What is the evidence that sound travels as fhw ,22dldgh)o*a x k2a wave?

What is the evidence that sound is a form of eneradf )1te) c)v,l+h nthz+0hzmgy?

Children sometimes play with a homemade “telephone” by a0t3*alwu ssrz16rs7+f i tj /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 sound wave travels from one cup to the othew67/1*ltt+i ssaz u0f3a jrsrr.

When a sound wave passe r;pa .ecfla,w1(zq v,s from air into water, do you expect the frequency or wavelength ,lwcva,f;a(. ez1qpr to change?

What evidence can you give that the speed of sound in air does not depend signib3y;hbh af 9/rficantly a f;yrb h9h/b3on frequency?

The voice of a person who has inhaled helium sounds very high b(th a5,rol6;nbnk,;4u eviw-pitched. Why?

How will the air temp02ucx x;vnev7erature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ok87 vsix8flu7v5ntnl. 3 t7vpf sounds in various frequency ranges. (Anfvvs 35p7n8kllv7. i8u xtnt 7 example is a car muffler.)

Why are the frets on a guitar (Fis0mg6b; ix0wadr4; nzg. 12–30) spaced closer together as you move up the4zi a0smn 0;g6x;wrdb fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initi9 ojae0k)z-3 q/nsf,sdzw.l- k6sj fsally 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 noisssesk ) 3k/ ojz9qld-j-sw.60a,n zf fe. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be7*va -fm-6)v0b dd .,qd; pzvn.fllcsl.i dtk said to be due to “interference in space,” whereas beats can be said to be due to “iv6f.q-ldlda ,bv*nlp c)f d0ki7-.vtm s;d. znterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lower s9a ku dl9 f4a-)lfqq)bgm+(ted, would the points D and C (where destructive and constructive interference occur) move fm(aq9l4qt+-fs 9)d gakfulb) arther apart or closer together?

Traditional methods of protecting8k8 pbp,5xvxm :ontk 3 gts/+f the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reducp:3n88v,btk+x pgxs of /km5te 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 can be thought of as a y8 w*q81 ly/k tj-b4k ifpw4efsuperpositi*ewk4 tfy/88y4-i jq wfpk1 blon of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift hde 5 ve 4::6xek(voi.lfx e7*hcu o4zif the source and observer move in the same direction, with tz(4c6 dex 4:*k eoohuv7feih:l5.exvhe same velocity? Explain.

If a wind is blowing, wil ch3 oua e*48f8 ekda,1y qu/pokq1k(ml this alter the frequency of the sound heard by a person at 8a, / m1qku4*(ca8 hkofq3yedek 1up orest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.eie 9 8kd*r xtben72bhl, -vm- A monitor is blowing a whistle in fron2l8d *rhne-mb9vb -xt 7i,kee t of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for thgs5dzbwung2p - g6e) (e echo of her shout reflected by a cliff at the far end dgz enp w)-6u2b(g5 gsof 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 sidauie:1z/3a 9j hf+ t;rgkd.pme of his ship just below 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 is 159:;red3+a.1/fjpa t ukgi zmh60 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wa6gz:k5 o/wsuvvelengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just abo xgap9 op)*rx4ve 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 muc a9rx )gxp4*poh time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splashcv1xw:/ o+fdw it makes when striking the water below is:+dvof/ xcw w1 heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hqw/h6 26c61aahl ;pwt+srt6d s sl z5cuge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels i /al6swt+ tz;q1 hahc6c62rld65wsps n 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 maftib8ema euvb6i (7; 8de over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if teiuabv 67e(8 ;ftmb8i he temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soundpn uub4+0ruc f0vb; 3i at the pain 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 oniv; 5vwdzm 0hzo ,2b,f a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fi:o dcw;+mml3hred simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intw dm3:lmc h;+oensities, not dB’s.]    dB

  A person standing a certain distanceu4:dst4 ukn5z 5l28zj yj8ewp 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 all but one engine? [Hint: Add inte2u4tlw z5sd yj5u 88jpkn:4eznsities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noq .(an 4n/ g1o; 4iqh/opttrifise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dBtrqi;o4t(ph i/n/a. no 1gf4q =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound f39 s ,kjyxm n1ix9:/amle y 6c9gseh3from a person speaking in normal conversation. Use Table 12–2. As1es,3 : 9kyf9im mlgh a3jsxec6/xn9ysume the sound 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 strikesh:pjb5o k::7c3c.c3ua x q chs 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, while the more modest amplifier cn9ii3u y dz)9B 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 turn to each ampzy 9dicn3i)9u .$I_{250}$ =    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 fronw-uw2v1 pupj,jc z5(vsv:cq( t of a loudspeaker on th-v wv(2j vu:c(puqw1 jz,s5pce stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Wha zal7k(7l/hvk 3jndw.t is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.] .lv3k 7h(k7ld/awjnz$\approx$   

  If the amplitude of an7n ghus-;. )v4qszat sound wave is tripled, (a) by what factor will the intensity incvq -.;t) gnhuss7a4nz rease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have pb ot m2gxm 2u+2svjzc:4v ;0lequal displacement amplitudes, but one has twice the frequency of the other. What is the ratio; +top 2vs 2m 0:uzxlbvc42gmj of their intensities?   

  What would be the soms4zx -5lo rp6und level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz5ols4zx6rp -m ?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that rl5cyir 0d4p:fq ) c kvt90,o8l5 aqfnhas an,cir5:ltva y0 0f k)r49 coqf5lp8 dq 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest freqo tmd,g-;vuxq1q0 op xw2t bc0g1o(p2uencies that an ear can detect when the sound level is 30 dB?tw -(q u ogmbvp21t1xpcd0x0 ;2o,ogq (See Fig. 12–6.)

  Your auditory system can accommo,d zigtp/58x;8tzl xx date a huge range of sound levels. What is the ratio of highest x/, dp5ztl8 gizt ;x8xto lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of ) grs8:g5obogthe vibrating poo5rs8bg) :gg ortion 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 fundamental and first three a ) 88kz.w5f1hbojbi , ykw-ygl51un6hbvhr7q udible ovewqrk,b.ky5 bj zi)w 15nhh -v hl17guof6by8 8rtones 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 yostof1 +bcsdhp) 8 : yu5li2(ywu expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed 1s(uyo8:cipywlft ) 25+ds h bit 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-o( ; gwqlxbvk 9njea,5zc *b27tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would ba *eg ;b2vjcw n(5q kzb,olx79e the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as zt0ltw( uss9a4r4tt7its third harmonic. What will be its fu a 7409 swtttlrs4z(tundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovehg ca 4jnjvqzp7 9/)u1q+gfm; middle C (330 Hz).h7ujj gq+; ncp4fmq 9 vazg/)1
(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) wheno(x 0asyuoa.u4 b9 h.z the temperature .zso(a ux.ya o40b9huis 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 t)jbdyrl34rc- jh;.v y ;g+ bx20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie-n u fk. cxn,sz5*8aovce of the flute in Example 12–10 should the hole be that must be uncovered to plo*an ,fus.-nczk x5v8ay 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 resonate at 264 Hz,,9w ur qf9f*kw 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clq9,r* wuf9f wkosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both eo:.n8 ydzzm(lay -1viqem k 79nds. It resonates at two successive harmo.:yki yo1da8zv-lm9nq m 7z (enics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 yuxevdw2*4 8 t;;1.dkuzmrcy$^{\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 audible range for a 2.14-m-long organ: 6/bsph: 7dgyb-bder ghbe rd7ybd-psb:/: 6pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. Itlp:2,;57deq mcb- dad) 4la i7pe5gn/kw b pip 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 re5p bi4d7ein;lbk 7 )dg-l/w c:q appa,p2 m5edlationship 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 ever c7pmt*2rn )y:s (rgzwy 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stringm2twg*nr7 )(yzc:spr ? ±    Hz

  What is the beat frequency if middle C (262 Hz) aiciq lj43sw-9wc;ji i7 ue.4sfa05j wnd $C^＃$ (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 another (brand X) jr;d00fqhn-fp bw.a u*f;ip3 operates at an unknown frequency. If neither whistle can be h;3 f-n*h0i u0d fpfja;qwbp .reard 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 produces 4 beats/s when sounded with a 350-Hz tuta ng8 ku0w*)8dw/w/sp rf3,s.ang vcning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your /*0,)s wuw./pr8t fdavgg3asc kwn8nreasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The td 6.:p( jifn6gq3jy7 ewdvdj+ension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two n pvjefiyg :3d7w 6(.+d6jqjd strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical j 4fgnu9 wuh56flutes each try to play middle C (262 Hzhg4w 596ufjun ), 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 has a fruz:9v1k zvt/3dya /isequency of 441 Hz; when Ayu3/vvi:9 s/z1kdt za and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are 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 apari* fceqc *29 .pant uu/o,5ab0zhr3mut. A person stands 3.00 m from one speaker and 3.f3,/* bh2 0pq azmcueot *nuic ru.a9550 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 su4 r +mgz 4jz),lynx/x/cuayh6 pposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 yhmlu/ cxan)yrzzj44 x 6/g ,+Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How ma/n48fj t7pqr9nnnul3 ny beats per second will be heard? (Assume T = 20 np947/nfjt3q 8lru n n$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engi ccv0xfpf.z k )5q 9zvz.dh5p;ne’s siren is 1550 Hz when at rest. What freqk vf 5 v9phzq)d5;.xc f.z0cpzuency 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. What frequencyy5a383rd2 .ut +fw)lcclavv c do you detect if a fire engine whose siren emits at 1550 Hz moves at a )wru cd.av lc+5y8 f32cla 3vtspeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towasqa4)jdn.a r)*6jib k rd you at 15 m/s versus yjk.b )a an *rdq4s6)jiou 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 oneptg2vc6v kl uhg .93t7 is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assumt932ug vv h.pltk7cg 6e T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them retdegv :xl k2qt6w2)v 5r6;w0psks: zquurw6)sl6 k wz5p02sug::td;rqkqxe2 vvned from an object moving directly 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 of 5 m/s As it flies, 7q hubktc,a;vj u4 ai,,p,m *qthe bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hea qiuv jc;, p4tkbu,aq,a7*h,mr in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fla5 m:voxsyp8 gc sdtf/(aqo e v2);vy(6t train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in tmvs yqe/vo6oy(s()xc;f8 gtp ad2:v5 he 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 uss tc,d x55t )mec3 dke,jya0k;es ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is ta jdxmkccs3 teyed,k;0,5a)t 5ken 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 frequel,va5qs;n ao;wim, 7ancy $2.25 \times10^{ 6}$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 freq :s44qxbe + 8+ay bywmv+d2s1;ckl vtquency 570 Hz. When the wind velocity is 12 m/s from the north, what frequen4s ey8 ++sw; km4a1x:yc b2bt+ qvdvlqcy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its t6z -q 9z0g5e-r*gc0 jthpce3,sgi wd 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 sound is 310:e 3yepe u+o.g m/s (a) What is the angle the shocku +.oeegy3:ep wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soolylhoz7 5).u+j+nfe und is only about 35jhue.z l5 ylf+7+ )ono 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 7s ulwek8:f ovzr,d9e ah,y68the ocean. Determine the shock wave angle it p : ,auv8h6s,doyzwe f97 rle8kroduces
(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 mm ne s;3tq51brm9 jj1*. kasq$/theta$ 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 exacexv(eh 4alm4tm/ nz. zcn65n9tly 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 distance of 2.0 kv/t4z6mnn(4 9lamn. ezxeh5 cm. 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 20,007gmc(e:p 0fi8u7l c oi0-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water iu7 o 0pi87c:mge(clf)?    s

  Approximately how many octaves ar :mesegrox0 8:e there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a seg:bl dc7tfv4zvn. vl cg b( 20c0q*c9uwer pipe symphony. It consists of many plastic pipes of vug(.9vqd:lv 7lczn40cb fv g02c*c tb arious 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 pe6ss(n ui40 nbsjo(qdjyc8 8-qrson makes a sound close to the threshold of human hearing (0 dB). Whqi0on(qdcnujs88y(sb6- sj 4 at will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sounel m4k vngymbk0-inbm7 d9 7.z u952nid level when an 82-dB sound and an 87-dB sound are heabun n.v 9iz47k2me9k0 gm li7n-m b5ydrd simultaneously?    dB

  The sound level 12.0 m from a loudspeakeru+w/,j4k+j yal8whql ;a vq x0, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it ra;huykjl l0qq 8awa4x+ w,vj+/diates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The m914 qq0l-c:mzllccr power output drops by 10 dB at 15 kHz. Wh-1c rc4 qqmlz m9cl:0lat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraftilr0;w 1ccw bc.9 a.dd+5suti typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a a1 5; ib uw0dilcw td.ccrs9+.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, :rw o2e6g3j0mvw)hg xthe 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 nf x/p3e8xq+: kuzj h++qoc6g 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamentalk8( tdcqxogb.j8u;z qp3v3d + frequency of 440 Hz and a mass per unit length of d8pto+d3;b .uvk jcxz3 q8(gq$6.1 \times10^{-4 }$ 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 w /fb0*zc0la5h zg);ovcos 0gc ith 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 level is 0.125 m and again at 0 zg005co /s hgbcol*0c)af ;zv.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g i+d .5p,.bdzxz9tjd ts s near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it tdjx9tbz+,5dp dz..s is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed t:ne)f y (c*rn; 5vkjx tk;kgv+o 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 ra;juam1zw*b 3lfff* j8h75mj mnge coming from two sources. The sound is loudest at points equid fjl*a mb;fj1 *fm5u7m h38wjzistant 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 conducto oecdh4sc)j77l v1k h*r on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tr74 c71 klso vceh*jdh)ain?   m/s

  The frequency of a steam train whistle as it app xg6t,+ *fi wpmmi9av.ki-,kiroaches you is 538 Hz. After it passes yoii*6i,kawim+,k- 9 vmt.gpf xu, its frequency is measured 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 listening to)g6w* ksnkwh2cck+kpfv 0t 4: the difference in pitch of the engine noise betweetwfsv gk46) 2*c k0+pwh: nckkn 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,)+vqyhbp5m x9o3y, w8kpxt4u sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m )vqw xp+5x34y pku9omh 8y,t blong. How long is the other?    m

Two loudspeakers are at o.rhs 2b 5qkg5/ qm8s1eupb3e vbpj+jf*)f5bx pposite ends 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 frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of thep f2b5 xb r* ebu/jp)1jhq+ss.85fkm5e qv 3bg 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 bl4r9ho yz2qqrc 7v69b good flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of g2c ryvz7qo9hq4b6 r 9$1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spw 5jyrl- -0gcoeed 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 bayow 0c5rl--j gt after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenyv, fuq8dsgkz ,:kzw68 u1yv:cy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms gd,f kqv:1uzy,zuk6s:88yv w apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals* 70nfj7;aporqaqo8i yw o 31qw)qy.q 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 aw np)oq7 3oa.i rw7qy1yqfo80qjqa* ;s a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be* p1gb)zx2rk(ul. z xy compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a l2*)g zukx( .yz1 xrbpliving 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, sle r 5ggmtk,9eoqfyyw zl9( wov1b9c (-8nder 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, ringing sound. For a 90-cmybvz,oge9c-t9oryq5 w ( (9m1fg kwl8-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 humaz2;x+z83d o se1nbrpcd;2l r rn ear at a frequency of about 1000 Hzdsl2r1dce nr2zrz;xo +3bp 8 ; is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the wjj87hwm-yei.s97joka,5 vk sonic boom 1.5 min after the plane passes directly ovej,h.kkos myw7-e5v9a8wj7 ij rhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 j qtgkdd-1it: i-bgfi8,/ ( pj$^{\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