What is the evidence that spkbau/h 3p7jy(bk ucqf7(dbe ,;n h3:ound travels as a wave?

What is the evidence (sj6x zubv0f*beb y ewe ,(-t bk1v3l/that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attammdv7w7zm90z1u l 2eycux /h ;ching 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 cup to z wm;12yhl 09mzxuvcd 7 /e7muthe other.

When a sound wave passes from airees b22d 5q)aa into water, do you expect the frequency or wavelength to change2eabd5 qsa2) e?

What evidence can you give that the speed of sound in aiyn5r: p. g;whzr does not depend significantly : py;whgnr5z .on frequency?

The voice of a person who has inh7b 4dpk ,en54ypga;3kiaehw0 u 9i;gealed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pi9h,okuwzuh s6u:* 1so;mi 1cj tch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds wn qqztu/7jb6.,6f6zsa un/x in various frequency ranges. (An example is a car muffqx/zn u z/6 nja.fu7w6b,t6qsler.)

Why are the frets on a guitar (Fig. 12–3k8 ,y/kwo;bk j0) spaced closer together as you move up the fingerboard towarbw,kjko yk; /8d the bridge?

A noisy truck approaches you from behind a building. Initially kb:vji157eq,p 8rnjc j z+ t*jyou hear it but cannot see it. When it emcztb+,r qv j8k: *17jjij 5npeerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen +ezar /ayv;f gdy2+e)ce in space,” whereas beats can be sai r g/;a+z+vea2fy d)yed to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of tke jb3*gtn89of2,w3tj *yhy khe speakers were lowered, would the points D and C (where destructive and const8*ftbw, yh3ktj en*o9kj2 yg3ructive interference occur) move farther apart or closer together?

Traditional methods of protectt*gl l o0k:r6k1qct-ying the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headpho10rtok-k6 gtl *l cq:ynes are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as al6 u(*hmzrc 6j superposition of two sound waves with slightly different frequm6ru hzlj6 *c(encies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move inyh+sv dcwhy2 8;:cy6sp 1h lt( the same direction, with t2ch 8yydw6sspcyl h tv(:1;h+he same velocity? Explain.

If a wind is blowing, will this alter the freiy0a,+: nf5, zajzp lwquency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chania:zw y, 0l+znj, p5afged?

Figure 12–32 shows various posnx0) 16js1(8 0od alrhvkexghitions 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,0d 6x8ans1vlkh) r jx0e1h(og A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th rkb) s + vvbqo25/gh 3jsjujdj7o0,l(e length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. l b+jsqbjr j7o0 us/, )5 jvkghv(23doShe 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 87fzgkd65 dykbelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1567g ky 8kfz6dd50 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengevh+k4u rt :r)ml4f2 mths 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 y90xq6 p mhg)l 1ikn/qube9 6pa school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33h1 nme99ilb0x6ygp/)pku 6 q q). 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 striking th7*da a rg53ys9c xc-8 cndk9zde wate9y3ar9* -8dc sgcxk7nzc5d dar below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear tlcm8m (4 /ejidp-zc9c 0qdl c5o the ground, 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 1.1 s apart. How far away did the impact i4mq-pc0jc8l/zdd(emc 9 l5c occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent errolfutqin;y,0fgs 3(.t r made over one mile of distance by the “5-second rule” for estimating the distance from a ligh t3;.glunf0t( yf,qsitning strike if the 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?o,ar.b;kqlphj2j dpa h09z53++mjm z    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leveldd.dd d46qyiemx(5+ r of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level 0spd 2vomn +-3xosxf. of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint:-. x+xsf2d nvs03poom Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nois7 fmgdg*b. :egy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person egg .ge7d*: fbmxperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dbvnpi:9k x*-ysvj 4 i8,ae9sg+ duh-bB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each 4inghb 9 d *-xsviuvy j9+-:p8bske,adevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in hk 8 tfdz*g 1z.(mtl9pnormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centt zd98f(.t l*hpmkzg1ered 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 arb2 b* k7lzvc+gea 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 raq boz9rzj,3 iip6ej/-ted at 250 W, while the more modest amplifier B is ratebzj,z opqe9j36-ri/ i d 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 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 +r tgsb2tr 8zxd69hf+ 2.8 m in front of a lou9d6hs8r g2t trz fx+b+dspeaker 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 typicall0/knzz vwf7 k;y detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Skv/7kf 0wzn;zection 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledz8 vpns +u3i7f6zi* 0n9 7gwkaqjw*i7+hkffc , (a) by what factor will the intensity increase? 8w7si3kjzn+qwu7cp+ 0*7nzg6fv*f9 a ii fhk Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, 9dps*rf 4o gy(but one has twice the frequency of the other. Whap*ro9 d(syf4 gt is the ratio of their intensities?   

  What would be the sound fmk0y jc(ke2)pi6c )ulevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?cij2c )kumek6pf0(y)    dB

  A 6000-Hz tone must have what sound58l (kmwycyzq0pp 1*j level to seem as loud as a 100-Hz tone that has a 50-dB y zj 0(15c*8lw qkmppysound level? (See Fig. 12–6.)    dB

What are the lowest and highest*p/ok6oiwy b jca5qqwc9s9inr593m 9 frequencies that an ear can detect when the sound level is 30 dB? (See Fig. icok/ qy9wn596sprcw jbq i3a5 9o*9m12–6.)

  Your auditory system can accom:,; bh 8unwe l(bdxq1imodate a huge range of sound levels. What is the ratio of hi hnl b;id1 u8:x,we(bqghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has g a.v asip5(;ja fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.gj.ai (pv ;5sa35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wha7zrurq+uov * 3lmc 9;pt are the fundamental and first three audible overt3+zrlpqv;co9m * ur7uones 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 expe7 +kaf-*ks: *gpqblm b(h wgk,u7fi9nct from blowing across the top of an empty soda bottle that is 18 cm deep, if you +bw(n7kpl*kai*-qgb: s9u7gmf,fh k 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 opu)2mc 434q mpokugct53 c-gvlen-tube pipes spanning the range of human hecgv 5 q4gloutck)3pmc2m 43u-aring (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency ofhc,cyqzqs5(+ r(n.o b 540 Hz as its third harmonic. What will be its .hbc(qsc5 qr+o(z ny,fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long a) 4u+u;(q+qtp dlmrfk k;cb:bnd is tuned to play E above middle C (330 Hz).d+;kbqur lu4tq( p+ )b: fk;cm
(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 middle01ntab3yn/ byq)fcy- C (262 Hz) when the tbq/1f-y0ayn cbtn)3 y emperature 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 s0s4t+twu 1jq 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute ibo;wn r b0oha0zhzfe0(1/sezm - -*ek n Example 12–10 should the hole be that must be uncovered to play D above middle C at 2 zn(ke-ofsrw 0-z e*0aheohz;bbm1/094 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 Ht,9z 93m eun7in rv lmt,lsu 6t;,hy0fz, and 616 Hz, but not at any otherh ui; tvnt96 mt3em 0l,9z,f y,r7unsl 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 resonates at two shez ejyg29zd897 d zo7kf-di;uccessive harmonjg 9e7ydh98 -dk zfdizo;ez 72ics of frequencies 275 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 mn- xwy3:,xx,zp zrn,$^{\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 1gbsg6* ssg /xthe audible range for a 2.14-m-long organ pipe at 2xgg*s/g16 sbs 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 andk+2uv tcr1m*whi0 3w aq7 7fmp 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 relatioh+mtrmf3wp2v7i a qkw1 *7c0unship 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 p:/t1)rslrj x when trying to adjust two strings, one of which is sounding sx1ptrr:l)j /440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mid(ts qbr/8jy*vjlc/ ,kdle 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 ah.kyciz1,wceu ;0e x qa ,r0y1t 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneou,c,wze;1y cayh100qrk e i.u xsly, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with aaa(i5 i ;xiezk3gk 9n9 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is tgk ii;nkz iaaxe9 395(he vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tj-w:kqrrt*2m u pq *e qm*hemg:(hqrso68 o.6he tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hinthrqe m6w:mu-*erq poh.jg*:(rt os2qqk* m86: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cfb+(6lqrreph ns8 f4cx+k5myin.x*+ (262 Hz), but one is at 5.0°C and the other(i+xhqyp+rnn 8 e+kcf.sm6xb5*l fr4 at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wheoc vwkr0b g;q5lg 41(mn A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is50c rmlkw o b1qg(gv4; 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person standh;rrhkbzuu )85sw oe5 ( z3o:ts 3.00 m from one speaker and 3.5e;:r (zh hkt8 )3oru5 wbosz5u0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are suppor vpkq9ne(e:n4- d*pxsed to 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 132p-qr e*vn:n(kde9px 4 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 air. How many beats perk ytnk*r9 0s ).0rhfrr second wi)90r frnrksh 0tkry*.ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ce3+g azc-evu o9om7u9 mrtain fire engine’s siren is 1550 Hz when at rest. What frequency do youoemca- 3mu9v+7o zg9 u detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still.)h t1f 8k2ayn v:n-igmue4tp o(v o6i4 What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3y-t8eonhnv)v42o 6p gt(1a iiuf: 4mk2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sorw35eogrqq v4 )g2hu0v1 tq(2bemf *uurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly thqbqqe f*vv)4gwum(t r ueh13go5220re 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 thvgv7f.te:ux li1 5zf sf+it /3e same single frequency horn. When one is at rest and the other is moving toward the firstegv x+zs:5ffii.ltv f73 u1/t 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 them -j4g.ja j5pn7 e; cqqyreturned from an objectp j;457j-qnqegay j.c moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall s)o:sa n5pgv1qo9 vd9 at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What f9sovp qd o:159nv )sgarequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a pr yow 1bb6)zr84a-79bxektk tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tr9z1brb4kpat6ywo - k)8 ex b7uba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flo8 (55l,-eljjzv ac upaw speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expectepualj(j z5ea,l -v 58cd 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 of frequencaylb7 );. j5iupi-j v4 6-gm/tedsqbm y $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When tiw-*thyldwcl)j +j: *he wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at :cj) *hdl -wt+wyl*i jrest,
(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 its speed boe v7v xo :t*1nvo,h*x qt9x5at 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 o q)a ljn-y n49iz,dit.f sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airp.j4iai- nyz ,nl tq9d)lane’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 of soun2n6bs* tqdz y k/(u+qxd is only about 35 m/sdus*qqt (bkn6 z+x2y/
(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 mer* s ikg2j /dy5db1x+q90k srz9m0 yfuu)iy: /s strikes the ocean. Determine the shock wave anglef9y*y50yrku29k js xb u1/i:)mzedsdg+ rqi0 it 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 8p jb8p,q bco0$/theta$ 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 gr*0wqnlg ka,tnu4b* o4di89o.k0krgyound flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1,9 glw4b8 ku0n*odtq0g *. yranik4ok2–34. 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 d+fpi gyh/ b9at 1h.,)oy:pqkhevice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximuh,o:f9hp) yb +1tqh y/akp.gim depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how mafyl,bis/s 60, * 1kmdv odjqq 259fjlony octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dhs6 +gq/m1e *it ftj9wisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whi1theifq*ms/wjt g 6+ 9ch 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 fro o6ou m qb9c/7;5 pug2/ftu8leakx g3im a person makes a sound close to the threshold of human hearing (0 dB). What will be the/9q2feb kacg; 5uu3 xo guo m7/8tlip6 sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB /5awg e,p*zix sound and an 87-dB sound are heard simulta,/zg ap*eixw5 neously?    dB

  The sound level 12.0 m from a loudspeake(1gun*ajkz +8a gk :fwr, placed in the open, is 105 dB. What is (j a8a+un:*kgkw1zfg the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 1dpk+b1a86kr gx4eo) b50 W output at 1000 Hz. The power output drops by 10 dB at 15 kbb81 doe+k6r4) xpakgHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tyygw0v*c6iw; +qmbao 4)bdis) pically wear protective devices over their ears. Assume that the sound level o )i sb;*m4g)qo6vw+biwd0 y caf 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?    W

  In audio and communications syp et8u+r iejrwd9ltofo 2 f;9jc-3n.+ stems, 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 tun * 9dr 6(mrpcs -tvpmhrid.69a uene+)ed 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 vfc(9.yf/8 bwx5w hnx long between fixed points with a fundamental frequency of 440 c /fx.(5nhy98fxw vbwHz 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 watpxe4r f2u:0,r.luqu uer (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 at 0.395 m. What i.upf r u4ux,uelq2:0rs the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tum fcg3;9ng7 ) srerl/xbe that is open at one end and also 75 cm long. How much tension s;nms g9/e73flcr r)xghould 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 z dz a-l)hmv56full 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 ragyy kge..hz+oya z7 7a;q. q.id-tvn/nge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from 7-dy. z7..g ny.oa;g taqq ev/k hy+zione 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 qk i28 56vrfsgthe stationary train hears qg s rfk86i25va 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 apprtgw: 1/jrmhvig)* (shotd ) ;koaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movv :w1j ;sdmh ro)/h)tg*( gktiing (assume constant velocity)?    m/s

  At a race track, you ca9 i.a+rgh(ye zkb7uw; n estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding e(h k+u7b. g9wyaizr;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, soundinwwp b+:,e0+km 76o 0sxb,oniua9luyt7on)nog together, produce a beat frequency of 11 Hz. The shorter one iay0n t)owswo,+b7n 6x9 o:nie 7mbk+olupu 0,s 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railrv pvmxvs6 u 7,owur,:*oad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the 7w vvoux:sm6r p,,v*u speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s(.2otudmgz .e 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 t(t u.ezdgo.m2he waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying t i7kyr .vtt *c/a8c(ywoward the bat at speed 5 m/s The bat emits a so/( 7rycity tck.8 v*awund 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 apprp v* hbng5g+0a 0 my+4lanwry2oaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mh5p2++y4law gny m*0bar g 0vnoth 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 si(m*,(abni . xj3myaf 5l a(mxvgnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fum,x3mf bvyn((.ja( mi5lx *aandamental 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 prese8vaoy6dmu+ts , ;f:qw4-d fs phea,(knce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies ysu8, 6:t,fawsf -a(m;e+q4p hvokddfor the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumin 66977gjso2)icjbh5kkyjy wgt f vk*0 um rod held in the hand near the rod’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 asc t y7 0 b*vy29ojgh)jk5w66fgj 7kik 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 forbkgb fy+;l(j.joq )8r the human ear at a frequency of about rkjybq8 ogj+;(b). lf1000 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 7bg0ob.ji sg bfbx.3i bf 4/m0puu ,k)on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? f ,i4bibu0. sjup7b.xkog0 / m)3bgbf   $ \times10^{4 }$ m

  The wake of a speedboat is 15 dd3wu91h *kit $^{\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