What is the evidence that sound trbjvv1 +dar+. f hnb ogc)y88bq 5,lzy-avels as a wave?

What is the evidence tq+0 ss 5d9xhtohat sound is a form of energy?

Children sometimes play with a homemade “telephone” npdem3z4x, 4f by attaching a string to the bottoms of two paper cups. Whx,fnp4 zd4 e3men 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 from air into water, do you expect the frequency or x1bhytyst; 9qxg-6s4gb o7g8wavelength to changey9 o; 18 xxsq7b4thggby -gst6?

What evidence can you g/yn sszb0i -ioef8.l 5ive that the speed of sound in air does not depend signife.yi/no 5- s8z0 bfsliicantly on frequency?

The voice of a person who has inhaled helium3x2e rei u em9bk09zt4: let7v sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pi9 dn.af vr4j6spes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds r wz mxo3v*m:r9 k+wy gkc0rrim47 s)6in various frequency rarm*zoc)w7 v x04mygsk:r3kmr96r w+inges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as g..fjbtjch:5:v3u zt*dau k 0 b0i.zz you move up the fingekh t uf0b:ad.: v0zz3* u.zgc.tj jbi5rboard toward the bridge?

A noisy truck approaches you froj4:r,dhi-xq 4 16mosbohq+/u do p-j zm behind a building. Initially you hear it but cannot see it. When it emerges and you do see ido,sxh4pq /+ d o4-iqbzmh j o16:-jrut, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saidj5gzn. co39)rn2zmhlo ml51 p to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explaigmhr)2nncmzp 51 j 5.zllo93 on.

In Fig. 12–16, if the 6rzj8;( ypw+h zo8ecnijn 7p0frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) mwnjpjczyn0h7 8 o(e; +iz6r8 pove farther apart or closer together?

Traditional methods of pove7k;rnh v. 64m *dbqrotecting 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 noise. How could adding more noise reduce the sound levels reaching tr*kve46no7hbdv mq. ;he ears?

Consider the two waves shown ca)bkh4v8.z e in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, b4z.kheca8v )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 directiomwk6s, hnzr lj0:79dvn, with the same velocity? mjv9:7 ,lwrzh6dns0k Explain.

If a wind is blowing, w2pz ic39q6n4:h/y vgf i.ekzcill this alter the frequency of the sound heard by a person at rest with respect t fynz2i69/iz:qkv g3. hec4cpo the source? Is the wavelength or velocity changed?

Figure 12–32 shows vario6-h.uc0 b4:+k*lddozh)f pktbi * a jhus positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the a 4 dl uo*htd6hbi* pc-: 0+)jzf.kbkhhighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fore kr j46s9*opl6g ku;0(r gazx the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate 0r6ug j osk;(*egzr k4xp9 a6lthe length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below /3n7 z0ul-uhk bfl2yn3l jb8n the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater 3yfl-kluh78 u 2bbj ln0/z3 nnis 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air igou5navx e b56j*7l 9 8wlgp9at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftingy5ft1cj s1g5ycqmd rp+ ,jk 74 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 befor 14yk1mccj5trfs+7gq j,yd5 pe the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes rnet d4-( d5s0dy1jaowhen striking the water below is heard 3.5 s later. How high is the cliff( y doe5rtdsj14 d0an-?    m

  A person, with his ea,bt4d7rkr w lrk4vt5+r to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one trtl4 rbwrdkk,r7 +tv 54avels in the air and the 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 miledf u-v(;ifa*i of distance by the “5-second rule” for estimating the distance from a(;f -*uiv fiad 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 levcf mw4r, (v:yoel 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 of a sounp8+p p 30cnjwnd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousld// sp b6vjc0vy at a 0vc / sbp6jdv/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 a)iu:su)5wcp5 cr qiz0u .u qr1irplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level woul:c.ur5ic)u5w qq) u1spiur0 zd 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-to-noise r5/ll(e; 96+khj o dto8yk9 e7nxipzgsatio of 58 dB, whereas for a CD player it is 95g;o8l5yi7+/oz 9npe es kjh 6tlx d9k( dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the poweb u; lr,uxwjp ;-f+*dfr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughlr xfb-* +;;uudl, wjpfy 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 whoj45p o esdqg2dki ),1kse 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 25d5mnc(d4ttwn1w,do3 /sbsd )0 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 loudspeaker connected in tn(sdm )dt s/d51 tbd wo,n3wc4urn 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 13kso *y33pxpsxo 1u1 3n0 dB when placed 2.8 m in front of a loud 1xoukps *sx 3n3yp31ospeaker 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 ow0phupz o lrq-zi)8. 2f 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 20rpu)q i-hpwl .zzo811–9.]$\approx$   

  If the amplitude of a sound wave isif 4)e ih3kc7t tripled, (a) by what factor will the intensity in )4hk3eftic7 icrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displj:21c jy;3+cnm p57d* mn lmbm hlyci*acement amplitudes, but one has twice the frequency of th ylhnp2mj+ 5c3y*mclj7; m1n* dib:cme other. What is the ratio of their intensities?   

  What would be the sound level (in dB) /ktdq.,vud; q6 o 193kqx evwoc4tep8of a sound wave in air that corresponds to a displacement amplitude of vibrating air mkv4/tod9ut qq e.kpw cv e38x6q,o;1dolecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud ash y,a rhe 33v6ll)8hi-)xp.9 xchyukx a 100-Hz tone that hashv). )xh9r3x,al3yhuekl8px6y hi- c a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest vzrns( c.se +hm(s.(vfrequencies that an ear can detect when the soundn..s s(szeh+(mvv( cr level is 30 dB? (See Fig. 12–6.)

  Your auditory systema2sx *o03rvtr can accommodate a huge range of sound levels. What is the ratio of highest to lowest t03rv as2* orxintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin :4om)qrq +iip has a fundamental frequency of 440 Hz. The length of the vibrating porti+ pi4m :qroq)ion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundame3fq/ gmc: 4dytntal and first three audible overtones if the pipe is d: c3q4ty/f gm
(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 expect frogw:z 2-b1g y6bxflw5 gm blowing across the top of an empty soda bottle that is 18 cm defgyw-:5gw1 xlzb g 2b6ep, 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 pi30s:gtea w9 2lvdxobut ,(, vlpes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths ov(d gl xl e,0a v3wbtsuto92:,f 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 haw8+v,-f+ / v.nmc o6nbnujcji rmonic. What will be its fundamental frequennwnibu8foj /j+-nvcc,+v6 . mcy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long my e+7kbxyz4z.he 10r5an7ix and is tuned to play E above middle C (330 H zx0a1ixhyyne 5.4k7m7ze +rb z).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wx+t o,d*1834qlsi: lonrwjp h hen the temperaturdn3,: l * xhjrspitolq1o84+w e 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 at9 tghvi8sf lp qs2,k:, 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 Example 12–10 shou5bu)4ntz mhj6/.a s 5so wa4efld the hole be that must be uncovered 56us 4/eamohb4.f ) tzsaw nj5to 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 can-(*t/ 4(v oukwbh v9tydz 0hqa resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an opebh uk(-t40vq w9ya/z* td(vhon or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.8hx 2 l7xth3vizlwchi.p-wu/h;)5 r,p0 m long is open at both ends. It resonates at two successive harmonics of freqzwcuthp3x 75;vl/hrx i , p2-hh.w)liuencies 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 clrix8t nxon+ ,bn/yns0 *dcei.1-y4$^{\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 the1uh 0pimf c*(+c drjv6 audible range for a 2.14-m-long organ pipe a6r (jf+1ducc imvp 0h*t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is app80c cn7dvu i-nh8 o8qmroximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in thi 0q7c o8 u-h8vd8ncmne 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 r5:feb zq5qnxr uw;vmg(. q:):a s )iaevery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in fr( x qvmi:;)rbw snqq: r.a55z):afeugequency is the other string? ±    Hz

  What is the beat frequen f5qgl4kxch );cy if middle 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 whistl9u 4rb0 ynotq(e operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when 90o4 qtb nury(played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounde +ufy 66fczop,d with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the6pufz6f, oy+ c vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to th/y45izmh1m; j wzub+ 1bcoog *e same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the bhybm +5g/ow;*1mjui zczo b14eat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twowa*0k38 o p2njpc ,4 )+af8bygzdyqpz identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and*pk8z 4w gopqy3pnz,)f2 aby8+0j dca the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of *y we2)kkqiocc/sy-6ur)gy 6 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundecrk /) yy q )k*ow2i6sc6-yuegd 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 person standwjs1+n 0+q iix q5fr vyc+2xj+6goy m2s 3.00 m from one speaker and 3.50 m from the otherf2+ j+ycr +0y2six+1x oq6 niqg mjvw5.
(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, butc, 0vrfz:p6w9 rfm:nq a piano tuner hears three beats every 2.0 s when they are played togethf:f: wz0pn6,r vrcqm 9er. (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 tpb1 bro1cx+d-my l4, m in air. How many beats per second will be heard? (Assume1ydl ,optmcrb4b+x1 - T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirsl +ws7jgk+uc lq1 js z;k;+a3en is 1550 Hz when at rest. What frequency do you detect if you move qu7s w zks13+gjlklac+;s+j ;with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whai kh4cl h1+ju/d3st4i t frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at34h h4ksc+i ji/ul1td a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift ixw b te,g 8yev94apnq 5n.;zz9n frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moxn 9za gzpvn ,b4e;t8e5yq9w.ving 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 frequeyv(r;(l3is5 aywnmk , .7nlbxncy 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. ba v,mynlsn7 w.i ly3;((k5x rWhat 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 an2 fx-2w 2sbxg .pbw6vyd receives them returned from an object moving d.-w bw6bpv22fy 2xgs xirectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed o5 *2aip.:krf0xws bg09v* jemzy hz:n f 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflect9n:* 0r.vk2w:yiepj zsa fg5xzb *h0m ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuby w8-z:gjh4 tfa was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rthzj8:4 - wgfyest 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 speeds. S0x/4nste zocqq2, .f ;0zzq eiuppose the device emits sound at 3.5 MHz, /4t,qqc ;e z .0fz2iqsznoxe0and 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/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waverl 1 qmi0 s+4vyawnhg:6l,g9jvns,:fs 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 frequencyn hwwgv lcgv i0)5(0e4 570 Hz. When the wind velocity is 12 m/s from the north, what frnwlve 5v(wg4ihg0 0 c)equency 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 lan4nmj1bbx p 6f5d 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 speed of x-y(6hcvd inyx32r4csound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’cxxiy (6h3v y- d24ncrs 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 k ei(d;3psxoav +g)/ oatmosphere of a planet where the speed of sound is only about 3v)odo;egsk/+ ( pxa3i5 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. Dets+2ke/h wi yb3ermine the shock wave angle it p3yh ks2e+ib /wroduces
(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 sbt(ub 6l(w/p$/theta$ 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 qa h,vz-g3e381n etuu 3 d4ohuground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has 33ae,4e1zuth8 vnhd3q-og uutraveled 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 20,0b xvka,/fh+w ab*7 :hr00-Hz sound pulses downward from the bottom of the boat, and thv+h b/ w*r7kfahab:, xen detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humimivjc6,v (.x an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consist- hyunrs165dvs of many plastic pipes of various lengths, which are open uyv1 h6-s rd5non 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 per/wshl::+,tjcti q6h zson makes a sound close to the threshold of human hearing (0 dB). What will be the sound lev :,shj/q:zt6l +wthc iel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 875k uq0:3ozhu s-dB sound are heard simultaneosh3 q:u zu0k5ously?    dB

  The sound level 12.0 m frod ):hngy3qp*a cpjszgmk(:()m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) ocj p*p ):gg) (qmnkyz3:(dash f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. T:jh+z m,bu lhu.in )2rn(w fy-ymk 46mhe power output drops by 10 dB at 15 kHz. What is the power output in watts at 6. mrbu4mmluk,h-jnnyz)(i: +wy 2hf 15 kHz?    dB

  Workers around jet aircraft typicallyda.d6 9c j-q)bpzsa2n 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 hundb 6-p2c)aj.dz s aq9man 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 sy b o/-rdlfudo362v4nustems, 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 frequency xvsjtjv- e , chanh/h 76)g4g/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 pointgkker1: q d-;olx)ma 7s with a fundamental frequency of 440 Hz and a mass per unit lea)kelr-xmo :g 1;k7 dqngth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled l p t9tvb(jq +.l;e8fhwith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in 9l8+h ;ptqj.v fbe(tl 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 neks h1f7q:luf4r5h: gtar 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 mode) with the third harmonic lug71h4 :qtfr5: skf hin the tube?    $ \times10^{ 2}$ N

A highway overpass was ob kin kagv.(; c6rh,2wuserved 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 ran z +ewqf4f*ahmdzl 7*.5bs md4ge coming from two sources. The som dzb z fde5ma*ls+.qhf4*w47und 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 frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductorvlhg/0kl 5/ns on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whhl gs//0k nvl5at is the speed of the moving train?   m/s

  The frequency of a steam train eq9xc: bt*x kifi;6v4whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving9kfbtxv;6:eci4 xiq* (assume constant velocity)?    m/s

  At a race track, you can estam5 dh wqu n foznw-jz)24l(:2imate the speed of cars just by listening to the differ4):l(nzwa 2 f ndjw25zu-mqohence 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 the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency vzub/a( isk ki-j) (d5-s h3wxof 11 Hz. The shorter one is 2.40 m lzdx( avks5h iwi)k/(3 sub--jong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car a1zy/q 7, picmr hl/:mis it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he heiz:1rc, lmp /h /iqy7mars the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta isf 7s7lb6;t jn6 buef9sfpnk ;4 normally about 0.32 m/s what beat frequency would you expect ifkfel9u; n64bt7jp6f;n7 sf bs 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 mo m-4f4rdc rdyha,fyl84lawpo :/*4h lth 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 kHz. What is the frequency of the wave detected by the bat after that w o:wprc4a*h hdyal4 ml-yf rl4,4d/8 fave reflects off the moth?    kHz

  A bat emits a series of high fry3 hli-k/ :t4h*md 7sjrlx)drequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth b lry hxh4*3d7stmi :j/k) -rlde 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 p5cxu*k 1b(ye 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 overto y ux5kbcp*e(1ne is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listenin3 5vkf)i9jgv31jzcs ug can be compromised by the presence of standing waves, wu 3c95fj 1ks3iv gjz)vhich can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slenderdtzk4i6a rp2iflz.e h -54(qj aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringinf (i42-iehl 6dz4j. rktpazq5 g 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 *mva5,;v7e 2;bt )vrlwkyc2r s jwgj4 threshold of hearing for the human ear at a frequency of about 1000 Hzv;) mv,y vgj7rks2b*4w2al r ;5wtejc 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 hex9 rye5; jscs;ars the sonic boom 1.5 min after the plane scres 5y ;jx;9passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iv715n ark ter j:oc.w6s 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