What is the evidence that sounedi )f/m(k0x3z sxv 4ld travels as a wave?

What is the evidence that sound is a form of topl-sevs--ta 7bww2o8 5 1k zenergy?

Children sometimes play with a homemade “telepu7bbo u,vxy2n ,y4(q ehone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the souu yq,y4uv7obb 2ne( ,xnd wave travels from one cup to the other.

When a sound wave passes from air into water, 3mt0g jst-*lfi:7f:wwn ci y0do you expect the frequency or wavelength to cha3 00: t :*jwwnigmff-s7 tilcynge?

What evidence can you give that the speed of sound in aitwjb: t3q6lr ;r does not depend significant;: ltb6q3jwrtly on frequency?

The voice of a persons:fw 2q d(a*hu who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affeamwc(1 5.23yzatbj vqct the pitch of organ pipes?

Explain how a tube might be used as a filterj2iqmmx 8++sdp golp*/v 5;ji to reduce the amplitude of sounds in various frequency ranges. (An example is a car m/mp qx8o *2 i ijv++5jgpdslm;uffler.)

Why are the frets on a dl0:b- gz4v 8se6ic vrguitar (Fig. 12–30) spaced closer together as you move up the fingerirv -0d4szg : cve6bl8board toward the bridge?

A noisy truck approaches you from behind a building. Initially y)y dpf.j7 rp. 2mlnqo7ou hear it but cannot see it. When it emerges and you do see it, its sound is suddeljo7.r)m 2.ppq fn7 dynly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said 1+pgzh g3 x f(qk9/g sk*mebf3to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” gpb xgefq9gk3 z+* (f/m13k hsExplain.

In Fig. 12–16, if the frequency of theorw7 ewkhj0 p,;5xl :h speakers were lowered, would the points D and C (where destructive and constructive interference occur) mo0wk,oh5 w:lhjpe ;r7 xve farther apart or closer together?

Traditional methods of protecting the heacz9lmj146y vqq0 :xa jxp b42kring of people who work in areas with very high noise lev9v4bjj:42 p1qzmlca k x y60xqels 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 the ears?

Consider the two waves shown in Fig. 12–31. Each wave canyz1z5/*sm ob,-ei cu 7 bmarb, be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Ism/b, u1-zza 5 ec*r7 bbyi,mon 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 obserjm3kh2rvoovq) j mrj/sx - 2.f.+2kdxver move in the same direction, with the sam2v2+x mo/dv.h kxr) jq2km.s 3jr-jfo e velocity? Explain.

If a wind is blowing, will this altemken*/0:gjj y r the frequency of the sound heard by a person at rest with respect0m:jg /*ejny k to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions p6 *hnznmc,-5;r 6c(ku xr7jal4 ry ndof 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 highest 6x kr;-yd4rzncrjuph m6 ln*5c7n,a(frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoutymn 9o+*c cp1s9kz yd5xnr,a3 reflected by a cliff at the far end r1y5y9s9oxzkcnpn dc ,+ m*a3of 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 7t v)d:njdjghtk90 a6 the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assum9d 7jv6ttdk hng:0a) je 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 20n0+ /b,h: xxme1m:r (qqchgrr $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a fogdie dfnl3bos fs p :8:.pl g;:iq3,d+ngy day. Without warning, an engine bai l d g qpde8s:3nbfnl, i+ofs.:;p3:dckfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a ho4g l qlpg+:6ghe /,a6s4dllcliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cli/ph :h+4g l4ogel dl ,sqga66lff?    m

  A person, with his ejdrz )e,/r9 5wv t6jijar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How frjvj/6) tij5zdre,9w ar away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by thk/+c6uu au6udx*b 2j8 gqvw;f6/a qmye “5-second rule” for estimatingugu6/6afdu q8a /;k *+uw cm6qb 2vjxy 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)v1spp;uy 0op+ ht-oy level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity r-c 2rz/u)n ew jq.iu:is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneo7 6qviurudj/w/6mkv e-ln x g36c ,c1lusly at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not ull6w-v6n ci,gmeudc3kx j/q 7r6/ 1vdB’s.]    dB

  A person standing a certain dist*bw+mh ke1w9,ghpie -22io qkance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on paiew22qbhom k + *-ihp g19wke,in, 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 mu/4/ + i7ey4ecmxeyq a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and th4cmi/4 7 eyuxem+ q/eye background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perso3ar ca7ynne -:cf/g*zn speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly n *ac-nfr:ey /a zcg73uniformly 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 stringmh;n:c n p/9p e1os1kes an eardrum whose 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, whre+7u6 mt0z qer5 e p-dex./gvile 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 cexm+ 6-e0tqer7du /zrg epv.5onnected 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 plac c +*c c2ob+6cg;ioyhyed 2.8 m in front of a lougi; h c6ybcyo+2+cc* odspeaker 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 soundpyurk)zk5, pih/:l b6 level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels dhirp6l )k5:pyb z /,ukiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wha: /e42s d maf7zalohy.d z3u4st factor will the intensity increase? azf ds2s74.d/hlu aeyzm 4:3oIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eak:ko9 2b3ahk qual displacement amplitudes, but one has twice the frequency of the other. Whata932o akkh: bk is the ratio of their intensities?   

  What would be the sound level (in g01 kau-k;osfhs13iddB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at3uas- 1fkok1 0d;hisg 300 Hz?    dB

  A 6000-Hz tone must h 1vv lq ys 4jrz;lvo7w+s2g3x1ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (ssy wl;gv1q1zr+3j4xvlo2 v 7See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cq9xk z3wuddt6gq5i36 f6 ul.uan detect when the sound level is 30 dB? (See Figg36 x6td6ki.quf3qu5 9 zd lwu. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What 60(zdo+iub l nnbc46gm gwx:)(( tfmwis the ratio of highe tbx46oinu(( f+)b (0nwg:6mlzm wgdc st 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 funddtj*r2ib.0is d1q0d zamental frequency 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 string be placed0biqt* z2dj1si r. 0dd?    N

  An organ pipe is 112 cm long. What are the fundamental and fu(hk xkqao)2 sh8 ,i9birst three audible overto8khq)(k ib,xa 29hu sones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acroy.q fu 7upzo)-5d0kwyss the top of an empty soda bottle that is 18 cm deep, if yoqfyu w dp0uz)y-k.57 ou assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spa*;39rscmpt-0dmu7 0k th cll znning the range of human hearin;mtspch*r 0u70kzclm d-l93t g (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has cu1u7 mb;kc7p 9be(ci a frequency of 540 Hz as its third harmonic. What will be its fundamental freque77(u e;c kcu1bpmcb i9ncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long 9xely 7 9qcwnztzlj,b;n8 0r7 and is tuned to play E above middle C (330 H 7n0nxj er 7zc9bllqt9 ;z8,ywz).
(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 org0 scqm9, wt,d8/ ygjhjan pipe that emits middle C (262 Hz) when the tq t9c/0jjmh,,ygw 8d semperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 21nwmy xcamxb, av4*4(0 $^{\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 tj.,+p : uesfqshould the hole be that must be uncovered to play D above mpq,sej.uf: +t iddle 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 re:3ka *tb lefe v6i9gow*t eb3)sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any oth:v a 39 eetlgfb ek*o6it*w)b3er frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m ( 1u9t1kavy zv2*ufjo wv55um long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz andw9z uo*v5k yam1vt(ufj521u v 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 j 9 ar0k6zrr gte7+v5k$^{\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 audib-(zig +oq6o p.z6ohe ple range for a 2.14-m-long organ pipe at+o ipho(z-oz qg6pe.6 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal i )pyvy(f7.mhx s approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the inf(yyh7 x.pv m)formation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, iyf7xs/ *j;2 tx0hd sk,:mm8si to)zmjig f;)one of which is sounding 440 Hz. How far off in frequency is the:zd,f i0xmjjyt ;8 mi ;7*og tss2)k)ih/mxsf other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)4j6gag 8ll r-t 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 anothe:n qfhc:dl,r5r (brand X) operates at an unknown frequency. If neither whistle can be heaf n,l:5rc :qdhrd by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string producunmp9(syo*59: ;dpru+ , xxd pdn6 cpwes 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency 56u:np(x9ry *do,p+ pc dxw n;9umsp dof the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in.r7d6;:pkvncjvh) g1)t y2mpnpxf v4 one string is then decreased by 2.0%. What will be the beat frequency heard when the twohd r )pjny n7kv .vm)1vg62;4cpp:xtf strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two il9tnnra ras7 uo-9bg91h +d q+dentical flutes each try to play middle C (262 u7oa 1 bgql rn9at9+nd9h-rs +Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hpkh(4bie/qfwv s0*8p5.3iie fw9u bc as a frequency 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 i5 bp/bfiqv30 ew9ie*k.u whfi c(8ps4s 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. /d 9f ;pc6 s/ux ;n pu7k(tkj70xuqkbrw 4x,uxA person stands 3.00 m from one speaker and 3.50 nukc;x9t b4/dpu/ k7w;jqur0 7xx,(kxsu f6p m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratii 96copg2swzhrr t ;u*u, un7:+gg4qx mfdy75ng at 132 Hz, but a piano tuner hears three beats every74m+p gf;gtwyo7s*iguq9urhx 2nr:z,6 dcu5 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wb;zb yr:v5actdv14 1f0 q xsk)avelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 2bd1;yqkv)t5 xc0 a1s4fz vrb:0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sireq+ 8m/n) *rxt2q pp auqz)/apkp6x7wrn is 1550 Hz when at rest. What frequency do you de 7a+ktxp)q)p/nwq6a u2px *rrzp /m8qtect 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. What frequency do you detect if a fire engine whose nvd 7686kmsq*ml+ngosiren emits at 15l7n dm 6ns+*qov6km8g50 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f9v; t(micw/b1r x 8 1lazqq-(kwyu gi3requency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it 9g1/8rw av-l((3ctu;m xwyq i1iqbz k 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.53rxzbka sx,il /-owf(xlx as7)*kx: When one is at rest and the other is x/srfxs)l kow 3za 7ai,x5kxlx*(b:- moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonici3li+;nerwi e2 8d tovf/as9 2gov77a sound waves at 50.0 kHz and receives them returned from an object moving directly away from it aa2is 7n+i l3a/frev ; tdi97go 8ovwe2t 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 53x.swlf g sl37 m/s As it flies, the bat emits an ultrasonic sound wave with frequenssgx3w. 3fll7 cy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubrjjv;3 3fey x6(l)hs :r ampv218dt npa 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 rest in the railway station. What beat frequency was heard if the train car approached the sta;6s( j 3 j:pn h xr)tyl1ve8mf2avrdp3tion at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flm 7t 45jelgl:taomf30ow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of soundtmj :3oa f5le4gml 07t 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 waves of frequeba4w8)ysl x wbbr*;p 0ncy $2.25 \times10^{ 6}$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 soul13bq:ffj/-ou du z8snd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observbf/qslu8 :ou jdf13z-ers 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 vtl8 c kidcg1oq9,x1 4moving on land 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 sp.gs-m c (v)ozfeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motiosfm-)o (zgc.vn?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sk5 +okey42 )m0lypc ceound is only about)e4ey cc mk 2lk+5oy0p 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 8500ssrg 7 6, axdhz/.q2yc x/e+nw m/s strikes the ocean. Determine the shock wave angle it prn7yrz w a/ 2ed.x+ /6hsxsgc,qoduces
(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 li/+*pnms5 t6gx)ly4u zqt k0 $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a planel qtq ajf/ m4j7m;q,/m exactly 1.5 km above the ground flying faster than the speed of sound. By t /t jj4qml,qf7/ qm;amhe time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz soun )ln1jqy56 ;qpgxr+ rzy0vm/yd pulses downward from the bottom of the bo)6;q xvlyr/1mg ypjry5 n0zq +at, and then 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 human audibl . rklf.79 d6azsb6(o c:jeluze range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphobbru w;9r5 p,sny. It consists of many bsw 5pur;b,r 9plastic 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 pers423 s xg( h8wouh,o zkqafmi.*(hlkn 2on makes a sound close to the threshold of human hearinu3s khog( nxf4*q w,8 l2ohi2m(ak.zh g (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level 1w: snuoc yb e;41)skta2t j(9n2iaifwhen an 82-dB sound and an 87-dB sound are heard simuat:an 9)4ejiok( bu n wsy1s;it2fc12ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the openbcq z3v q z+hgi3nvoo(j493/c , is 105 dB. What is the acoustic power output (W) 3oo+bgq3c9vz n/(4ij vzqhc3of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at d23n (dnk z7-9 ryz5mjhk mp+r150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 9j k pd (5rmm+y 2znr7h3zdnk-15 kHz?    dB

  Workers around jet aircraft typically wear protective devi9ogxdww4( l)zn )nhu4ces over their ears. Ass( )dowunlz)x 4 9nh4wgume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiow*k57w +0h6au1 qq xym ylvpq7:tu0tens 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 frequency k0qi, flea2q .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 betw.agb k9k +bls*een fixed points with a fundamental frequency of 440 Hz sb k*l+bag 9.kand a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibratioyo sbd2 , 3f c.b;sxvmpau,;m9n above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to;bpxumc3; 9o svya fm,b2s,. d drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What 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 opgxd yi iuj0v1 )m;6.euen 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 th1ju; gdev i)6mi0yu.xird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass w89/4+ hy6kayhv xuic aas observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from t3v u8qpk uhi900ap *dgwo sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person dk hia0p89v*u q0p3ug 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 stattif,adt6;pa )ijjf0 2 myjc 5)m5i)amionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the otherji a05 m fimm6at2c)5t j)jfd ,ypai); train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you q8t8y -pclz /nr10wnyis 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)-c t/1yq 8rzlwp8ynn0?    m/s

  At a race track, you can estinw yr -d0xh(ezzfsx;)t/ -hg7 mate the speed of cars just by listening to the differe/ 7t- h nrxwh0;zz(sdxe-fg) ynce 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 of 11 Hz.i 9kw 31 7k+qecn m,r4iib xpm+elu1,u The shorter one is 2.40 m long. How kbuenerxk4131p, i+, c7+i 9wiuqlm m long is the other?    m

Two loudspeakers are at opposite ends of a b683vrz2z.wj4 iv(xtai 2ox l railroad car as it moves past a stationary obsej(.lwvvtz 62br 3oi axi8x42zrver 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 hears the speakers after they have passed him, at C?

  If the velocity of blood flow in agu:fleqz(n9knf 65t u22 5bu the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultr ut:2n25febza69( qkf n5uulgasound 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 moth ishyx-f4 ):jyfb 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 :h b4 fyf-)yxjdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencynkn *e m- cl-ghi(9r5u 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 be detected by the bat so that the echo fre r*9-kg(n5mihl-ucn om one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Arkq(k ;is1 r9nlpine 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 sh;r ksr (k91qniarp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence ,r)sjp5uy. qs ppc s*pphv( oscr/) )9of standing waves, which can cause apr)p* vs)yp.s(pjc p sq)r/o5c,h s9ucoustic “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, slendgkx 3df66-g3nozy1j8)d c+wd4 s0h yr hq*zheer 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, ringing1kef3 dd-s86)3gh6y 4*j0x dyn zzorhcgq+w h 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 g5vrapx en-s4t h65u *for the human ear at a frequency of abou* trep6hag5v5xnus-4t 1000 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 obsrev-rgz56 xc /o0n8fb erver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitox e z5bn0-r6vr g8/fcude?    $ \times10^{4 }$ m

  The wake of a speedboat:3r 6fpplsb ;o is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h