What is the evidence th..p12v ekl+0(pcgldd3rfqo z at sound travels as a wave?

What is the evidence that sound is a form of e v.;:f 8mkevz)uf5p banergy?

Children sometimes play with a homemade “telephone” by at 8bdj0nekaf(m xv82t5 taching 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 dma(vj5 e0x 8n8fkt2bother cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into w gkthqwa qmvz3.zg326. f/jc:ater, do you expect the frequency or wavelength to ch/ct6:zagq3 jfq kz.v3hgmw 2 .ange?

What evidence can you give that the speed of sound in air does not depend 2re0uva9(u m rsignificantly on frequ mru9v0 (ure2aency?

The voice of a person who has inhaled helium soundsll+lm1 pc*(t+u n+nc y very high-pitched. Why?

How will the air temperature in 9wv,fu obvj mn9h1+c,a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce oaj 5zrtxqj3x85 ge z*; x-i9othe amplitude of sounds in various frequency ranges. 3 ;jr jxi gt5ze8 q-aox*9z5ox(An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced ci nzc+rn2f2qqn 4;flsfyk :mc j98,e1k8 svm)loser together as you move up the finnv 41r qf +q n:,c)k8jnfmmlf;9zk 8e2s2icysgerboard toward the bridge?

A noisy truck approaches you from behind a buildkjhh,q6,4e28c1 fcyg9um 5e5aits iming. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section h 6m hik ,gc4yc e,82q5etu9mi5fja1s 11–15 on diffraction.]

Standing waves can be sa+-5xvh-zr :qkduwzd;edtx t o 4vb);:id to be due to “interference in space,” whereas beats can be said td du)tvt: xez-q; ;zxd:v 4ro-whk5+bo be due to “interference in time.” Explain.

In Fig. 12–16, if the frsndigqs2 (boz7t(q6z1y *ee (equency of the speakers were lowered, would the points D and C * 6(g qb(zsoq7ety(i2 nse1zd(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing,0xry4q wi gh( of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relativwyh rx0,gqi4( ely new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be though5kw(c1ue-zj c t of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are (ccu-kw 1z ej5the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move e/ob1tdrq+-ey(qjb *7q g3 khin the same direction, with the same vy17(+/ - qbjrgqhetokbe *d3qelocity? Explain.

If a wind is blowing, will this alter the frequency of thek2u+q./oy a3e+baoxp sound heard by a person at rest with respect to the source? I.axe3 +byup oq2a+/ok s the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on ad-1.-o akwr pkj:/pv0f caqu r: (0hgh swing. A monitor is blowing a whistle in front of the child on the gfo-g1r aaw( dc rq0jv0 uh:kp.k-hp:/round. 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 listenzpzzl0i/82rr+wyo xy7a6k cana0;2 n ing for the echo of her shout reflected by a cliff at the far e2z; +rnp x7r8/20i ko6a0czywyzalannd 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 the ech:8 , lw0biv(xblli9 v0lcx)lco of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oceai0b v wlc)v0lli 89(b,xcll: xn 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 20lx(f z5a/rr /x $^{\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.xlug 3ia;g5u 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 elapses before the backfire is heard (a) uali3g .gx;u5 by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top o(; l3acu0b- f*9xe )omyawhdjf a cliff. The splash it makes when striking the water below is heard 3.5u 9fwxe0o*h-j)d ( y3a;calmb s later. How high is the cliff?    m

  A person, with his ear to the g29o; 6wn x+fzdu)foy zround, 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 fd9nuofy 6oz+ w ;xz2)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 “5-second ru,v .fjaekcve 07i++pb le” for estimating the distance from a lightning strike if the temperature isv+,if ae. k0+b7 pjvce (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level ofvey/w )j - fzsq4/ug;nuvrh4yq3/l vm-e*; tv 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a soun0p,p(s fqj 5zvd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoum8ck+t6*rwg zsly at a certain zwtgrm6k8 * +cplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distances1iiv9kavx + * from an airplane 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 allv va*xii1+9sk but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-2; tce6fvv-gwnoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio ve2fg6vtw;-c of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakiv,i0b81c z65gjcw i e:r1;waffyf 2lyng in normal conversation. Use Table 12–2. Assume the ,0a6w25rbc; izic8fy1gfye :f jw v1lsound 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 whgz 6d 9wmx5-w;oyn *exose 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 ra1ovs m:63fewmd6,jh pted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lo3h mpw,6v61jd fo esm:udspeaker 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 a1 9 0w1g ep+ itbjq/bn-cx20i7mi qcxm loudspeaker onp/imcqi0i2197gj1m 0 ex+ wbcn-b q xt 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 typicall +5g3f3e + 8kns fisdcm::xwxgy 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? ss d5ic:mg8 3+xk+ nf:fxew3 g[Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavnj/fxyd5pl h *98o u+( 7pyzgie is tripled, (a) by what factor will the intensity increase? Inc9ofdzp(xy7lu5g h j*p8 +iy/nrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equas ku1al1 rok)x2z8t m)l displacement amplitudes, but one has twice the frequency of the ot)rum )kt ko1x18la2z sher. What is the ratio of their intensities?   

  What would be the sound level (in dB) of ai-mmi.2sb,:umao 4gi sound wave in air that corresponds to a displacement amplitude of vibrating air moleculib ,-ua.g4 mm2o msi:ies of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levelt+bz ;i3r;p./zh7huq ie na .n to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6;.nqa; . +rzz/b3ihutnh7e pi.)    dB

What are the lowest and vz7f,+5ilh du highest frequencies that an ear can detect when the sound leve5f zh d,v7iu+ll is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is 8x2fs:2uikep9 bh: c tnn9ml0the ratio of highest to lowee ic t8:2u:bl9f9n02k nhxpmsst 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 frequen qa bt9a wrsk96t ,9e2esnt/r9cy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the w929tss,eek an/b6ar9 9 qttr string be placed?    N

  An organ pipe is 112 5j0pzlyy- vu*1-nvaqcm long. What are the fundamental and first three audible ovvn0p 1yau-ly -j v*zq5ertones 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 woul;euj2g8jf .ye36bj w ed you expect from blowing across the top of an empty soda boj3wf8g6 j u; e.j2byeettle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ witqx51 *svz*d tlfw7lv;/d ced8h open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requiv;e wc7z x8 */vf*dl5ds1dqtlred? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What*c5vpy*h fs(k will be its fundamental frequency if it is fingered at a lengt 5*vh *fckpsy(h of only 60% of its original length?   Hz

  An unfingered guitar string 1k0h1dwi bk egoj3l7 +is 0.73 m long and is tuned to play E above middle C (330 Hg0k 1bij1dk+ 37 lhowez).
(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 thaq, h,lq 4d6 ofpe(g7o6rbbc9 :demq7p t emits middle C (262 Hz) when the qp(ofr7qdledg,ph b,o9e4m6qb7c :6 temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune ate+/ji 0d oh+9y4ycv jurfjr0 9 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutz ywb bnh36 /azo6v20nx )2y1dsonzg0 e in Example 12–10 should the hole be that must be uncovered to play D above middle C ab/ny3box6z22 yvowdg0 zn0) za h16s nt 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but noo2e cuj3hw ;c*t at any other frequencies in between. (a) Show why this is an open or a ch e2cwc3* ;ojulosed 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 a o*;ai klrma6s1rhp; 8t both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What isrr1alk*p ;m s6;ah8io
(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 iz2/nrydvv+fe*+jn4s2 z/k f/eu+ yaa +xw v7$^{\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 aar ni *t(8cuncy p80/jre present within the audible range for a 2.14-m-long organ pipe at 2ctniy8/ajru0 (*8 pnc 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm 2p :p wfkk:erfa0um56 long. It is open to the outside and is closed at the other end by the:6 akw fuk2 mrppe0:f5 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 beat every 2dzp(mt nzz4 8t z.5y3f.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ±zt3pdyt4(fnm.58 zzz    Hz

  What is the beat frequency if middle C (262ac40*;4dgfo. *jz:x ox5(et+q/p eedk qnufz 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 anbal)(esucf , 9other (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)cas uef9 (bl, frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork anduijt 542lr tj+66i uwm 9 beats/s when sounded with m ji 2u+tru5l6w 64ijta 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned k;g6ppx- ,yvi8nzw8 n 5jrjw2 to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be th8jwj2 n,wv 6- nir5pk8 xpygz;e 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 flutes each try to play middle C es-0bdop )f y fx7ncae+*,m3n(26p+,x7md * enyef )s30 -aoncfb2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, Bi+kq. d ;n fgx3ts)x33n-ib6rih vm kd t5t)2z, and C. Fork B has a frequency of 441 Hz; when A and B are sounded togethir-g)tz263 f ix5 s;)t3mdkn .b+vh kq ndxti3er, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A pers*sfej:-eh ;c4u 5sbb d z1wsne t,kv78on stands 3.00 m from one speaker and 3.50 me u1*fb d4bcvetjsesh,zw; 8 kn:75-s 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 suppgn,x w4(ou3xhznav3+osed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a)(wguv34xa3 hxn, n+oz 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 wavelengtcy5a8 vg; )cms isp63rhs 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T5 8)s;a rym s6vcg3icp = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenq6jkdtr w8:rnp -(8yb0uk t j*cy of a certain fire engine’s siren is 1550 Hz when at rest.twd *0rjn6jtq(pu-bk ryk :88 What frequency do you 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.wfd0di170b) 9ln:v dxqz7(fo gdjn+z What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a g7j70v d dx 1b+lw)9fd0qzinofdz(n:speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequenvtlbv3j (tib7t0b 5cl q0q2:w cy if a 2000-Hz source is moving toward you at 15 m/s70vilw0 cvqt t3 j t(bbb5:lq2 versus you moving toward it 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 one is a k/hzdtia+m; :t 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 frequenckz+:adthm ;i /y the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 d36vr4tmffp 1g; xh w8kHz and receives them returned from an object moving directly away from it at 25 m/s What is the r rpgxw31 h6m;f84f dtveceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ultp e 1g f4j9n nk,365vnumkt1wgrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear i5mn6ej4 g vgtk9 w3nu,k11nfpn the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movink6ur(u(h n ;e7q;;kkjrf z4ie g flat train car at a frequency of 75 Hz, and a second idefjr 4 ;(qu k(hkk;e;n6z7 uirentical tuba 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-flow speed 66y.oupss*zeaydsmif c ) vdvm-l+z ;9 4dg-6s. 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 blood is flowing in large leg arteries at 2 cm/6om-9 +66d azsyds*.v ypficsm-v;gez dl u 4)s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequ-n:kuso7k l k: 84i9oj yklri:y3hk v/ency $2.25 \times10^{ 6}$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 w* bibdv y.69jv2d l1geind velocity is 12 m/bi e69dgy*jb1vl .dv2s from the north, what frequency 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 landn77(jvuk7y s3x;meyij ci p,( if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the m o5/)8yepo4pi /ea: s0rpumfspeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of memo yr0f/au)p iso /p4:8ep5the 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 twuv2u8dld0c d xt 3a;2he speed of sound is only about a d30uwx 8t uv;cd2l2d35 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 the ocean. Determine the shockv-orcveife (;7 .2mfs wave angle it prodec72i r(;f .vmesfov-uces
(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 .0*he tu eunj,9cm.f h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane9fgn 9wqpj)l zafo8(j,n4 .ml exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal d9f(npjw nz)48.qm 9g ,fjllaoistance 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 pulse3.* t pcptyop1s downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m1ocp *ty3.pt p, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oct u 2r oed6lttkah(l)6urfv. ol6h/,h( aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipecbo;8uxmg-g2n 09jml symphony. It consists of many plastic pipes of various lengths, which are open on both ends.g b9m08ocjgn lm; xu-2
(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 makes69udi)gd6*olqu a*6gt ll o8n a sound close to the threshold of human hearing (0 dB). What will be the soundllndg69ou8g6uta i* dq6 )*ol level of 1000 such mosquitoes?    dB

  What is the resultant sound levelmy4yi48 5uzpj when an 82-dB sound and an 87-dB sound are heard simultayu zp4j8y i5m4neously?    dB

  The sound level 12.0 m from a loudspeaker, placed inh(1u(.huk oh i the open, is 105 dB. What is the acoust.huu(ih hk1o (ic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpu14i87 .evtm6hlk6velnr wz0f t drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHmwvl041zf7k6ien.t 86 rvhel z?    dB

  Workers around jet aplpgk1 ule 83 i5z40agey,+lgircraft typically wear protective devices over their ears. Assume that the sound level l4a5g u1 g30igzkeplylp,8+ eof 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, the gai+ 3rvxfycg 4(qxn 05ogn, $\beta$ 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 vioxm/dfqc1.ds;5ep 6gr( gl 7holin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a viols4xakh na1kemf5 6( wb+s i-;lin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a ma-+isakk165a lewfshb 4 m(x;nss 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 vezg6r b-z,ym44v +gej trtical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water lezz+ te6my grvj,-44bgvel 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 t( iwtjn47 bm7jhat 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 fundaj4(n7timw7 jb mental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t o2f kt5c)zkxf let 4vfb.;)z3o 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 -nv - g, y duxj0p;cx 8t1+n3re/ywoeasources. 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 other. What is the frequen1xra/nuw-+v8top ye ejn cgy;x3, d-0cy of the sound?   Hz

  Two trains emit 424-Hz whistles. One train d-a7r n7r)yqxxvu4e1 is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other 4x7axnr1ved )r uqy-7train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistfwprq e8cs4 ;yls 5)h -jgkl05le as it approaches you is 538 Hz. After it passes you, its frequency is measur-j)sylp; hq8fk5cse4 w5 rl0ged as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by uded*-m j2.2ar+rghalistening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sor-hag+j* ur d22amd.e und of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beapv9k v,;1mbmi t frequency of 11 Hz. The shorter one is 2.40 m i1 m,9;kbvmpv long. How long is the other?    m

Two loudspeakers are at opposite ends*myiycp0cac-/ 2dj 0h of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequ*i/-ymacjd 2h pccy0 0encies 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 flmch)01vold h 3tv91no/vso ;how in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wav1h 9v)l 3omovtnc 1o;sdh0vh/es 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 0ecl si 0.u2ex8/sbz smoth at speed 6.5 m/s while the moth is flying toward the bat at speed 5euesx2is /08l b 0.zcs m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pha3.ol3(r yy culses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awa3hr.ycl yao3(y 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) wap . 3)5fleitlf 8b h8(*amvpags once used 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 *v.lfl pf aa)ih5bp(g8t8m 3eF sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stz(mgaynk a 07,os 6w.kanding waves, which can cause acoustic “dead spots” at the locations of the pre . naka7wk(gys60z om,ssure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calc-fiddp-ihry13y 89w 2v9)hyy +ypmbled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is sy d ycry )iw2y-19b9hh-8 ippdmy3f v+troked 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 frequencyo67,/g,gsfv)ccxx sd of about 1x)c7f6/csgsv o,gxd ,000 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. A,as5i ngry; v9n observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whatn9; gvary5si , is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is p4v*mb0n8 j;j-b rzpm 2v hxq)/ne:xl 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