What is the evidence that soundb)mq039i*5 v 4oqxry,;z:y) y tisoi(unexsz travels as a wave?

What is the evidence that sound is a form of energ3ut9pxqj2,r 6iq ihs9y?

Children sometimes play with a homemade “telephone” by attaching a string to tpv;zr37yk k6aw.6i 3 whm* pvcz 7o0sq84w dxphe 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).6w6 y 8vz3v aoksh7xpp.;qcipzm7rdw0 34k*w Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from airc5vhz5m,ke .j , gc)7pn1pesh into water, do you expect the frequency or wavele.)k v ez5hgp, ,5ejcp17ns mchngth to change?

What evidence can you give that the speed of sound in air does not dec (4yq1+tje4 iwrhn,udd5p( kpend signific,pn+wr5 q(h kj (ci4t1eyud4dantly on frequency?

The voice of a person who h3ac/xcjq rg8 0as inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect thysdch4,/ 7r3 ays.c * k3lbirqe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds /ku /*,aw ibjwin various frequency ranges. (An example is a car muff j*abki,u//wwler.)

Why are the frets on a guitar (Fig. 12–30) spacj neyz:x8:q)vjo h,s+ed closer together as you move up the fingerboard towao8jnx: q) h+y:szv,jerd the bridge?

A noisy truck approaches you from behind a building. Initially you hear ic8u.*mjnnfduqu *9 ;zt but cannot see c qdnmuzfu;n*8*u .9jit. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferencblbk8o +v- 0 2s ihbx11ayv+0 zikx;ute in space,” whereas beats can be said to be due to “interference in time.+vosb0k1 hx8xt2i1av-+ ub; ykzb li0” Explain.

In Fig. 12–16, if the frequency of the speakmbsp ont,n g.l9j3o+gg; it(* ers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apat ml,.3g*9bnso otg ji;gn+p(rt or closer together?

Traditional methods of protecting the hearing of people who work in areas w5ic+9tve toj 6ith very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relativelytjev6t5 9oc+i 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 +wacke8o63eu y97gk b wave can be thought of as a supo+9aekkb37wucgy8 6 e erposition 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 if the source and observer move3utgz hbe3 2u/h;7gp n in the same direction, with the same velocity? E32hnu g3e;t/ zhpubg7 xplain.

If a wind is blowing, will this alter theht)y8q26xq2( ioz ahl frequency of the sound heard by a person at rest with respect to the source? Is the wavele(2l8 qhaqti h)6zox 2yngth or velocity changed?

Figure 12–32 shows various positions of a child i44x09k)gsf2d*a kwl-ut w*r mj wd;di n 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 frequency for the sound ofg 4s dmf0k*9)j ;- w*dw 4dwraxtiklu2 the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening f jh-nfng6 oan-8lm x33or the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afteax-ng6ol3n j8 mn-h3f r shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below theq o(kg p7+n)uf 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 sn op(q)7u kfg+peed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen a-:tri/viuc+ gths 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 dria hk3mqy; /7tcfting 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)mtch/ ;3qak7 y. 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 cliff. The splash it makes when striking ;9r1pr.brpn kfsi7p n y 13b0xthe water bpk7nbrbprf p119n3r ix y;.0selow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a h7 7u(qlk;ytd2 t.cokql1w9 wu uge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other ik(udo;.7yqllq t2ct w1 wku97n the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the rf n.vg7cmhk d k*h7-r()-0r pozp6 zd“5-second rule” for estimating the distance from a lightning* n. h 0rhkzrg7p)kv-6rpofd7c(d-zm 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 lr2l0fg s7f; xq(1bgaievel 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 5ma0pv5t4i i: xuo /bn*uwut3e)v y9 ja sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at s:mjh4 p(kl1hw p(.nta certain place, what will be the sound level if only on . w1mp hn(skh:(pl4jte is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fromeqao ,p1:n1gpf mg4 c6 an airplane with four equally noisy jet engines is experiencing a sound level bo pqe4mg 611gp c:fao,nrdering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise fjtb9k6 f*e s1ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal ajetbf 1k s*96fnd the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal c8wedh*6a4ka y onversation. Use Table 12–2. Assume the sound spreads roughly uniformk4 e8a6*ah wdyly 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 whose ar; o;354k0o45r rfbxkybphef eea 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 a)cu12u0rgz48kwo/ np9 ex bbet 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from 1 )08/xb94c2 ouwkgnbzu pere a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dBo0p d* :4d:ocqk wjklv05jp 1b meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ok0c:j q5djdwob:401pvlp k*
(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. What ij4cfdg 9k d6k+s the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Segk9+ 46d jcdfkction 11–9.]$\approx$   

  If the amplitude of a sound (k6 ly ;mft6j wi91bsywave is tripled, (a) by what factor will the intensity increass;yb69w l jy6mfk (1tie? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the fr z go0g4au/jdsl ,*q/tequency oo0,zq jg/agult*s /d4f the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound waj7g)z s.p8ycun8- wcf dnvb 16ve in air that corresponds to a d8d1b zy 6c7n )s8.p-fwvjucg nisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must havz9(6omaz70ld c/ttw xgj/7 p oe what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound l pm0(zj97aozxod6w c l//7 tgtevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequenciesx4bq yyg ,:o1/xh ape9 that an ear can detect when the sound level is 30 dB? (See Fig. 12y1pxh:o xe,b9a/q y g4–6.)

  Your auditory system can accommodate a huge range of sound levels. Whatqy:;zf**eoo n is the ratqo: ze;* *ynfoio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency o;z:lnsiw8lta 9tm; -k f 440 Hz. The length of the vibrating portion is 32 cm, and it has a itmn8 k-tw9zsl;l 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 audibleivfky79e1ue, g6z6iqhwcv -5g k v1,k overtones iy9z ,5efik,7 kuqwk- v1h66viggce1v f 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 bly9kcj9s8e*mbiee 8 p f/awr4 9owing across the top of an empty soda bottle fye8m4pk sj9re8* /ew9bcia 9that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ w,u6x9lrlein ,s - lg4vu, 8u xy*8tdiqith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ra8 x9g n,4setq*ui8l,uuvl,-xi yl6 drnge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string h77b kwvgegw(( -2rksqas a frequency of 540 Hz as its third harmonic. What will be its s wq-g7r2(wv ke(g7kbfundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo:*dt- mc4vh gjx *;beo-idte(ng and is tuned to play E above middle C 4xoj dgmt*cde ;t*bv-h :ei-( (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whev*obpb:ohfx;( *a,vhn the teohv,x bba;* :fvp(* homperature 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 20y6e cajp+9vu2eeq.q)-/t uc g $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpaka. 5iqiu c72s.u0nciece of the flute in Example 12–10 should the hole be that0 ukais.c cn7.i ua52q must be uncovered to 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 resojbp eo.b:hk5 x/ qsfts1y.1 .onate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clo1k.t5f/ b:p o1 .oys sxj.heqbsed 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 bothauz 9c (a8 wh8ij 0fh2lyyir)8 ends. It resonates at two successive harmonics of frlahz 80y iw ryj i98)8h(ufc2aequencies 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 b5 nbe)hjv4i b fi+u7;$^{\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;h,aega qa yrjr,v328 2.14-m-long organ pj vrh;82qgraa,ey, a3ipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is openvzrm9:/h3 h ek to the outside and is closed at the other end by the eardrum. Estimate t h/re9: vh3kmzhe frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying nq,/z v,n.t xd8n owh8to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other vnhdo ,nxt,w/ z8qn.8string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and g lav7n )w9m,tmiy3.k $C^＃$ (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) operates9;y wuf,w7rw t at an unknown frequency. If nei9uf7w,ytw ; wrther whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fqjer:90kdwdhp2 4wgj5) lf h)ork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoningjewd9)0p2 g:dqjhl k5w4f r )h.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in onfc 351jwucp w.e string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–133wju fc1wc.p5.]    Hz

  How many beats will be heard ifrb ygx vaa0-(jmamb6-mbatvf: 4 *,3 .uz;vmc two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and abgaayfb6 ma v :ut(m0,c rbxvz 3mv-j4 -*m;.the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork hcoa8;h;tmk3 low9 4 gB has 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 is 4 Hz. Wha;84hc tl9gw oo3mhk;at 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 murvzavm34j *m6 e9g*qrn 8*lz apart. A person stands 3.00 m from one speaker and 3.50 m from the gqn a9lm*zr 8z* e3vu4vj6rm *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 vibrating at 132 Hz, but a pianomm6(kk;x k/r0knt/+pusu 6wm tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of thekumuwkpxs+k0r/6 m; (k 6nm t/ other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats peo z /5;4gxl(lrc 3d-wb; qhfysr second will be heard? (Assume T = 2;(cdzbwrq3 ls/5yx ;f 4-l hog0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ.rralx 5kjs0a; s;v7*vgg*uh3o 2 ydeency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect r;5g37 xo sgka0y2ul*.h e* svj;ra dvif 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 deteco0l.h*joigj4n yi 31 ot if a fire engine whose siren emits at ho4jloyj ng o13.i0i* 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz some;; wax aw 5.*,cdquburce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are theaa*, ;d;ewu xbq5w cm. 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 onee-,jil3u5voy)(yyw k is at rest and thjyy,vyueo-3 lkw5 )i (e 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic souyxdk/ c.xx jj+v1k jsuw1.0w;nd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fr jd1 x ukyck +.sw1xx0.;jjwv/equency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5- h3xz9++ee1jbwj xlo m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bzehwe+b l9x3j xj1o+-at hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originv5e40nxpa x0h xz.b5y+ qim (jal Doppler experiments, a tuba 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 he0hzm.bn(4xjq5 5pyviex0 +axard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measurem rwe*x7pz80 es oqxq*,.bdh 0 blood-flow speeds. Suppose the device emits sb8,eqd07x*xhr.0emspz w o* qound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frvc ad;r -mqs 1+dw(h;requency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12 j xh +zkvkwr6d 6u;)htc+y*mv ac;2 x6m/s from the north, what frequency wvh dw jvc+m6+ hx2);tzkr6ax *cyu;6kill 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 ize;vim)3 .xw 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 sound is 310 jfp.f/mwt ngx4)x(a)m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motioxg()txwm ja /n.p ff)4n?    $^{\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 ,pb6 + tiw4 quk3wspp va;:)xtwhere the speed of sound is onlps3 )p4,pwqu atx;btv +6ki w:y about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes 4.ldk7w2 ylig x2mh -1oasse/the ocean. Determine the shock wave angle it pro4lm x7ig.eo/1as - k2hdwsy2lduces
(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 p6wc hw83n6)oncc *s:vuuu3v9 t qa62lcu*z h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and se-4jv9+dsos mi e a plane exactly 1.5 km above the ground flying faster thaod94ji -vs ms+n the speed of sound. By the 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 20,00u8j l,ij 9cpe;xxb1i p0i.c8o0-Hz sound pulses downward from the bottom of the boat, and th, iic1p8.lx0j ; oi jp8ueb9cxen 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 audi2lc)vayyw5d md y f+,fto(;( dble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consnv najn0;z/b9 ists of many pla/n bnjz90an; vstic 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 aujzo;0 ;vs q8n*+zea j person makes a sound close to the threshold of human hearing (0 dB). What will be thes8unj+z0*vqa; oj;z e sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound 6y5zriae 7i88;s d pagand an 87-dB sound are heard simultaneousypi8i e5z a8rg; asd76ly?    dB

  The sound level 12.0 75ay .k fwrcc2m from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiatey w7rccfak 2.5s equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10003xheps692hbw Hz. The power output drops by 10 dB at 15 kHz. What is tbh6e h39s2x wphe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typich0 :uquu t;xgt:ch. f0ally 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 theu;.hu:uh gqt00t xc: f 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 syst8ag4 zq l;cr)e;g hgl7nxdddqk9; 6v .ems, 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 to7s n4 ac- o70yulyc)jei(ob* n a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long beeuus . wr:j9 wd+,huc ,of**satween fixed points with a fundamental frequency of 440 Hz and a mass pew9uj,*af sd *hwu :,rucs.o+er unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filledd1lu -cam7 z+xff8(sk with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance fro lfz-1+m x(8au7f cdksm the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one n von(16 r5u.+enx-r c /ga,qmwtm,w tend and also 75 cm long. How much tension should be in the string if it is to produce reso.ear /nq,nmt6r v n1u o+m-gwwt x,c(5nance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wae8u297 bsono9.z vlnas 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 5 zo8j 8cob/w z*5ukforange coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one sou j8foz zou/ 5wkcbo58*rce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conl;r7wxw/ tqow;x5uh .ductor on the stationary train hears a 3.0-Hz beat frequency when the other 7/;.lxwwqxwho u; tr5 train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.w extwh8e1 *f9z+3dya After it passes you, its frequency is measured as 486 Hz. How fast ww+f91 3hx zdeatye*8was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the difyby/+kp: ,*go*twkeb ference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octaveypb:gok+e*/b*y, wtk (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 q* bj+rz4c,4jo 82 u-k cu)ld)jvfnjd of 11 Hz. The shoro4ddj8fcl b ) )c *r-u4jz+jq uj,vkn2ter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pafhvf 3p(e q4w-st 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 hears the speakers after they have ppwvh qe3 4(f-fassed him, at C?

  If the velocity of blood flow in the aorta ixw l,nje*x n36s 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 cell l*wxnn,ej3 x6s? 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 u 34mp1tk fck2 qn(fi7m/s while the moth is flying toward the bat at speed 5 m/s The bat emitc7 kfq4f3p1k 2im(u nts a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it apr tqlpah,4;0f 43vysmproaches 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 b03 ,art4f;hvq4ly pms at so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12– gbhc/pzu dro7ly--::sn* qe038) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is *u- 0p/ cnd:rs 7olhby-qg ze: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 listenicpb bl6f(l.g/g6 ;wmcng can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider ap6ll gcc(gbw;6m. b /f 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,” n (ct/vdxc:(m involves a long, slender 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 ccxdmc:v( t/n(an be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the dmxf2 ;yijz8 vacd r,zxazg)v60 y)ej un*+ 41human ear at a frequency of abou d1fix,2 ) u +gz4 axmv;r*ye6c)zayjd z8jnv0t 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 observer on the ground hearse: a5coyf*+w m the sonic boom 1.5 min after the plane passes directly overhead. What is the planfw+:c*eyo 5 mae’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15k3p*4dqwb .;/z 6i1 k 4oi hauwhsh;zy $^{\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