What is the evidence that sound travels as a wnvc(c1 27rr wnave?

What is the evidence that sound vzqr)zvc9+)yk; g 0neb-;dx uis a form of energy?

Children sometimes play with a homemade “-so;9j b kml(2:n aad-waqj 9ttelephone” 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 csb9aj q nm;j l:-(d tkw9-oa2aup to the other.

When a sound wave passes from air into water, do yozxdf *t))1 trau expect the frequency or waveleng* 1tfza r)td)xth to change?

What evidence can you give that the speed ofgusc*ap1 k +8o9xwie6r scl) 3 sound in air does not depend significantly on fre8s x ci1 egc9)3pku+s *ar6lwoquency?

The voice of a person who has inhaled helifv(n gxq -f6rg(pt t5*um sounds very high-pitched. Why?

How will the air temperature in a r9rs 4/gp/od tv1mfo* qoom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce qngrx1sa. )9h the amplitude of sounds in various frequency9rag n.x1shq) ranges. (An example is a car muffler.)

Why are the frets on a guidi sn)x1 0dz:zamoc;nr0 .qoz+m xj)8tar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the brczz1d 8xi0jz0):amoxno s +q.d;r)nm idge?

A noisy truck approaches you from ako 1gpvhbh39w /qimbebhe6an)/q2 f *z/;l7behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frenh e/; hmgpz vq/b/obaiqe1bh3f)kl w296a7*quency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats )j(zrl*umb dv - (rnaqd2g+ (ncan be said to be due to “interference in timer dqm+nu-((dzlj 2vrnba*() g.” Explain.

In Fig. 12–16, if the frequency of the speake d. f)e3m1pzn2laija ,rs were lowered, would the points D and C (whnmla pif2azj), .e 13dere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ao 5dad6rs iz(sv)0;otreas 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 io 6(0;o z5vd)rsstadit to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be tho*lw f:a*ea6(txiof8 gught 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 componf6fa*(tg8iw loe*a: xent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mov6rji3z / l+ou 22-gjcmlub (pee in the same direction, with the same velu3o gpb2zjrl/e (u-m62+i cjl ocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard ;59ah w7efvj oby a perso; wjvh afe597on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions dtf ,6:t1q yioj ;cqsqj*v ow.jvc2+(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, will the child hear the highest frequency for the sound o26;jvtsjtj*1+,oq (cfo .: c iydwqqvf the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening o2 1)tdkqve+mczr6 r 5for the echo of her shout reflected by a cliff at the far end of the la1ceqdr)zm5v2 6 ok+trke. 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 waterl*v ivgegp0/ be)bjx f+7t,b8t ine. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with de*e/ t8bgbe)+ gbtvi,xjf7pv 0 pth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a2a 7kd4j hbz+gt 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 driftinjs fosnj *nqq or9q6.2daqwm -1+k). b.bl2g ug 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).)oubf6rn 2 .ql9j1 jbnks-2q*q g+sqdom.wa. How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikingvs 3xwc.xb*)/wxd ux er*dn:- th*exs)c .* bd/xvw:r xx nu-wd3e water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the groujnz7h4bmu da(( fp() bnd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 7m4 (zjp u(b dan()hfb1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent-yl4 ryj t(ii fh2w5v1 error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if tyvjilw(4htfr52 i1y- he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?sfxct, bi-kp: xu z 7t+np(u:e/wa s73    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 soundmu -qvbc1 71ws whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pro4 n :(-08 udmnxmeylmd3ce/o nduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitm/( numndl8 :e3d- xmyc 4n0oeies, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally w ip; 9j1c6mr;pgjqb5 noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if b;1jijqm5 p9g c;6wrpthe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig;/ulw4lg hn hm-h7b7dx: o 3rinal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the raod3mxh ng:rbhi4;h7uw/ l-7l tio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spebq(h,,lfo:e zaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a soe b(hf,l,z q:phere 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 whfse 3zbsdd-f:,e;p /f ose 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 i7q li :cyz/ 64/jy7q6defpu7l7y odzjs rated at 250 W, while the more modest amplifier B is rated at4ucy 6ld7/d7qy oej7 zz :l7ifq/yjp6 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 a w. -s rr h7z)r,0g-yqbvsv.yjpfx;h*loudspeaker on the stagex-.qs g jyh0sr rfzv.v,*-p;yh7br )w.
(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 ofm/yho ne z 2nr.(8nntpt m:+l0 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint:+ne:mlmy8/ .hn0tt( 2nro pn z See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by ja f1wb7c d/)wc91 7v r3vjvgrwhat factor will the intensity increase? Increas1bwgv/rvfc1rjwd97 jav73) ce by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but osf5yrerp v ohfd1h70k-0j7 .lne has twice the frequency of the other. What is the ratio of their int0ej-ylpv.dh kfos rf1r h0577 ensities?   

  What would be the sound level (in dB) of tf7a s2 v3pwa5re-0yla sound wave in air that corresponds to a displacement amplitude of ly07w 3 e5 tfsa2-apvrvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sfppf3 l44fs -lrm,ld.ound level to seem as loud as a 100-Hz tone that has a 50-dB soudfl 4pf lrf-l4s3, .mpnd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an2.u6y fo v2fbs ear can detect when the sound levfs ouyf2v2 6b.el is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sou0,lhn2enim; kk -ri+otb: *dqnd levels. What is the ratio of highest to lowest intensik,t+;o med2qnrh il -0k*b:nity 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 fundamental9n5fa udj9df , frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string udd9n59fjf, abe placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first threeqfk()nacwvjwuk5+o *cxi) m c7v j(83 audible overtones if the pipe juwcfn(j)8a w(* x 5m3k+kovqcicv) 7is
(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 qzfws* u4fdw+(.3 wrowould you expect from blowing across the top of an empty soda bottle that is 18 cm deeo3 q d*w4. fswur+(fwzp, 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 pipezi j -l5q2:g8n*e+ swya+nhyy s spanning the range of human hearing (20 Hz to 20 kHz), what would be the range z+i5wnh ye l8j:2ay*+nq syg-of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thwnjt/46tv2c t e 7nqp-ird harmonic. What will be its f2vtc6ptn/ewqtj 7- n4 undamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string j- annf8-q pb3 l,zpv;is 0.73 m long and is tuned to play E above middle C (np3zp-f q; bja8v-l, n330 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) whenk:vmf yc2.n3ksk+ 6ie the kk.yi+:fvce36k m2s n 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 202ch5yt 6l,0dmh xb*w 3 wagp9g $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the fl( 9sbla pdwpjz .5c7t7ute in Example 12–10 should the hole be that must be uncovered to play D abo9sd7cw zjp l7(5b.tpave 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 616uv a+ r717qls5* c xec9e,yuov Hz, but not at any+v,u5lx sy71r v o*q9ec7ecau other frequencies in 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. It resonaheok- yk;h56h iu iipuo i2g;,k0b)0vtes at two successive harmonics of frequencies 275 Hz and 330 Hz.u ypb kii,vikh; 6iuhk502-0oho;) eg 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 gpu1pkiu2 2n6v)m.ok $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-p zimo3jo28,y*a ) -vh+wm dq28k dvaum-long organ pipe at puz 3m ivmq 88)da*2k+-o2a yhvw o,dj20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is ope fht vw)k:.n;kn to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relations);wh: k kfvnt.hip 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 everyk. :u9 qcq4mhud+p me5 2.0 s when trying to adjust two strings, one of which is sounding 4q5pm.:9 +qekdh cu4mu40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if tgs8(k cjjq2 5middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while a d,-hc9o : nkm2asiyj*nother (brand X) operates at an unknown frequency. If neither whistle can be heard by humand2oyij ha mkncs:,-*9 s when played separately, but a shrill whine 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 with a 3kqtqk0zj s.imq 9j914 50-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strkismz.qt 9j 1q kq094jing? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fretzfcw7cwm:( ;mh 1(xi xzwx*4quency, 294 Hz. The tension in one string icz(7*w;4mxt wmh: 1wzcxfx(is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if s bo4 x33nirg.two identical flutes each try to play middle C (262 Hz), but onb. 4o33gx rsine is 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(-zl 8xayrvami *u e:6sua5* y frequency of 441 Hz; when A and B are sounded together, a beatmla5y6sev (xa -:yi *rau*z8u 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 1.80 sesqw fy4rp3;hh0 h ;,m apart. A person stands 3.00 m from one speaker and 3.50 m frr,w3h;sehh y p s4q0;fom 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 vibrating at 132 Hz, but a pi1m3.b ,ffsoh iano tuner hears three beats every 2.0 s when they are played together ,fom.bi3h1fs. (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 2.64cc 8-+lvbjsk2xc7 g3-g7kdc(wqon :g m and 2.76 m in air. How many beats per second w 7v2 +d3scc--nlgco(wk7 g8 jcb: qkgxill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of b0je. nopd)dze: 0l3 va certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed oendd). pevl3b: joz00 f 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detemav++.3fx ge0w+p+bxmh l-qg ct if a fire engine whose siren emits atf+ -l+vmxx03gagwmqp .b+h e+ 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 moving toward you at 1h , d(9 nipgyvw*wy,zrzzd s/21))bk s5 m/s versus you moving toward it at 15 m/s Are the two frequencies exactl*p/vib)zn g1s ,, dhzw)kz 92w(drys yy the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whetp2v 0ja-xev( n one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume tp e-v2va0j x(T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5zp 8pqln;yx::xqy 0kwrt*: 9k0.0 kHz and receives them returned from an object moving directly awatkp0:r ; zp:y*: nywlxq 9kqx8y from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a;l cqaz2(z 74j;ucf(l(wsc hft a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whazflh7cf s2cjaql ;(cw(;u z( 4t frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba y/-avb cmso )h1bnw o;6bn4n,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 approacovb; ,say- 4hm1n/wnbno )cb6 hed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasounmb 3o0yk:r puwj7q22nd waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in ho:72qb2r03wj k pn uymuman 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 waves o;p6f/b kil s,df 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*rr(nz3b y,:jgb q8jm sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency willy zn 3q* bgmbj,8rrj:( 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 if ky*x5 r4ms;jsq4 5 veit(fs0. rvk el 5q)u,poits 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 siss dxp+jd*59ound is 310 m/s (a) What is the angle the shock wave makes with the direction sx+dp5d *s9ijof 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 planet3,72if mwj /jy g6 p2ne:gsupv where the speed of sound is only about i m,2:j 7epg63gnjwy v 2/psuf35 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 9qq:sz+d8d su500 m/s strikes the ocean. Determine the shock wave angle it98s:dsd +uqqz produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle jpgn -ux1ckw1 x..o) mr*-qtyqa*3 zm$/theta$ 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 ground flyinyy:6f2jg (e8bg jxr ) p*xb)1pyznm-ng faster than the speed of sound. By the time you hear the sonic boom, the plane 8(- )b:r)*xxnpgym fj bzy ejp612gynhas 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 t8n2r kc/l1iy l+)gjrdevice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (i+ i )12rjyln ckrl8gt/n fresh water)?    s

  Approximately how many octaves are j)w ,. pz9fj;cvsdx)q there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disalltescc5g9nf ws82h4/ 23 uok ns+6dplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both gc k9f 82o/ncd+ ea52snhlus6 ltsw34 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 make8 e9r,k:ubo ylhy ko7)s a sound close to the threshold of human hearing (0 dB). What will be the sound levh7:y r ly9oube)ok ,8kel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and dqtpvg3ok .6usq8 )d.an 87-dB sound are heard simo ut63d. 8qv.p)sqg dkultaneously?    dB

  The sound level 12.0 m froswd); kdilj.kgx*q) (. zpxtpm6gx+c1 wgu8 5m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equkpx l6 .idggj 1 xz)m.ts+)* w xuq8w(pd;gck5ally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops b h2k,u- rtv5yoy 10 dB at 15 kHz. What is t,2ro-u5khy vthe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices oveeyjz qwus /9p1h- s6*pr their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?h/w szu qp6j* yse-19p    W

  In audio and communications systems, the ga6i(jja g dw0)v2h3d(k(zt zk xin, $\beta$ 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 violip a.o1 e6p 2rqy:x49b2itzklk n 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 betweeeuf;5rvj s v2rh,h*3qn fixed points with a fundamental frequencyqrj*r5 2s ;he, vvhuf3 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 opena8h kuqu-el,cs4-3(yo9kdsx 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 iscau dh8kx- qekl(u49s3-,s y o heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a 7t1lbt*nxkfqk.utf(r:x k36 tube that is open at one end and also 75 cm long. How mfk7kx*bntt3urk.t 6( lq:xf1 uch 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 reson2z :/a o -o5t/afb.n5 gnkdx; .zrvlbnate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range co:6kvpot 0d*ah /8mrz xming from two sources. The sound is loudest at points equ 6:h80vk tazx *rpdom/idistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistfe ) 68r4jp8mw ti(.web +lskho-7 dizles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of twr( z-it 8ef6+kj shb4od8ew.p)l7i mhe moving train?   m/s

  The frequency of a steam train whistle asd1 tce5z9 . 5fyojvv6v it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast o.y cv55v vdfz jt9e61was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jubd;kyj6rjvbd ufoh;h ,)tnn :+c.64p st by listening to the difference in pitch of the engine noise between approaching anvn c4 6;;dyjuoh)fk. rb,b+hnt :dp6jd 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, fw+vxly im//i geq5cz-r5 l,/ -c3d ahsounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?m /yvgrl e-wfd5x-zc,3+i i//ac q lh5    m

Two loudspeakers are at of,.+ j(e1ti s7k2kggcir,g ffpposite ends of a railroad 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 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in fg 2 fiktfgc(.i,s+e1fg7, jr kront of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/sh8v qto6 hk,n/ 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 waves travel wit6v/tho h, nqk8h a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speedmc/mq 6q;u)yhk qn- ,n;; m)wb yln*ze 6.5 m/s while the moth is flying toward the bat at speed 5 ;y* ) yk;bmwu;nln)hmq /qm 6nz-,ec qm/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 off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moqhpi9vo2wdq,o+ gh3,ci( r; ath. The pulses a(ap q+v9hioq,i3;2d c ,r wghore 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onerdya-2fbd )tycm ,r6( 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 ()m6 y-d aytbf, dc2rrF 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 compromis,a 842,jlxf2g*twff kc wh/mzed 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 funwl2 akg8hf,zfjf/* ct, xw2m 4damental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calle*:s2 ydx-h zgrd “singing rods,” involves a long, slender aluminum rod held in the hand near the ro *sxh gry-:d2zd’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold ofpdgrbgm: v*gpcf ec8/oi ,d m24 z36e9 hearing for the human ear at a frequency of about 1000 Hzmg4d8rc d6m3c * op:b /gv9zep2,efi g 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 the groud:c n j+j39dr4gpmvu .nd hears the sonic boom 1.5 min after the plane passes directly overhead. Whad:3d+4 pc9jmru. n jgvt is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatv p thrf4)/b)fjmt,u +suiys-3fbh17 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