What is the evidence that sou3f vufyx j;.8fy :5cadnd travels as a wave?

What is the evidence that sound is a form of eneob,c0t c6 d1 1hx+4lxrel p4zvrgy?

Children sometimes play with a home isk8p- ngre/5v;h)+u dgp-sc made “telephone” by attaching a string to the bottoms of two paper cups. When the string isv)/hgr gpenkc ;dis5 pu--s8+ stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intoj1g:khsplsf1k2,2 dked6xez mm ; a:9 water, do you expect the frequency or wavelength to ch6 2,9gm:;xk21 jeak 1sdmzdlsef :k phange?

What evidence can you give thqb igvf.g 8d9f8z6/ac at the speed of sound in air does not depend significantlyzfva.i6g8 qgbd9cf /8 on frequency?

The voice of a person who has inhaled heb.*hzh 4l yl*flium sounds very high-pitched. Why?

How will the air temperature in a room af1moh4hhof7 v 1ylr/*bfect the pitch of organ pipes?

Explain how a tube mighgl:62gnmad a / mqbacnkz )0(3t be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An exada kn0l6(mq3g:am/bg az)c2 nmple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move )5y224.xyq pv wcqb02fcxx aq up the fingerboard toward the bridg v pwyx)0.52qqa qxfyx 4c2cb2e?

A noisy truck approaches you from behixpkiq+/ ud *6i2o: eatnd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you k a pd*ei6i2ou/+tq:xhear 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 spg9zgfg/le vpt,;51s gace,” whereas beats can be said to be due to “interference in ges,zg pl1 / ft;vgg95time.” Explain.

In Fig. 12–16, if the frequency of th+rmdn0llln9q mx; p5*yf n-4v e speakers were lowered, would the points D and C (where d+4fnl5lmv9d l-p0xq; ym*nnrestructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the h1h*au3,x :n02t plp4srrg 7ucsob vx,earing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a re rtu x 1p20gs p:sro4xu*ah 3c,nb,v7llatively 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. Eac be (k;z)k3lwbt t)te7h 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 frequencies farther apart? Explail eb7 (ttk)ek3twzb); n.
(12-31)
(12-18)

Is there a Doppler shift if the sou 6 jyrumk6vieb5i.0kd d/z, f1rce and observer move in the same direction, with the same velocity? Exp. v,kdm5 e ijyuzrb6/1f0k6dilain.

If a wind is blowing, will this alter thl aw4c: x e nd..3r6w5rqwa.gtd -5rphe frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chan.3 n.4cpwar:6qax.5rl- g whwd 5dtreged?

Figure 12–32 shows various positions of a child in motip9 (dvm(vx .4llwj7weon on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will v(xdwme4j plw (7l.v9 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 khi fw2r7m4vr,mn)u:for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estr4,nm2 hk7vr )mwf: uiimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be 4ful3mpij61 jlow 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 sou 1 6jmjufp3i4lnd in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavel6)egtz 0z1ma ;oz8mgdengths 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:/pq)ipckoye1l;x c 3 just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish kyi)1;o3pcp c l:/xeq,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it mpy + rucy88p(,e.tqspakes when striking the water below is heard 3.5 s lapy .8 (t,qcp syu8+perter. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike thef1hz/cy6b b2n concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and yhn2/1f b cb6zthe 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 +u0 wws*y3)axmlq0l2 7spmbb error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike l00uwpqxw7sb3sa+ y*2b mm) l if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound atd . tturmrwr3 k-u5+;e kz1a3pr jyj,* 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 whos2 l(+8cc ) r j,aygxtrgkuv1)ie intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producc 0yb: .w ajk/3kev2kfksn;+ze a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [H3 .+yv:cbka nk szew0;kj/fk 2int: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy hlj1/ab 80iskxs *vi5 jet engines is experiencing a sound level*j1 bv8is s0hi/ 5kxal bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is nyy4bk e6::p 7s(nyvosaid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is : n o:(pksey6 y4yn7bvthe ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound m)piz m:9d. vcy.vkyg /8s:m lfrom a person speaking in normal conversation. Use Table 12–2. Assume the sound sprea/v cyyv.gpksi d9:m zm ):.m8lds 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 an eardrum whose area isrxs. 7gpn r*1d $5 \times10^{ -5} m^2$ (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 ampliec76rl4v qkdrh8gi.6l 9 t3 kqfier B is rated kt dr466c i8 klr.el3hgqqv9 7at 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 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 registered 130 dB when placed 2.8 m in front of 0uh 9cg pxdn()a loudspeaker on the stage. )(n0du 9cpxhg
(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 dcdlq/sa6ud z9 r1c52 wB. What is the ratio of the amplitudes of two sounds whose levels differ by this u c w1q2rc5s/ l69dadzamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by w,h:tsiwsgadqku) 2ncf7 8s 20 hat factor will the intensity increase? Incr ,tsw: 0hs)uacd7 2nfisq2g8kease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace4/d /ibij uru,ment amplitudes, but one has twice the frequency of the other. What is the ratio of their intensiti,ri dibu 4u//jes?   

  What would be the sound level (in dB) o78ntky3queb0,z 2 qp pf a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 278 yb0,pq3u ktenqpz mm at 300 Hz?    dB

  A 6000-Hz tone must have w, pr0iz zrxeq5d/ ae7*zbw(q7hat sound level to seem as loud as a 100-Hz tone that has a 50-d(qax w0zq7 r7,epz5e*r/iz bd B sound level? (See Fig. 12–6.)    dB

What are the lowest and hig*b;j uo69qcesu5u: s10 gscgqhest frequencies that an ear can detect when the sound leve :jogguqu965 cue; bs10c* qssl is 30 dB? (See Fig. 12–6.)

  Your auditory system can -hsq71axm5d cqhpoc oey3 .:2 accommodate a huge range of sound levels. What is the ratio of highest to lowest intens7hx1.e32ad qs:yo cc ho-5qmp ity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. T e 0 xy(9rt5 fwc(:e,woqzg9zghe length of the vibrating portion is 32 cmwge5 9rx , efq90y( gz:wztc(o, 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. rps8ln0 gj6da c3pz1 the fundamental and first three audible overtonecpp 83jzgan6ls dr. 10s 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 thipv*:r6awwi z0e351)gmm4il : bagm r e top of an empty sewi6grm*li3 pm 4ai01 :br5mg zw:v )aoda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thz 7t l jakq9,lqgl87235hx sdte range of human hearing (20 Hz to 20 kHz), what would be tk 9zh al85l7j2sgd,q37lxq tthe range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency4yj vksoe nz0 :q813hz of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingee31h z:o0kjq s84vzny red at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.oybf 1nr9(i 0g73 m long and is tuned to play E above middle C gb091iyrno( f (330 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 leng+4iqm eeob 8l (v7k,a9zhl2ev6rj jw;th of an open organ pipe that emits middle C (262 Hz) when the temperaturew rjl oe ;zi7av48l6meh9,2+(v kbq ej 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 20 ji q;+ tmvqgf 4oe6y-;arh3w/$^{\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 12–10 should the hoq*ls:f 6b(xz zle be that must be uncovered to play D above middle:zsq6(fbl z*x 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,pn zle62:osu gf;gw(1n1r f6y and 616 Hz, but not at any other frequencies in fw 1n;rglse6zo: fup (yng216 between. (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. vr,9 9i1qut azIt resonates at two successive harmonics of frequencies iz,quv9a91tr275 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 bhz;+mvg)wwtn4;uv,5cus*2k- c1d mp0h hau$^{\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 ayqxd4mehm lvhf,g fve4 o8 ;vg6o)6, 3sxk5u/ udible range for a 2.14-m-long organ py48;h oxd4 )meev6/f6,xm3g fs ul5gvqohk,vipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lonnm 7dfw qnirv4m4 v 90j;9/zaag. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the ;mqn rada9i/z4 v f 097jw4nvmstanding 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/2a q2mhss r),sw:gbs when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other strin/ ws:22gbs shqsa )rm,g? ±    Hz

  What is the beat frequency if middle C (262 Hz),:c: cb 7xtedh0wrk6i 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 anotheru59ktp 2 pp/mr (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whin9puk/tpp5r 2m e 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 whenfvw66hed. w ,o sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reh.wwf oedv 66,asoning.    Hz

  Two violin strings are tuned to the same frequency, 294add 75:ip :wcm/v 5ygh 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 together? [Hint: Recall mpcihd:a/ 7 gd :wyv55Eq. 11–13.]    Hz

  How many beats will be heard if two identical flut.jsro14jd* gies each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0.r 1ds4ojj ig* $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. F g..v o;zq/jzfork B has a frequency of 441 Hz; when A and B are sounded v.j.z /gqzof; together, a beat frequency of 3 Hz 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.m/-,g 3ylm;y ofrxeb5z je, u*80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the ot e3r-bm,xy zf ,elj/5um;o*gyher.
(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 toj(hzlq1t.3sc sxt tq; u vc+h83s28il be vibrating 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 b8vt8qt;h hi2scc+tu33j(. lzs 1xlq s e 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 o9pvci(yy4tmgky,c *-r yl31y f wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Avtp c9k3yyr*i -1, yc(lgym y4ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s k-gv8p78 c6ev r:gr,dgdc6c d siren is 1550 Hz when at rest. What frequency do you detect if you move witc 7veg- 6,8d68 krr:vggc dpdch a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequen-ttz2c; sksqjb+zp gd, 08kl 1cy do you detect if a fire engine whose siren emits at 1550j b-8+d,;st02qsp ckzgt1kl z 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 moving toward you a45z(uzbq 2hnt 7 dd:byzf/4h mt 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are :2nbdq7t45 mzzbuz f4 h(hdy/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 horn. When one iw:v 381lh e/xic +txcos at rest and the other is mx+c:vwcloi h/x 1et 38oving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives themk/i y7mtcp.y 7 returned from an object c m/p7 yt.ik7ymoving 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, v0j + q 3kd)v o85q9b(yni(:93 htlwulybd rbithe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflect9( 8d)bqjh:+vu i rl0nyi9lb w ty3d(5qo3 kvbed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experim p g6iaj*+.ade*w hkb8ents, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same ton*jak8*+w agh.6pb ed ie 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 measure blood-flow speeds. Sfk;np5g *(wv3vz :n 8sussr 7fuppose 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 blop(* 3v 7s:v;ufss rnkgz 8fw5nod is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o8;l+nsckz4.v , r ffatj1ak7lj 1d e(hf 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. Wheni,*snaf0d mmz:f 4hi. the wind velocity is 12 m/s from the north, what freqn f h. *ida:,4izfm0smuency 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 6n nc(gm uvkc6l3-ol- -/ov co0.mytd 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 5nbt a 4-r5)+ eyjfbrd2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the n5 5j)r+a4- btdyfrbeairplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed o i:/xd 9zm2uj ( tqy+*ncui:xvf sound is o vin( tj/duz 2:x:c*yumq+9xinly 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 8.yx +2b+ p94liaz;gs x*xlcs:tdna- kh**fns500 m/s strikes the ocean. Determine the shock wave angle it producex+b4fh k9d lxas+y *nl. a:x;s c*pi*tn2-gszs
(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 hnganpafbd 9s,3*- n($/theta$ 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 ex6mgvcq- x4)r)es z et3actly 1.5 km above the ground flying faster than tezq e)mv3)ct4- sg6rxhe speed of 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 2 *1n2rbyiy,mhx6a c6b 0,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi6riyy *ma,6nx21bbh c gned 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 au9p4y0gtdyq z7 dible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a v- n 1;;;f4mkkwa 3k0ni dhmcxsewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. a;k013;dfcv kinhn4kw-xm ;m
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold o c72+d,id ni+hn6b gklf human hearing (0 dB). What 2 ci k+dh,nnl+bg76diwill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and anv/ fq dx52u3au 87-dB sound are heard simu3/5v fqxd 2auultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whaa 6cwzo:i hi9)t is the acoustic power output (W) of the speaker, assuming it radiates azi)c ihw 9:6oequally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.b0fjcy9t: wo;5)oykb The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15t;bcb9:wy k )o0fy o5j kHz?    dB

  Workers around jet aircraft typically wear protective +w(i)mv c imw1devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB ic1 wi+vm)mw(, and that the average 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 communifvyvp wf53v( *cations 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 viol1b -x-f2dgxp ,j-e*w; prl:r cuxz6 jqin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with uc1 q qrko)5x:a fundamental frequency 1uq) 5koqcrx: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 jkgb; +sm2wht5 cjus+8+3cs nfilled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again s2h +n5 sjck+ws tu3mcb;jg +8at 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 g8bs(vfe* xay5e1+r u end and also 75 cm long. How mube5e y1(xga*vsu r8+fch tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lfi5b b6id/( xiify3 ,zoop ($\frac{1}{2}\lambda$) 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 toj 1f z21*ishvbne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what theh2 1b*1isjz fv 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 whistlec 6 .xh4slh6b8cnc9vbs. One train is stationary. The conductor on the statnl.8h6c9xcbvhc6 sb4ionary 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 whistle as it approachestvd,9e) zv ng2,t,otu you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocitytevot)vtd 2g z9,un,, )?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dq t2.k kuct4 31fw0iimifference in pitch of the engine noise between approaching 2tfiw3i40 tu .1cm kqkand 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 is it going?    m/s

  Two open organ pipes, sounding together, produce a beat cx.ai*o6d,ry frequency of 11 Hz. The shortec axr.6yo d,i*r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a stu gv,i6ga y xmu-hk2+a)u+ 9qoationary observer at 10 m/s as shown in Fig. 12–37. If the speakers u a v h-k6q)g9y+ouu+xmig,a2have 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 fb dlloff-5+fuz. b +uxszp0qm f;meepl62*);low in the aorta is normally 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 cells? Assume that the wavdb;ubf oszl)+ 6.lm;0 f- +plqmezef*x5 p2fues travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tok6g 3vspqligd c12/ gg i ,me;wnc.k:.ward 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 waggdik,/vlc63 :cgqwmin 2.e1 s; p.gkve reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap s+* t8-ap+bcq hri8uhc/f/z uproaches a moth. The pulses are approximately z*fbcr/qtuh -h/ spui88+ca + 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villal*06enag / x2fhgn+fage 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 /l*nahg 6f e0naxfg 2+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 by the prese*2;aed z:fjie npzk:rm/: :e pnce of standing waves, which can cause acoustic “dead spots” at the locatijezdae2n im::fr/p :;:pez *k ons 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,0p f:3usfiwra79 f+1do/tkan slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a li fuw1 da f+:rfs 3a/7on9ti0pkttle 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 ae/hm w*1dn(5i-iv fugd 77 wiut a frequency of abg*-vii5w iuwd7/ hne 7m(1duf out 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 travelingizp0+iwj/ js;jm1d62 tc9w3*vx xokp at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min afte 1 *6;k+xtjjjdw wxp s0i3vm2o/pcz9ir the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat .ta*p -5cd-ty (hpqib 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