What is the evidence that voteqv+j1xu* - uva-*po;pe:sound travels as a wave?

What is the evidence that sound is a form of energy?cnxpjs 0z+x )n i;h(j1uelzo, i0;yn3

Children sometimes play with a homemade “telephone” by attaching 1ip. al- )+7e2 (mjm wxh+ij wluoo8gwa string to the bottoms of two paper cups. When the string is stretchea8x+go)o ll 7 u ww.(-h m+jjmpw21iied and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expec xu0n;7*hfa x+ tu-jdft the frequency or wavelength to change? ; u-tx7 auxfjd*hf0+n

What evidence can you give that the speed of sound iju6:e7n.qj ly 6ywk62 -kolwkl*hhx3n air does not depend significantly76u qn.6*w :ykxlhhwj ljl y2 k63-koe on frequency?

The voice of a person who has inhaled helium sounds.m(pk ;dl:pu- okxsy 9 very high-pitched. Why?

How will the air temperature in a room affect kn0s .qj*cahdp b81gh6w j7(nthe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce61:ytle b 2a yg,.w ijzcf6kt4 the amplitude of sounds in various fwa6:f.ittl4y gz k yc 12,6jebrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov )qa:m9 s4a e(nxi32iccxf z8knk5*q qe up the fingerbonkqfqi nxs8:ci( 5m 3 2c9*4aqe)zkaxard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it b0yhqe9vk rp yb /;md: p(p+ c lt1w3nuutx);w.ut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the0 qrb m:vdp .t uw;yy;)xlwh 3 t1+9epp/nkcu( high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be dx;04ekp r9 hsgue to “interference in space,” whereas beats can be said to be due to “interferenchgps ex;9kr04 e in time.” Explain.

In Fig. 12–16, if the fr ce+.x:y istl6f fes+l;t3o1aequency of the speakers were lowered, would the points D and ti+ :l;lt3+y6es efsc.foa 1xC (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectine6glsi*4 i j/nc82q9qgi 6vwt g the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noiswgv 4ql9g6/ jcii e6int2s8q*e, 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 t su; 7y1weqk(thought of as a superposition of two sound waves withyq(se ku17;w t 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 so: 5oy u+yg9jf /z1lxxxurce and observer move in the same direction, with the same velocity? Explai:y1f x9lyuox xj g5+z/n.

If a wind is blowing, will this alic0o3m (car7/ clfu w/ter the frequency of the sound heard by a person at rest with respect to the source? a7/oucic w(m0cf/3lrIs the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion 9pddyd+g *,htj4/y saon 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 of the whistle? Explaidg94j d/ah,+yyt*d ps n your reasoning.

  A hiker determines the length of a lake by listening for the f7a9iqg yqqepdv+w;;- yxd::q 9h8hdecho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s ax ;i eygyw9 p7qa8+:hfqvq9dhq-d;d :fter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.7 k j(/,xztmzf 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 1560 m/s (Table 12–1) and does 7f/mtz ( kxj,znot vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths p ou cid8rn/6/pu,b0m ;;zoirin 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 above a school n p hgl;aip9uq5(73ioof tuna on a foggy day. Without 59ip 3o ;laiqnu(p hg7warning, an engine backfire 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 2 ivxck5piz3+ctg (a dmw() d6the top of a cliff. The splash it makes when striking the water below it3kcxad(i6mizg+( v cd)pw25s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike 8si h )39 fxg)* yda+qmjp:uj fyn06l-yn:cphthe concrete pavement. A moment later two sounds are y f+ l fmyx*dhh:uj nj9y30 cs6gq-8a)nipp: )heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent cn.f )5)txtmi error made over one mile of distance by the “5-second rule” for estimating the distance fromxmt))tf. n5ic 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 level of6)nng2qc l.ttn wv 9ay0bnv,7 120 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*l*cc jkckb/; is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9:6t6h7z k t,ouzqcan)67t +y c7jy dje5 dB when fired simultaneously at a certain place, what will be the sound level if only one is expcnh6 e6dt7jt, t7ck)6z 7zuoaj: y+yqloded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisun/s8qqtmg kh )92.cicp+;vj can5;c y jet engines is experiencing a sound level bordering on pain, 120 dB. What soag/2 s+tcq qimvuc9;j5 h8 nkc)cp;n.und 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-to7 (dedi.ltg ;6f )vjjq0dcy ;f-noise ratio of 58 dB, whereas for a CD player7( j; tcyidegdq );v0df6 jf.l it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a fmiu r i.(v5hc 4(8ypnperson speaking in normal conversation. Use Table 12–2. Assume the soundc58i4 f(h i vry.p(umn spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose aream +)(d3gkwj8t gpc ;yy 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 28tu z3uc3-0 bp8hza8n4ggd sq 50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound b- p0u43cnadg z8g sh883zt qulevel in decibels you would expect at a point 3.5 m from 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 dB mete*ft4v *c9 : tuoluuw zw+z 2r.m*h;hxrr registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage owfv+l:x *mr2 rhw;uttu*u*zhzc9 .4.
(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 )ba wew40*urg 8x nx2qin sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section xx bg082reaw4wqu*) n11–9.]$\approx$   

  If the amplitude of a9zye wccf y5ww 6wv,-4 sound wave is tripled, (a) by what factor will the intensity increase? Increase bvw9,eyfy4w6- z cw cw5y 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 tt12 yw2h)ahmg he frequency of th2y t1w2a ghm)he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that cor .e7e:n,qvhkeww d2, cf 7,tedresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 H7enw.t7kce2d e:fe,,w, vdqh z?    dB

  A 6000-Hz tone must have what sound level to seem as loud as au9kbws9wzgg)z-g4 c/r tmw;5 100-Hz tone that has a 50-dB sound level? (See Fig. 12mcs tbwz9 /gu-5)wr w;49 zkgg–6.)    dB

What are the lowest and highest frequencies that an ear can detect when ao;cb pdyrdtm.8d9 68the sound level is 30 dBprt8;c6 dmoa.8 d d9by? (See Fig. 12–6.)

  Your auditory system can accommodate a huge ranf/ :f lnvye20rge of sound levels. What is the ratio of highest to lowest intensity a 0v2/yneflrf: t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a w1l8/8i l uz,e a. ;kxn)drzccfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it hasnr );a .i/l8 clxzd8 zwu,ec1k 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 audibl::rj*bkz kxq6bbe t.: e overtones if the pipe is .qx6j: bk erkt*:bb :z
(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 freqwr6k k 4- frn)w;jj 5ho2/gjknuency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if-krhfgj2 6j/wk jro;n4kw5 )n you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning .53)5cueh :0/s*na v5j v acd+uhreiws/oyx vthe range of human hearing (20 Hz to 20 kHz), what would be the rangeixch*v u/n:dyohs/v 0vaew 3cr . u)5sa5e5j+ of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a d5db j)m cdqm1h1r ;cxw-(6icfrequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingere)d 5id cjdw(xm1r- ch6cq 1;bmd at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and w995zlu2/y k2atkc;o d7 bp(bih/ zpris tuned to play E above middle C (330 H92h kdcpbtbry 9 ;zpk(/ ao/ u725lwziz).
(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) wheoooq *t;y o8s0p 3ojcmh-+8 iwn the temperaw80 o8ojptos y+*micq -3o h;oture 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 tx*-a5 s 0eli 5po ;gwnlek/,o20 $^{\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 should th myvhnrz-+w0 rum0/9pe hole be that must be uncor ym9prvw+ uz-n 0/0hmvered 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 resonate at 264 Hz, 440 Hz, a8lbxia9 96 63cfqtnciia -/:) guqfibnd 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closiafnqx6ta) f6cbcul i98iqb9/ : ig-3ed 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 ends. It resonat /g+34kiprqnp es at two successive harmonics of frequencies 2g ipqp/ 3+krn475 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 x/i52.l nszb ::retxi $^{\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 aud/0gyb do 1ts9pw p;1ql-sm qt4ible range for a 2.14-m-long organ pipe at 20 g0p1-t ;s/l q1 4bysowqdptm9$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside ar r6*c dsvde1y6/fxc0nd is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Wha 66/xrvecrdfd1s c*y 0t 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 tryrnxli71t2 t:i yt4z(ging to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is 1(y 42xn:lt7gititz rthe other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and fre4jyg 1 ol/)f9t:de $C^＃$ (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 9bwn:3,qbdl0y ,akcp operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand Xyqa 0p9nc,3: dbw kbl,.    kHz

  A guitar string produces 4 beats.mitfc1xxwou h g , - q+yk/15t;bm2jf/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 frequq1ciuxt 2, 5 -;om b/tgmf+ 1jhwf.xykency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensmz1*u uv)q- gaion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. gq u1maz)-*uv 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middq(m mebe60rd (j -m d4,dw-dvhr2 ph-nle C (262 Hz), but4-(n hdbve mjrp ddm-hw0d rq(-me 62, 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 juj 7 e 5p(5ved);mi/ofon+yg 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. What are the possible frequencies of A and C? What beat frd p;/e +gu 7y 5nijv)(oeomj5fequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stakz* (rrakv1y 9nds 3.00 m from one speaker and 3.50 (yarrk v9k1z* 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 vibrating at 1 6 p*uhxep :qs*:u7lrd32 Hz, but a piano tuner hears three :6ue*r: 7dsqpx lpuh*beats every 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 wavelengths 2+eadfck6a, tr3, ncpn(3kf , n.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 6p3 cf,r+,ckn,d ka(n3etfn a $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren n *yl x-bo;n9oge2 d/nis 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/ o29-/y;ndngonb* x les
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you de,/i +c4na/u y z jfq2d lukj7)p/pu4dgtect if a fire engine whose siren emits at 1550 Hz moves at udgyunpa/4)q/7p4lc 2 ,+/fdkzu jij 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 sourcfe;0y,t+ wok za.w*pve is moving toward you at 15 m/s versus you moving toward it a a0.eo * +z,ytv;wfkwpt 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.u , av8eps.gr o70g:jobb*uu the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a. uu:pe8*v,u ba0.7 ojs ogrbg 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 ult:jhzcz5/fjf b(n s;u8rasonic sound waves at 50.0 kHz and receives them returned from an object movingzbfch8(j; zs j:fn5/u 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, the bay6,iw9a (y8rxrg 7cch7qo zl8un *hu+ t emits an ultrason q9z,wucxhu rc( g76lr8*yaoin +hy87ic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moc(ax p+f8f8m fwm.ou1ving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at mwc. +ffm818ofx u p(arest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter r1 1xi5;,fimrxb2ebnuses 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 taken to be 1540 m/s What ir1xnx2ibb1i e m, r5;fs 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 ultrasondr. 8efcxun:* ic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequencgta , 38elf0bjy 570 Hz. When the wind velocity is 12 m/s frome fb0g,83ljat the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed a ed;kqu . ,teiof;8he1t 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 8a)(:2 9sft ljuuvz0*csj: j ef5kjhr the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of eusl089jfjj t2j()v5: azu:* rck hs fthe 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 atmospho 662gi3a steduq q-7xere of a planet where the speed of sound is only about 35 m/ssxq662iaq -7dg3e uto
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the sh4, q*c9 nv* n7giesvzkock wave angle itgnq z,ncsv97 k*v4i*e produces
(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 h-zg .jx*y5t/n c,z ,yvt lc1m$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheau c-(v ;litys;d and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12i; s;lvu-cty (–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 x40ypykpu7tl2p: u5n sends 20,000-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 betweenxyn 24pp:kup 57lu0yt pulses (in fresh water)?    s

  Approximately how man1k)r*+s g/uw4acrst o y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mansax +3rx-r80csapx9ry plastic pipes of various lengths, which are open on both en90r 3xrx8sa+-sc parx ds.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold ofcq/joi2a rd k48-64 kc wxsx:q human hearing (0 dB). What will be the sound level of 1000 such mos8 6:a-xc w4scqk2/ k4xjrqido quitoes?    dB

  What is the resultant sound levep0qyd+u ,/zz5 atf:ja*tik v-l when an 82-dB sound and an 87-dB sound are heart5q,fv* zju-+kiayta/0d pz: d simultaneously?    dB

  The sound level 12.0 m from a l fysde3/. 9m 5u,r lpqifojr6(oudspeaker, placed in the open, is 105 dB. What is the acousticy9uo i, f j5/dp(fr6q .smle3r power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Th63 aqho hdt(s+e power output drops by 10 dB at 15 kHz. What is thea d hh+s(6toq3 power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicas(l gz)ta l(5wlly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at l(w )ats(g5lza distance of 30 m from a jet airplane engine?    W

  In audio and communicati-gf6i2t qd.;e0f b zguqkz .(mons 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 1a: hb)hbdm4htgacixcf8xuu y j2;(+ va19q2)$\frac{1}{2}$ 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 vid-ju0 6b;qlzl8pc )violin is 32 cm long between fixed points with a fundamental frequency of ijlcq )06z8dp- luvb; 440 Hz and 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 vibration above a vertical x/6y*jmvytq (open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, tqtv/y* x j6ym(he 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 l/28wva n mtbaxuwli,;)mqc e.co,j76 tg q90is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mod,/axn aowq,)iw l7jt .c98;2b tqecmmg6ulv0e) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass waw;n twgd6*:2j* tugvbil 4kft26wa :is 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 twjzzzr16qq5 0o4-acox o 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 mq j6 caq5orx4zoz 1z0- farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistle5i)gticp t. + rb5k0jgs. One train is stationary. The conductor on the stationary train hearspggc)5j +it5.kr 0 tbi a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistlyyxmmv13xt35/gg evuwt1 3irc mg 6 4;e as it approaches you is 538 Hz. After it passes you, its frequency is measured a6yre i5 m;gmm1x3 xctvg31t3uvyg/4w s 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 lise 0lgqu j 1t19;c8aoostening to the difference 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 oj90s1u1ecq ao;g8 ltthe straightaway. How fast is it going?    m/s

  Two open organ pipes,fozcg h+s/5 0nd*smb; wf8 bj1 sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How j ws ;scb5/m0g 1 8d+hnfzfb*olong is the other?    m

Two loudspeakers are at opposite ends of a railroad car asbny.l 5bd* 6ww it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (d wbnb5*6l.yw c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow inlpu d:h koduk44ln1,: the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along t:p4u un4:1o,dlhkdl khe 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 is flying towar- d+f*aoc /yiod the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave det/- aoo y+di*fcected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses snk+2n a* hx)zas 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*h+z2)xnasn k echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) 7hn; emp)popi0/5a ppwas 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 pn/mpp)oape7p p 50hi;layed as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening cqtncxt(90yki *wt6q .an be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing ww yc( x0k q6it9ntt*q.aves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstra9zi ,9q+tio dstion, called “singing rods,” 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 can q9i9+ot,zd is 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 hhi gd2m:p )8l txkatd w0m1(+human ear at a frequency of abou d21axd )8t+mhm ptg h:wk(0ilt 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 Man jihl*+jc:ap-o e+k4ch 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is *jl-+ eok 4apn+ icj:hthe plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat k szo vfo(q(q()pp//kis 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