What is the evidence that sotf(h, a,y6yx wc29kta und travels as a wave?

What is the evidence that sound isltv:i mw:hb3 / a form of energy?

Children sometimes play wif3x j emqgt**m*zmun3).7k c uth a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretu3*cg m* .mn3zj)fmx 7*uetqkched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air in ftblpat6 k3dc1/7e ho c(5 6:otoo4bjto water, do you expect the frequency or wavelength3 d1(4 7 attlbf k5c6/o :c6peojotobh to change?

What evidence can you give that the speed of s/ls l0vp73eb /x* q *lcvm7plvound in air does not depend significantly*ep0c7/lpb*ml 3lvx 7lq sv/v on frequency?

The voice of a person who has inhaled helhbu v2ca8h: v:e v(kw1ium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ +u e( eq9l:sm6mzia 7epipes?

Explain how a tube might be used as a filter to hww2/7)creza hogb9 g n4s(9freduce the amplitude of sounds in various frequency ranges. (An example is r49g/b97owea hsnwh fz2g) c( a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tqdl s odg0/rjr) 5v9+dogether as you move up the fin)jdr9d0g5lq s/+r dvo gerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially yku21ciynjd4f h 82j, you hear it but cannot see it. When it emerges and you do see it, its jh4dfn k2,j 1i8uy y2csound 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 “interferdx;e t3jls* 0faqz ;4bence in space,” whereas beats can be said to be due to “interferenc xd; 3ef;bls *qtz0j4ae in time.” Explain.

In Fig. 12–16, if the frequency of thd6 +62g+0 (slaw woycier b:hce speakers were lowered, would the points D and C (where destructive and constructiveco+b6 ye whlaidw0c +rs2g:6( interference occur) move farther apart or closer together?

Traditional methods of protecting the h3d0 q)2h atthbagk+fe d)g+xm2a4 am1earing 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 ambie t2g daek2430aghfb d+m1xt ha+)mq)ant noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavxsj4ye+ f .qc8bj0/ mwe can be thought of as a superposition of two sound waves with slightly different freqx8syfmbwj+4q0 jec /.uencies, 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 in the same dsd0 s1blmya l v;31gx;irection, wi;as11 vxm y0 3lglb;sdth the same velocity? Explain.

If a wind is blowing, will xv ic*zjq y-1w+c /vu8this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength jwv-+yx cqz c/v1*iu 8or velocity changed?

Figure 12–32 shows various positions of a child in motion :d+,t)zp dlj b*v pvd/v:q9 kvon 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 ofv vvjzp) ldv:,qp/ : k*9dt+bd the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fo7 c n idq,b(.4-ytveaqr the echo of her shout ref vbae-qiq y4(ctd.,n7lected 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 side of his ship just below the waterline. He hears nymg /r5 kyb1a7c.x )ithe 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 seawatexk )ny./1 gy ricb5m7ar is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavbgbf pe0s4 a.1g 3:jigelengths 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 boaplh ln 1p mgh*-7ew64rg2j g0llx4k/d2 o3cbyt is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses6 j1gxo0nlbhg rl wpe4c/l7* dm24pyh 3-gl2k before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from y pyahu: a byp8nas7/y- aqt 61)rp5clp5yx7) the top of a cliff. The splash it makes when striking the water below is hea 1-ypa5rt586bu)/yxyyh qas:n a7 7) l ppycpard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the a0aaxpug29 fxf6wii.* - 8da xconcrete 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 far6x dfix xgfw.aua*82 aiap-09 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made (,k(rpc y fz/ndfa6w4 over one mile of distance by the “5-second rule d ((fp6rf4, a/nwzykc” for estimating the distance from a lightning 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?*,e oax2v) -xoqo97sc g: xqrk    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity ipil7 b(:z k,ah;)gqba s $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously+ otasd3qd3 0c+wg2laaya. ; dopc4 m7 at a certain place, wha mg0+ 7 3y scqpl3.a;a2a woco+dd4tadt 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 airplane witjhgynee 3-w1 n9f (b1eh four equally noisy jet engines is experiencing a sound (ye1 b9je-w nhgf13en level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tpp(/iu b-t. 5d 9 oponvhg.q0yo-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the .notod50py/.vg9bi p h q(u-p 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 speakiy9h hou+z: :oi g- n(y*sqk8rvng in normal conversation. Use Table 12–2. Assume the souz9rvhyk:on i-u(y+ q 8 hg:so*nd spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum who8-1yw 9tjzgeh se area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while y;ezr2fh )il*ong: 6i the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decin6ili*y 2 :fh)z eor;gbels 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 fronpr m f5fj.0v8l(ealr)t of a loudspeaker on theej5.lmlf0vpra r (8)f 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 dif 7nzs 2x6zwq8zference in sound level of 2.0 dB. What is the ratio of the amplit7z qs zzw862xnudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what xaa.wfm 3t*n1th ql75factor will the intensity qhn.t m3fa5at 7x1l w*increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the f:6+x e1solgm y +vdo1wrequency ofgms odvylx o:6+11we + the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of an2a p4 2g vf4-nf:ivxk sound wave in air that corresponds to a displacement amplitude of vibratifg22fpvn4k4 vx :i-na ng air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatb:oj p 2za5c pa;l)s4fm hxm() has a 50-pm)p z)5j a m(:lx4fsc o;h2abdB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequpa,ay0jwwu4iqui9;bo+ r 2:z mi+ao*encies that an ear can detect when the soundi+pmij +uo;u2b*w:,zaa9a 4ywqr i 0o level is 30 dB? (See Fig. 12–6.)

  Your auditory system can acco9+vq jgvsv9 z-+ zxehgn9bv+.mmodate a huge range of sound levels. What is the ratio of-jqb.zx9sgzg+ vh env +9 vv+9 highest 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 a fundamental frequency of 440 Hz. T 64(0rqq xqgjcpbir.i0 il--jhe length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strj6lrxi(j-bi4igp -. 00 qqqr cing be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first c7 20z (kh aox ctl.u(4dkzym-three audible overtones if the pipe is ylm0c 2 uzd-(o 4k tzck.ah(7x
(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 uv1lc *uyh ,6hsj: fvq62 t,ylexpect from blowing across the top of an empty soda bottle that is 18 cm deep, ifj hlv,sluyq 1* 26fctv6h: y,u 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 f 4iwe+861lggp2 *x kbo als-nxaiz-5with open-tube pipes spanning the range of human hearing (20 Hz to 20 k2ln wa ixofegz-8+-as5p*ix b46 lgk1 Hz), 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 harh +rcbzjgv 212monic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leng c vgjbz1r2+h2th?   Hz

  An unfingered guitar string s/33u2j6qib/hd hh 9kdp2vra is 0.73 m long and is tuned to play E above middle C (922qh/3hd/p k ri 3uvdhb 6jsa330 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 lenu9qb yh5*vm4t zyx i/3gth of an open organ pipe that emits middle C (262 Hz) when the temperatty 5zu3qy*xi bm/94vhure 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 at7fwsv u,n(1247mzake;p+ ev;hh az md 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in se-1z -kpjrc8 Example 12–10 should the hole be that must be uncovered to play D above-r 8ce1jzskp- 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 cvn9o:7qli 0 riry( ti7an resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Showniol70(ivq:yt r79 r i 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. Iti(+v)8lnl: dii 2 9snc+d9dcy, lkkfs resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is is 9+,kdc2ddk s lv+nilyl9n8fc):i (
(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 ox( crw6i4:ng $^{\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 *hfc)uox(pgpxmp.. 1* os nrn) t,jq1audible range for a 2.14-m-long organ p gjnoof*(cns,r.1 xhm x))*q.1 uptpp ipe at 20 $^{\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 ou30fzby o6,kx wtside and is closed at th oz3,xfkwyb06e other 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 yy hem5sgxh/2*h6z eo ize i**8um9;w beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is yzemxeiehg y*6/h 9*uih;o*m5zs28w the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and l;y jz.s6gx9u $C^＃$ (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, whileettzo/u6.;yqoq dw7 h. o rlye8 n(.o+ 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 simultaneously, esot /horl zw. e.ne;6qo 7d(yuty.+o8q timate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when ,z;ba(k8fy4 r.zq5ataf j ez6sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fre;z b, 5qytaare.6kj8f4zzfa (quency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned g-c, 6xs.zqxne 0iue8to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recqxz6ue -., e0g8ixcns all Eq. 11–13.]    Hz

  How many beats will be heard iff47ng) xw3 dtl:( doy oba0b5a two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other a 7xab dobdg4ay:)3wlo n(0tf5t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fgh o1zj :hmt gyl5:,i:requency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are poszhmy: gth::1l 5o,igjsible 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 apa vr n3 fdm+nyxx);a9a9rt. A person stands 3.00 m from one speaker and 3.50 m from the other yda+3) fna;mn9x 9xrv.
(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 piano tuner /z6(1p gj +rckwwhin an 70wo:hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must ber0g+p z6:awc( h 7jinnkw/1wo 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 bea d 9+/jplo3ffu5yfyr )ts per seco9f3 fy/o) r+udljp5fynd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15nr,p3r;d jkkm0* lzch7xk .0u 50 Hz when at rest. What frequency do you detect if you move with a kl; n7mz0.3jxkdkur0 hpc,r*speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginn qgryecct-; 1f300 jre whose siren emits at 1crc-y 0 etjnf;gq r130550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fred:f6 y4 y b+m-w4ddkgbquency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exact6y -dyb4g+bdk m wfd4:ly 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 66tuk,iam3n ln yz (9othe same single frequency horn. When 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 freq9( l ny o6ia,tnm3uzk6uency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrason, 25jeci iweb(yi .*p1-juzyl ic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the rec-.pcwjib1 5 2ejel ui ,(yiz*yeived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the e7+s( ovyn:cykgq3kb;o.2n h bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ;o(g.qk ykcv2+ne3syhb7: o n in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on vpv34z mvue0:wky/lj+ 8f :5cr br3jx 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 ry+xk3melp4 w5vjv3v:j:8 bu/fcrz 0 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-flowj/g vuyh4+ r ghjcv:.+ 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 frequency if bh+hj+rv gcygv uj./ 4:lood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrktf+dj9 /,how+h:ua fasonic 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 frequenc2w,jmybx ,8jj.+r o nny 570 Hz. When the wind velocity is 12 m/s from the north, what frequencmn.j jjrwyb28o ,+n,x y will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 20 es5ck mt s8sy./( w+lhyb-(nq$^{\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/b;slf l* 7h* xqrqb/p 83ordo.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave m 8o3bs/h /dlx*br*l qpqr;o f7akes with 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 entersr94npw q+nmelb, d0c2 the thin atmosphere of a planet where the speed of sound is only9, 0npw+ lecrbd4m 2nq about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes thes5f. dbwi( dy o*9hf7n ocean. Determine the shock wave angle it produ h bdw 9i(s5yfdfo7.*nces
(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 m9n dp9mgn+rf8c(- h oz2q0hc(uctt.$/theta$ 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 +iqu 9)2ybc lzthe ground flying faster than the speed of sound. By the time you hear clu )zq y2i+9bthe 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 pulses downwj fp0 mad+t)p ay/ote 5y7ah74ard from the bottom of the boat, and then detects echoes. If the maximum depth for which it is deso)f/ yda+h pem75ttpjay047 aigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves areanguzx mi. k3 1*0g 2(i d3g0lrcy1zwe there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ca;o*t6 y 4hvqmj( oecw:lled a sewer pipe symphony. It consists of many qho vtw(y:jm4*e6c;o plastic 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 person makes a sound closmt+.o mk.izg 7e to the threshold of human hearing (0 dB). What mg7ok i..+mtz will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an nxt4/lf( fo8p 82-dB sound and an 87-dB sound are heard simultaneoustfx on(f8l/p4ly?    dB

  The sound level 12.0 m from uzuv d7-7b6bh a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alld-buh6u7vzb 7 directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pu ze+6i (5gsypower output drops by 10 dB at 15 kHzsue(6y5p i g+z. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ0.c l v;fcc3tlk +) -/9twi3qxmwfmy gically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average ;+9fmky.wlgi ) -tf c m/x0cv3ltc 3wqhuman 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 communicationbnwe0eazy614 s systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a h 9diofb49.-rfrmcfd0u6 j1 j 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 uw uaqwp.* u8xm.2fb9a; b5nafundamental frequency of 440 Hz and a mass pe . m9.fu58 *xuwb2ua;qabpw nar 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 fic)t+w5zz)9+m 6+l yow e4 cccid kl-uulled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, tyicc 6c)-lkuzld 5t)+ ue+ocm 4+zw9whe 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 is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one end ley8q9xl2gs 3 and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamentals8g9e lq2 3xyl mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ob ((atv wy*jp7+4qu ajyserved 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 toqz; .km8jb c(fne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what 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 ojqfz. ck(8b ;mther. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles.rzg bmy e3lm4p-j84v ;oap2c) One train is stationary. The conductor on the stationary train heaev34 p mboc;pjly z-)ar g24m8rs a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whisi+hvw+p g/* wy7ogvgd35s 2wjmo.ld4tle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant wj3.5g+4g2 wo*pd+o7h/g vvd wly ismvelocity)?    m/s

  At a race track, you can estimate the speed of cars just by (x*lfjma1qvq)1rr8 5k k)ivzlistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on thrv8)1 f)(kmkq1jazx rq5v i*le straightaway. How fast is it going?    m/s

  Two open organ pipes, g *tmwxu;)/: kdk7v1zhf qq9usounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long :h 9 zmfu wt/kq1xdk7;u)g*q vis the other?    m

Two loudspeakers are at opposite en9l3yc+g8c olfds of a railroad car as it moves past a stationary observer at 10 m/s as shown 8 cg f9oclyl+3in 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 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 what bea kl2v:aj82 )8zc ueujcb,7k cgutlv p +t3+/iat 2cit 7tccagvz,puu+l) lk:uj+ 8j 3vkae 8/ 2bfrequency 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 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 mkktfd).7o : .,e cvs5esumku+oth is flying toward the bat at speed 5 m/s The bat emits a soun vet5ks.) : ,7k.oekdu+cusmf d 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 appro u1+k0yv 956 o+bklgy8puzajaaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo fromg ua5zu pl 68kvoy0 ya9jb1+k+ one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once uset.xh h0.r)tqhd to send signals 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 this horn, and which overtone is close to F sq ht..th0h )xrharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of 7yrb u/i*s81vxjqsq 3 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. Calculvs*s7/iju1qr8y3 b qxate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” zr7b9vy)h 5zd1 5z hugtt ey..involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stro17t)g.hb vrdhyz euzt.z55y 9 ked 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 of hearing for the human ear at a frequen6surfg8n,-on4 -g z gkcy of about fsg-6,r knong8 z-gu41000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boom m;psyv(cac0 - 1.5 min after the plane passes directly op;sv0 y-c mc(averhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15jzc)9zfd 5 5r3 k,tcpbd o(sn+ $^{\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