7pr) sk40y8w e:rmz tially you hear it but cannot see it. When it emergrswk x zy0rm:)8 p7em4es 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 saiduo 2vkv +ca17qh i ht:nn26kz9 to be due to “interference in space,” whereas beats can be savh 9cuo:a6t2v q7k21nhkn +z iid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,v3zfh,g9i-k x would the points D and C (where destructive and constructive interference occur) move farther apart or c3vxh ik,gfz-9 loser together?

Traditional methods of protecting the hearing of people wh xu1xkxa)anjf8i7gfy 01d t)( o work in 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. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise.)f(xk gy1tix 8u7 njx1da0af) How could adding more noise reduce the sound levels reaching the ears?

Consider the two wav0w1km/iidv k1o aq49qzywvdaa wrv ;qw- 4 ,07es shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component freque4y wdo r7wvk1i-,1 m0aa;v0v4 wiawdq/q 9qkz ncies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and cuu*bleypqb7 d0 : )*dobserver move in the same direction, with the scbu qdu :*)db7 elpy0*ame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heardw1 yc;:mwet (t by a person at res ect (;ww:ymt1t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions c i8(xyrs6xbct4 mx,(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 through E,cx6r c,x((b 8yixms4t 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 echo of her shout mu+oecngu4 b3, .mo8vk3r 1fo reflected bmuc n.3g+ouo veo8 13b4m kfr,y a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. kybvn,0r 3vi.qex6lm.qm8 ohuw2 43fHe hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the.vumrx 8e vob f wnq3q2k,y06hi.4l3 m 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 wavelf7be- hn s3. zwvnez70engths 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 above a sfx 8.z).9:tza k wkgsqchool 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 9fz:kwtsx .8)a.gz qkelapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when stritbjun4vq:zamb8q8:ie:0k 6mh d1kr4dyk+f 0 king the water below is heard 3.5 s later. How high is the 41d0:88rkfm:b6un bh+4i dykq:tzjvqae km0 cliff?    m

  A person, with his ear to the ground, sees a huwz jryq;d 2r12b;u;x xge stone strike the concrete pavement. A moment later two sounds are heqdj2bxrz u;;x y2w 1r;ard 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 rul)ruz;ac j1r29j spbz,i uj1: le” for estimating the distance from a lightning strike if the temperatura sj9 b1u :21ujrzp,cz;ilj )re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity oa5ixj 5/ 1yf11fu arkdf a sound 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 level of a sound whose in wohh; ;l-j3 (yaz(axmtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers ;a. s-f0wzcnf9a9lx8suska 8rnjd)6 produce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound leds;jfkr69) a.u cslxfnn9z-8aws08a vel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fouk f35e7p8xn/ k)rmsc dr equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would nkc)x3 se5k7fmr8p/ d 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 f84dc05 p+ hh1r oe/dr pofu(d+0dvmohave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiesh1(4c8 o5m hfp0ed r+v+orfodd pu0/d of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fx6 jwzy ze9i65rom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly 5wzjiex y6z96 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 an uph4.il u0 n3beardrum 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 8v a x/(cjft+h t,5w +vf.1jqfmqxm-v amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each w.h+v qvfj mvjtf1xx,/t5 -mf+ (8qcaamp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in fr arh3j2q lv2/1xzr*enont of a loudspeakervjnq x2*r/3 z h1a2lre on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What.h4p9jb( vtyr is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hin4.(r p9hjtbvy t: See Section 11–9.]$\approx$   

  If the amplitude of a sound/q(mfz (.2qcr k ,lfjl wave is tripled, (a) by what factor will the intensity increasjr/f (qm 2z(clf,.kq le? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bu ysh2h( t s+8prawl( whs*c:1st one has twice the frequency of the other. What is the ratio of a 2p:1s hytc+h*w l8whss((sr their intensities?   

  What would be the sound level (in dB)),l:f 0;h 0zeuazpl7s jl4 p9br h1lyy of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 sa1lpbh49)p l7fyzuje,ry z0;:hl0l Hz?    dB

  A 6000-Hz tone must hi+lc2 d 0*qbuzttp-k.n4ll -kave what sound level to seem as loud as a 100-Hz tone that has a 50-l t4c2nb zudip-*k-0.tk +l qldB sound level? (See Fig. 12–6.)    dB

What are the lowest andjb0fy /3eymx: 6rldpy1 /4rnr highest frequencies that an ear can detect when the sound level is 30yr/emdry34np1lb r0 :jxy6/f dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lev:n9v03)tk pc fb. gr bxz+ntezvf 4/v:els. What is the ratio of highest to lowest intensity atf:v g.nt c tkn 4vzfr0)9xe/zbpv:b+3
(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 44og wm bzgq6m+:3tap* zik)a/6 0 Hz. The length of the vibrating portion is 32 cmw6b gzma*i6qm+k3)pt:a og /z, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firstk.k+ l 1.x pvb(llyq i03de)ba three audible overtonesil qb )a+x0 k .edv.pb1llk(3y 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 th(4 sx 7aky s6hgt*a(gxe top of an empty soda bottle that is 18 cm deep, if you as(y( xt7* asg6ah k4xgssumed 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-tube pipes spanjs0 bnj pkcgm1v132kl/0k7s b ning the range of human hearing (20 Hz tos/s1c bj2mklg p1kkbv70 03jn 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 frexfjkj4ojs-+ b.z6 gfl+ j x5s:e9nhs:quency of 540 Hz as its third harmonic. What will be its fundamental frequen:gzjs6l.9fj j5j: +4neb sfksh - +xxocy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.6d yc( m*e;2 9wjsi+tsbva;05rb ai wb73 m long and is tuned to play E above middle C (3bt69sdbe(c b+;s*m5a0wiw ij2;v r ay30 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 middle C (262 Hz) w+kt9fscta z 6;hen t; tsftk 9c+za6he 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 20n7/0jua j5 fzp734g o ir/cxhyll .v)u $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute bx3r0isft7i)re(ohbhe1k9r0 v7c klv) sc/ 6in Example 12–10 should the hole be that must be uncovered to playv3 7b(ihb06rhlk0cier sk)xe7t c 91 v)sfro/ 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,;jkk y/vaz p+ Hz, but not at any other frequencies in betweek yvja/,k;+ pzn. (a) Show 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 resonates 8htnsiphx 2 :7;a q0nlat two successive harmonics of frequencies 275 Hz and 330 Hz.i8t27nah: ;pl xshn0q 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 j6(ngt: d6xeyhz g/i4n/ my4 .jq7vsz p6,xa b$^{\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 audib/o(ppfj ye 64ile range for a 2.14-m-long organ pipe at 26e/4ip yfj op(0 $^{\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 outside ard;yo /)zh(oi-5vtkrd l(fo 5nd is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing rkodzo;((yrtv5 )/ofidlh- 5 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 tryy+s+tlz cgwpd */0.8 pel zza6ing to adjust two strings, one of which is sounding 4 cdszt/g z8p*6yz+0l+ la epw.40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (2/jf+ tut axtq7/n7:wp6. evkv 62 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 (brand nr1 70,iuew i;7sx4p ;d ssooyX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occ nps7uwo,;1si0y7oi;e4r sxd urs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s/ 11fwitl kf-a0nb)sq when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibra1n/bf-l 1f iwkstqa)0 tional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned x,b p8 gj:j8lwto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency he xjpjw8,:g8l bard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flute0dvd)tr e ;qu+s each try to play middle C (262 Hz), but one iu )e+t;drd v0qs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency-c 2f0:c1dm2 shu a6iqwz spek7v1k2c of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are th 0w1k: zd-m6 he 2cik72 apvcsf1quc2se possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m frof y*2l-cnv3:q:n5i6gnnw chkm one speaker and 3.50 m from the other. nvn5ngl nhk*32: wiq c-:cy6f
(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)axpr 4*j-6 vkun f(oh be vibrating at 132 Hz, but a piano tuner hears three beats everyo-nh4*v kx 6r)fju p(a 2.0 s when 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 wavelengths 2.64 m and 2.76 m in aig*bl. 9:j6.ogvt; t4 y nvnkjqr. How many beats per secon kg 9ntj bqg;vnvjtl. 64oy*.:d will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f t kfvuv i25n9m2 fmd pg1*nsz9()-wozire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed ofsp (z kizmo99nmg )d f2v25-n1*v uwtf 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequenyr5 q h1hu5(sucy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 (sh r 5uq1yhu5m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourg;/dd 7t:ma 8-wn xgwxce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they 8 ;d n7-wtdgxwxa :/mgclose? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When on7 he6aqn()ce9 oq9idre is at rest and the other is moving toward the first at 15 dq)(ercn9 769hieoaq 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 sound waves at 50.0 kHz and recei /42s vm,ykkdxhs ybg4 +lu98z2qne9 uves them returnedyb/s2uvh sq94 +e dnk2,yu g9 4kz8lmx from an 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 spee0 ( :.wsvm:p r3 gqx),5hrt xsu1iyww96x njwjd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does i :3rhsn j,.(q 0tmy xp:sg5wjwu1wv9)xx r6w the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mec9w(l3 xmy,ns x4.yyoving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in nx my3.,xsy9eyl4c( wthe 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 measure b n11.fbf gps4bj,euz7lood-flow speeds. Suppose thf 7gn4pz fbsebj 1,.u1e 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 sound source?   Hz

  The Doppler effect using ultrasonic wavod f wni,;b75yes 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 frequency 570 Hff ( k .evzdc7ynxfi1(/x82h zz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, ec72v f(h.d1(/ fy8i kfzxnz x
(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 itshprhm a* 4/f 5ij6tfzc j;4t(n 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 +i*op)-bccq/- l. r da:v zuehof sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motiauvche .ilpr- qc+):zbo-d* /on?    $^{\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 b4gx3- djq,r vsound is or4vgdj,x3b q- nly 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 stxq,mg2s3jf du(,s( t8q jesg 7rikes the ocean. Determine the shock wave angle it producej qs32,tj qm8(fg dsu, x(ge7ss
(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 z )(8mgkbs ls:tby11f$/theta$ 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 1.5 km above the nt8 0 lrm25omaground flying faster than the speed ofm8om5n l0rt2a sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,0- 2t+ feq7nepsnse-s /00-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed tof+tss2e e -nsqp/ne7 - work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many 9zr8a2er rsxjwpc:rv/.9 - zkoctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal:ng+ z 9d 4pl6kjvh*fdqof3. fled a sewer pipe symphony. It consists of many plastic pipes of var fp4d: +.kdf fqvjgnzol3 h6*9ious 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 5.0 m from am4jokls4u 8 z- person makes a sound close to the threshold of human hearing (08-sumok4jl 4z dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sou- r2x -3homiacnd level when an 82-dB sound and an 87-dB sound are hear r-- oacimx32hd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What wfbyp1 r ./dg3is the acoustic power output (W) of the speaker, assuming it radiates equally in all dg1b fwy 3prd/.irections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpu ,/ heh e,mnch9.j3khtt drops by 10 dB at 15 kHz. What is the power output in watts ak,nm h.3he t, 9e/chhjt 15 kHz?    dB

  Workers around jet aircraft typically wear protective)smet twww*- .r h;fs( 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 a f;.tts)ww-wh(ms e *rverage human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications /j(v *c-oe a4f/ja i3m:yjceq 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 at 23z3i)wu x1be yvkd/ 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 violi)qiic;x3-tua 6+ x lwwn is 32 cm long between fixed points with a fundamental fr6wwauil- ;ct)x3+ iq xequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wategd nke9u2a2raj 98 jq+r (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 tu9dkg 2q9r8jena 2j a+he water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one end1oet (1ze ja4z 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 thirat4 ojez (ez11d harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lot2 j/*yh4iep 1 cvr0 (ishtlf0op ($\frac{1}{2}\lambda$) 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 cos2cj8dn- ea- orv:w f4ming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person movj: v-842oaenr-cdwfs es 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 stationary. The conductor on th3 t d-ncn e59yd7l(ckce sc9-k 7cndyd5ne( tc3l tationary train 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 i+h0 1yzki9* fv xp-ig5r7q3ia gbzi: whistle as it approaches you is 538 Hz. After it passes you -vi3+r1zi gh 5qg*:iy0k7 iba zpfx9i, 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 th4 cn* ;twyaf68ka,i oge 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 drops by a full octave (frequency halved) as it goes by on the straightaway. How fast ; 8i6gn,ytow 4fk*caais it going?    m/s

  Two open organ pipes, sounding together, produce+c w,wpw9j ttd3sp-a: a beat frequency of 11 Hz. The shorter one is 2.40s j, 9w 3w-p:apt+wdtc m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad t1wd(.ftpfg. *yrl4 wcar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the obse .(plf4w tyr*twfd .g1rver 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 agz a 36m*i960r ask(icf)tigabout 0.32 m/s what beat frequency would 6 *m(g90f r6ciiz ak)itsga3ayou 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.y3uk1 bo)s+qqvfh: /itcur- 85 m/s while 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 detected by the bat after that wave reflects of18hou-sry/uf :ibkvq t 3c+)qf the moth?    kHz

  A bat emits a series of hr+x8ib*nou.ll+, htln,rj4 xigh frequency 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 .ht*jlr,+, xiu n84 xol+rblnecho from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals avj d6m.y2o (zfrom 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 wayam.z j(y26vd o that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised ynobczc 4+ 3fy7j3l1qby the presence of standing waves, which can cause acoustic “deaofzyq4j3ync 7c3 bl+1d spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendej t 9r:r2y:psmr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a lsrrpy m9 :2jt:ittle 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 human ear att;m5c) nc;ejz a frequency of about 1000cjz)em5;c; nt 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 on:2h e, ;u0 arhnenrcy1 the ground hears the sonic boom 1.5 min after the plane pas;rneran1,y:c2 0 hu heses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 hfiz 8cxkn5635 $^{\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