What is the evidence tm 87xeb7qvd da: i*,orz1 bb )tcj+hp0fe1b -jhat sound travels as a wave?

What is the evidence that sound is a form)ntxwpk;k) , d of energy?

Children sometimes plah 1 9 qi-2nla+x2 gemshsx dndy.u08(jy with a homemade “telephone” by attaching a string to the bottoms of two paper cups. Whesqxx2inh+ (8dmg1l .h0jyades- un92 n 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 the other.

When a sound wave passes fr,u)tj r+8lnl03e rt 5qmeg o;6 ukii8iom air into water, do you expect the frequency or wavelength toe ;it,6uoj) ig m +83lql05tku8i nrre change?

What evidence can yo l:2-yplxo6-trhwb: c:(vfg gu give that the speed of sound in air does not depend signifi6xytfl: v:bgh: pgo2 (w-lcr-cantly on frequency?

The voice of a person who has inhaled hevs( 8k2 *metwflium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipesp18b;c w:* e1y yiu,k j9wyevq?

Explain how a tube might be used as a a2lunval/ eebz4l 0/z.pt to62zd2 4p filter to reduce the amplitude of sounds in various frequency ranges. ( z .42 ze uteb tdlnv0/la242a/pplo6zAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c 1s6kys a7+jjqloser together as you move up the fingerboajk+y176sq jsard toward the bridge?

A noisy truck approaches you from behind a building. Inic vr, ,oblz4c y8*gwv(lgl 3xqpb4+/ptially you hear it but cannot see it. When it emerges and you do see it, it,owl4 by8 *v,lb p+v czg4rpq(l/3cx gs 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 toiwcl k jp;-v4v/n2;n ,xal l*t be due to “interference in space,” whereas beats can be said to be due to “interference in t4l;ka;jn -vn2 txl,p l/ v*ciwime.” Explain.

In Fig. 12–16, if the frequency a+ yt8rt 5 iwc8 etco467qim a9wxyb05of the speakers were lowered, would the points D and C (where destruybc x8y4tt8qm5 ic5o e07w +air6a9twctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectinwtj-b x z7wbe,4u 4wx*5;lefm qd :mf*g 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, 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 nx4t e wuqw7;5,fm-j zb x4*:*de fbmwloise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave ca:64q 2(cgt vh(zv0btmh qy-c hn be thought of as a superposition of two sound waves with slightly differentht q0:hgcc 6 -zq4hvb((2vmty frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and o,,. f gvlqaoo an 447ducrgnp*05hecpy. 51mmbserver move in the same direction, w5nh0o*g5c 4,qpmyrg.p mvfd lc 7 a 4e,auo.1nith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of +gvybp 5e m-hng;4oezgo(o .3the sound heard by a person at resp3(5+o yggg 4zehvobo nm- ;e.t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in mobz0 kr ro3 ;qs49usw;qtion on a swing. A monitor is blowing a wh9 z 4sq;sorr3kq u0;bwistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hpll/b 8vr:f 5*f.8 tgn (tfeuzer shout reflected:/tzvf8 fg8r u* lb(enl5ftp. by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sid og xp+k-hvz9cyc)7 b4e of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly belohvk7)9y z4 pbgc-x o+cw 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20c7xfj2a . hdcuz 5oi)6 $^{\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 abn*hiiysl cdu1 n)5 w)7ove a school of tuna on a foggy day. Withon)hil id* w7cuy1ns5 )ut 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,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thd zkjlt6hv1 : jgmm.*:e splash it makes when striking the water bed* lh1jkj 6::.ztvm gmlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his earb5rj) 3f 9wy1bla.cs o to 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 thw oljsf3)9 15rbc ba.ye other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “ j0mk 2e(fo4ygzx/g 9t5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 x4(ye2jk go/09gtmfz $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pau+gb n3u* 6tqsin 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 ob:n:-h ivmu/z f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of ifog/qc)x e3: 95 dB when fired simultaneously at a) /o:cg xeqi3f certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an :h-s 6w gh+5o4q5vtur5zujp eairplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensiw54hu 5:5p6vtgo +usrej hq-zties, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of //ml9.w e6)pko fg lww58 dB, whereas for a CD player it is 95 dB. What is the ratio of intens)l/ /w6gk lww.9oefmpities 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 sp:buvzi4w( r9m u :ac+tnm wl:.eaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a spher9n4 lz:rmviau muwb (:tc:+w.e 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 is 2zobc: zu9)y/e ffz ihj8.8xz$5 \times10^{ -5} m^2$ (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 2;4yqmr0n cdx 4q.n6hbrqbh.h6 28kgg50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poig 0hxk; .8h.h2 mng 6q64nqybd4rqcrbnt 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 afoiyp ka npgkr.5.wq5:ppp1 , 4t g.d. .i k:kp,taw gp5o q5pp4 .d1ypf.n.grloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.t1+2qv2o sib ,tf+mfk*h5eib What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hinifio25ef+q, vb1*thkmbt+ 2 st: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intwadq0-g8 ir2t(y 0z 7h.oshgs ensity increase? Increas720g gs.8 d(-yiszohwa0 qhtre by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displact qyg r,926 tu8gdlz ux.7m/g:znq,rhement amplitudes, but one has twice the frequency of the other. What is the ratio 6q/dg, .z7l9ntu,:trx2my gzqh 8ug rof their intensities?   

  What would be the sound level (in dB) of a sound waver17z qf 7thne04 -m+2rphxdy7u d eca( in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? utc+q7rfphyd4a x( r-z md10e77en h2    dB

  A 6000-Hz tone must ha:uwmhx *hgn2v hx-p ,o;xz00dve what sound level to seem as loud as a 100-Hz tone that has a 50-dB ,hxwxn2hvh0gx0;o pdz : um*- sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when 49hy c.dvwxco/f*8ffthe soun*fffdwh/. oc8 x94vycd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can 0r l4*9 bzyo3zmnn0 hgw2p5slaccommodate a huge range of sound levels. What is the ratio of highest to lowest intensilhmwnsnlp*42yo9z0 5z r3b0gty 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 vr go ;0ksbs : brte28j94du;f440 Hz. The length of the vibrating portion is 32 cm, and it has a mass o0;tkb:r4ojfvue bd 82s ; 9rgsf 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three 0w4wvxi1azb(wwk; ,imc 0* a gaudible overtiabg c,( 0ai10wwx4wwv zm *k;ones 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 o cqdt+(+8roqsn rqy+n9w wn2s5h ;;sexpect from blowing across the top of an empty soda bottle t9qn w+s2;q;sctn+o+w (s nhr dqr58y ohat 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 the range of dkf1-o .20f*ilfjxp+mjb8nbhuman hearing (20 Hz to 20 kHz),k+82-bm njfid*0.fx jl1f op b 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 of 540 Hz as its third harmonic. What wi4r fhujhrrtl7 l2xdhbs2- 0o *e s8--all be its fundamental frequency if it is fingered at a lengd*-js4br xel oahl7s f-rt 02uhh 28r-th of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 j263hm k,gn5xhp ef-nq) qed) m long and is tuned to play E above middle C (330 Hz)h)n26x qknm h) gj-pe,dq53fe .
(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 min2 acvne2b,i;8u0c bx ddle C (262 Hz) when the temperature is 2c8x,2c nveu2 ab 0;inb1 $^{\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 atb q xcqpr2m/y-sh-9f()x ;a si 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mout ps:(q,mdjxk(hpiece of the flute in Example 12–10 should the hole be that must be unco:(dk j(,xmqs pvered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe 7o/zg 4fm*0j2ykkdsy(gz . dbe3rcs9 can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other fgbkjf2 r9/s c(g*zed moky3 0 zds4.7yrequencies 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 succgm1h0akgu kef6 ;c*fyo,7j- hessiveujcymfe kf,kg7h60 o;h -a1 *g harmonics 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 agl.s-c 3tx4h $^{\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 aujp r j-3bjz08kt;rjs+mn2 h2 fdible range for a 2.14-m-long organ fzh8mj;- jns2t32 pj+kjbr 0rpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima d22*bovd,bjlhgv1:xn39 hxtlw q0 / ttely 2.5 cm long. It is open to the outside and is closed at the othlbdl9 x,2h:v 2 1dvjg* wto3h0b/nt xqer end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beayrfqmu0 z.m9u3t )n- wt every 2.0 s when trying to adjust two strings, one of which is sou0w.r m fy)zq9-muun3 tnding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if m 3:hz:p8 pngptiddle 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 anot8x * hw9 9roki9xk0ndmher (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 simultaneously, estimate the operating frequency of brand X. 9xk9m9nhw 0*oxkr8 id   kHz

  A guitar string produces 4 beats/s(b i9tzw;wkat oo2-5l when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 35z(wokl9tb 2;5t ai-ow5-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T. fysdrzun 5a9k(*;spc x18;m9 ghgklhe tension in one string is then decreased ckx(. l5 z;gda pym8;kngh 1s*ru9sf9 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 two identical f tar7qy2tj tsq212d6 ave,h. ylutes each try to play middle C (262 Hz), but one is qht rvd7.ysq 622 aa2 ,yt1etjat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; - xs 1cmca7xkw3s;5tan7yx j ud)b2,a when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequenab23c cnuk-77a) jms xtx5s a wyd,1x;cy is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m 7) iyhtdn;8p6ut/59xtqondy from one speaker and 3.50 m from the other. ;optn y8dy 9t5 xq u7)ndt6i/h
(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 suppv oyn(h4jhh ob-6/y(.cq nq(gosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they a- h cq4 ng(yvyq(hoj.bho n6(/re played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats per 2: hzh/d6ywco second will be heard? (Assume T = 20 dhy 6:wz hc2/o$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire en/v/8psadv 8o du+ezst/nmr) 5gine’s siren is 1550 Hz when at rest. What frequency do you detect) /+o/stvrma5vp ds 88z/e udn if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing sti9v0uut lfu( ;xct6 w(ill. What frequency do you detect if a fire engine whose siren e6uil(; ufu v9 cxw0tt(mits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcb-( gqb4lkdqimzjf.+9( *b xoe is moving toward you at 15 m/s versus you moving toward iq9bgb-o4kl bzi.(j qm(d*+ xft at 15 m/s Are the two frequencies exactly 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. When on d3im)fb v(6ugi *usecc9,,one is at rest i9o(u6ic ,,sgmuc *df ev3n)band 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 T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and recei9o2f 4ib wfxv4ves them returned from an object moving directly away from it at 25 m/s What is the received sound frequency? v2 fbxi 9w4fo4   $ \times10^{ 4}$ Hz

  A bat flies toward a wall ag:v,b3t ofpg /itd1/ :vswl,x t a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. W1txi 3:wfp/ov t ls:,bgv /,dghat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was i89qu 0h7,tm;ss bkhjplayed 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 statibi 9m7, h0q ;uh8jtskson. 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 mmuwlv+ p /;y4;p8z yxkeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequenc8/;;+ p4lmvx ykupyzw y if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrauxf*zi odf +;eshf 68*sonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the)j lhtan akfja8/ 6u c7td2:3wc9of0l wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, n u )2hao wc/la cf:03jd6jlak8f t7t9
(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 4 9hn b-zvl3;/xxg+fuvlsleuv, x+.gits 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 thnb /+xawh,m z-e speed of sound is 310 m/s (a) What is the angle the shock wave makes withn /az -mx,hwb+ the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed +f+dx9bt z kxy*h1;j iof sound is only about 35 m/s ifbtzjx y;91k x+* d+h
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine 2 wm5+-cln;lvwb;pg;jopfa -the shock wave angle it producg wafblv-j;+l-pc;o pnm ;52wes
(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 23.ds a aj)qql3b,ulo$/theta$ 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 grou0ewk 3t7t6qt tnd flying faster than the speed of sound. By the time you he76t kt3t t0wqear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pm7z:q0w( yt8 y4yjebiulses 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 pulseq 8:7 be4zyy(y 0wjitms (in fresh water)?    s

  Approximately how many octaves are theregr78.-l 0 dd11qke1y gjtvdg3sqc ga7 in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displz p(07y n*z v)vc/bbrjay called a sewer pipe symphony. It consists of many plastipj 0)7rz vbnzy* (/vbcc pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a personhd: lx 8 5h ebq;gkki4qqz,-:a makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 sg8i; 4k h-qz5 :,dabheql xq:kuch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and ; +-d rz(3 . vkfi rv.e-a93vtjztpokban 87-dB sound are heard simultaneousl;t.bka3j+fkv9pv-zrr 3 ( .d oiezt-vy?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whaub/ + :ts )h+fembid)ht is the acoustic power output (W) of the speaker, assuming it radiates equally in all dirsbm: +htu bd/ )+efih)ections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropsk/b8wtf1h du ; by 10 dB at 15 kHz. What is the power output in wat8dkub 1;h f/twts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ece;; r ,v75r q(xx9kwnr-er dover their ears. Assume thatk r,e;ce;q-w7xxne(d9r vr5r 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?    W

  In audio and communications systems, th(gur2oh8 vbm .gzn plh649jw 8e gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned 94 jx(tfiphvsxwn,3o:jc e *.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 a funda r,(a xvkbwl80mental frequency of 440 rw0bk a(8 x,vlHz 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 p27rblz hdw(j17 c5bb filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is hd72czhr(l1b7b 5jw p beard 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 mav 5*e91uk bmnnzg/h5gss 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental m1mnkhun5e/*bg 5z9vg ode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsedzo;e.9crl mp f7*:ozrved to resonate 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 coming from two sources. Thgrhj6 + /t yc(gajjc07n(e2ove 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 one source than rto2 nvyj7ej gc(( c6/0gh+ja the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conducti hg y5:eor8*lk b/xh .t8yhs6or on the stationary train hears a 3.0-Hz beat frequency when r./y6li8t bsekg yh hh*85:xothe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistqp9 swm(f82) j p:mknele as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movi )mwkqsm:2f(j8p np9eng (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j ft.2z1xbo u5 ,ntf 9ni)jd6vh7sarn/ust by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certaijtaxtinu ),f/2d65nhvn f.9sz 7obr1n 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 frequency of 11 Hz,cae2 31j e xrz4nk44t 7vrxkgy.yo 9s. The shorter one is 2.40 m long. e.en v 14k79 xr oycs4xyt,r4j3zkga2How long is the other?    m

Two loudspeakers are at opposite ends ofoe:qy2rq 0l 0d a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If thr0d2e 0qy olq:e 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 0.327zg,l y l0c3mg m/s what beat frequency would you expect if 5.50-MHz ultrasound y gl30g 7ml,zcwaves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a+ rbd+zl3sqj dij*t1n+ 4)hpj moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kjj +hj q z+i*b+4ddtln3r 1)psHz. 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 moth. Thexly5 i8+nfw1,w;y :w2crvzdm xp :ez7jh77 ce pulses are approximately 70.0 ms apart, and each ie:25 fmxzw z yw7n1yr v+c7w:j8 eclpih7,xd ;s 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 sigdjkc*gu :ju 4d 1 brrng;a9p,g;cd* 6dnals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of thisgj*d6:9bg,cjc;ud;d1gdkn*ur 4p ra 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 presence usm)bf b r*3:df*hb t5of 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 :d5t fub *3*) rbbfsmhfundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”0bl+w;uc gi(sb x*yy c5i07l y involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the othei7scuw0biygc 5l b yx(yl 0;*+r 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 of hearing for the human eazpp/nk-( b8c er at a frequency of about 1000 Hz-p8ekn cz b/(p 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 ground h99xjz5.hstk nears the sonic boom 1.5 min after the plane passes directly oz9h5ns9k .t xjverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboawx4gd.ld9d l/vh )w1y 0ylsl6t 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