What is the evidence that sound travels as a wavjuq6zd,buwsd ,8w hf0h /sk/y+ gi5*se?

What is the evidence that sound is a f mrfx,pv1i b:x z mu03i;r/rk1n o,sz.orm of energy?

Children sometimes play with a homemadh:3+y ir6z7inbrdt: x e “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cui+n:t br 6y:z3drxh7i p (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes f61 )twqqh7c);oz h*p:w ld8 (zbuc(xxzb4z mq rom air into water, do you expect the frequency or wavelengthczw qxw ;qzhb):pc()h76u8 xzzq*d t(o4l1bm to change?

What evidence can you give that the speed of so g jts/jk4*vduy*2 y8cund in air does not depend significantlyg*cuts yd824jk*y/vj on frequency?

The voice of a person who has inhaled helium soundh1fu u;w(.ufx qb/ u0 cool0f2s very high-pitched. Why?

How will the air temperature in a room affect the pitch of or,uns me6;gil-s8k o:ggan pipes?

Explain how a tube might be eejy13a61)ipo n;g xeused as a filter to reduce the amplitude of sounds in variouag3;px ej6n eyeoi 1)1s frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (/6- paqer4idi* wpv5gFig. 12–30) spaced closer together as you move up the fingerboard towap4riwgq*a / idp5v -6erd the bridge?

A noisy truck approaches you from behind a building. Iniajzpju :/a8n68xni 9w(g1 a n msw88qltially you hear it but cannot see it. When it emem/zwx: a1u8p nqsnai(nl 88 g9 ajj68wrges 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 “interference in space,” w/p bdklfuc)1r5cbr +8 hereas beats can be8flr/r+ c p bdbku1c)5 said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou do 5o)knb:6 v+si+fogld the points D and C (where destructive and construcgno)o f65bdo+v:k+s itive interference occur) move farther apart or closer together?

Traditional methods of protectkxoy vbjf0es 4.7y7a7ing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the so4jye.so b07avf 7y xk7und levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought w.b )8b)rwzx se,/b3*ibfsw t of as a superposition 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 frequee twfbw ssbx*)b,.i/ r )83bzwncies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the rbi0r(: nnov9s mfd9o.7 nav5source and observer move in the same direction, with the same vev:f5rid.n7 vosn aon0b9( m9rlocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a pek8np7xf+z.xm3;z / x:i ltzo2gftbl00ww : yorson at rest wi :ow0b. iokw/zgtz3x7y n2f txp:80l;+ lxzf mth respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positier po.mv j/d) :fmv4*i6z7piions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of tprv:47m/p 6j m.dvo)fiiei*z he whistle? Explain your reasoning.

  A hiker determines the length o+nzhwk +) j*dmyql28 hf a lake by listening for the echo of her shout re zdj+*+hqkhwm)lyn 82 flected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his s c;s+p:-:e* o. dwibod zh;mhxhip 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 1560 m/s (Table 12–1x w*;o-zh;e+ hpsibm::.ddco ) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at;uphm/ *v;ih-i 4i cku 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 vx5w,i:4ln ,t/jss apa school of tuna on a foggy day. Without warning, an engine bn xi s4,jvwas,:l/5tp ackfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when str(v nv 40(2(tyzjt nuyuiking the water belo(n2tvyvutn 04( zuy(jw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete paxptvl8d6*w.lp6* fiagipx qr3 cc /f;f5vh7 3 vement. A moment later two sounds are heard from the impact: one /hpvfi 3c*37 ilqa x.* x rgcfdwl v665t8;fpptravels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over onetjp lw15(lz:7 i-e.sqawvb sfp4m8 9u mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperaturmvs7u5 4baesz-wil 9pwlq:p .t1 j( 8fe is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a so+df )f ;h* bbyz3mpp:tund 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 of a sound whosekevisblqn5 270u,t3pvh/ /o pw 7jmz7 intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atquwh-;j.z; q.n,wnh5 r57y6b cheaa r a certain place, what will be the sound level if only one is exploded? [Hint: Ad 5h-,wabay7qchzu r6n.j w . q;5eh;rnd intensities, not dB’s.]    dB

  A person standing a cer+ k; b9minkle0tain distance 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 o;ek 90+bnmik lne engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sigxei 09ek:: zutnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrou:e 0xtkiu:9zend noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea4mfgu)y fb yj)j 1i64vking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on uyv4 )j4fy)b6 gfjim1the 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 stri-,w zcgo mk k-(7nwuu-kes 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 modhi9 rm9 semy9 s3(b.v):by*byo0 bs cdest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m froirbmsvd b* y hsbs9()930mecb.:oy9 ym 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 meter retj9z6du)4fxj g8i-b3d vo -elgistered 130 dB when placed 2.8 m in front of a -6vi td zudgx9e8b3l)4 -jfjoloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically det uqov 9ak5f69u3ibx;o ect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of tkx ;au99ob 6i vuf53qowo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the iqecu0n, q2x g+wd*b :yntensit0e guc2qbyw * xqn+,d:y increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have 03lcdko (*lpyequal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of *y(lkd03ol cptheir intensities?   

  What would be the sound level (in dB) ( h4k3mk* xmdxmvq l1(of a sound wave in air that corresponds to a displacement amplidk m(mhxx(kq 3*vlm 41tude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what imtbk,ju ,d;6pia, e,4qtm) u sound level to seem as loud as a 100-Hz tone that has ,u,i)kpijqm;,etm a4td6 u b,a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de wy21mq6zdpw8lcg -/ htect when the sound level is/8qc 6lzywdm-h wp2g 1 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range qm;)hz)w7bs p. 5dbwo of sound levels. What is the ratio of highest to ldw5 w7mb b ;)).hzopsqowest 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 ofjd7x9*5qb e( -qnvem fi.f9j f 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g.fq i-j e.fbd9mxn5q7f* e 9j(v Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audib nr-s s.opp;o(le overtonesnpoor.- (;sps if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from q))s 9i knqob6/ wrh1pj3jdh2 blowing across the top of an empty soda bottle pq d 1kj9sr3oqi)2wj h /6nhb)that 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 with open-tube pipes spanning the range of hu:a1dt) r; nlr/nhuyo; man hearing (20 Hz to 20 kHz), what would be the ran nn t ;rh/droyau)l:1;ge 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 Hzd95;qe-ynj(nk3x mwf4 ec r:v as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengm95qyxd nr4:;en kv( wjfce3-th?   Hz

  An unfingered guitar string is 0.73 m long and is tuned en-2.r yomv.qgia.4k to play E above middle C (330.r4om.gkny 2 ev-a.i q 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 m8y7d h/(nlvdu) ;nyhu .ph)l eiddle C (262 Hz) when the temper8y .h(;v/eydl h7)nuhldn u)p ature 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 62h3gle62gmdt 5djy0 d tw1 zbat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in az3:r(5.o r tcv fre dq7h2nc*Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz 5*a cotec3rnv7q df2:rh(zr.?    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 p tu9o- +k xpw6tdp5 xv;xs+-dxipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this xsxv +t6tuxdd--xw9; + 5okp pis an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 mxi8 45oktn(; kcad 1ur6/vlbib wa0;b long is open at both ends. It resonates at two successive harmonics of frequeka;/b 6icva4unkr5 x i18t (;wld0b obncies 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 mrfi107rrw 9 z$^{\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-le6:e,mkwe0m opk; 3vzong organ pipe6; o3 ek0w z:veepm,km 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 open to the outside a+c52 btcz 4h1qa6fv3g3r q 2kdi .nizend is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of izg+dr5fn etiq3qz1 c.ahbv2 6 2c k43Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one lohi/j:/ ka ry m8/,mqof which is sounding 440 Hz. How far off in frej:,mqa o/k8h iy m/l/rquency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) d9p.gd 9zu0la and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand Xopy 3y+ z;qmzyc,f1.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 simul,z31 cfzym oq;yx p+y.taneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whs5xs. dvnpw;,8xhjr6bdo4 *ore 8ym5en sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your5w o4 rsmr xbv. ph,68yd8dsxe;jno*5 reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thmt5tqo e* n+*de tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: q*tde*o+mt5 n Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cxy9,o i4bpxq( (262 (ixq pb4o,9yx Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; whe-6a3dh zu yac0+q nh*qu fnk:3n 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 frequencies areqn*h3y- f:qcnu63d 0 kaau+hz 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 acgwsc 2.a39i57mvcu lcd+ 1yperson stands 3.00 m from one speaker and 3.50 m from the2ua1 wvdacsyg3 cc 9l.imc+75 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 dches4 tsdl7jz -+7r)at 132 Hz, but a piano tuner hears three beats evz s4jl)r- dceh7sd+t7ery 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 wav j s3wokij+;uht 8i l(x*kib- ; xo*a+4wguht,elengths 2.64 m and 2.76 m in air. How many beats per second will be heardoxw3i ku-us i+h*+h; ;g,w ijl*8b4 kaxt(toj? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire z(s 6t vy45malrmy96yengine’s siren is 1550 Hz when at rest. What frl4r6ma6y9yz sv 5(t myequency 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 frequen4bx3hw w+e. v2a gw:had-7ww kcy do you detect if a fire engine whose siren emits at 1550 Hz moves bexghwk74vwwh+d: 3a2aw-. w at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fre :g7-kg +nuksqquency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenciesn kg7 +kqsgu:- 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 one isgkbn+p/ ,8f y9afjs2 p ngyr01 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 g+92kaf8 ny pjrsp1bfy/n, 0g the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz ando/ )syq +oc(spde8q8t receives them returned from an object moving direc(qd+p8ooct qe8ys /s )tly 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 bat emits an ul8) fc hmdv)tdoezd:, * b,je;jtrasonic sound wave with frequency 30.0 kHz. What frequency does, mbv),do dte d*8ejz:;fj)hc the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler*ig2; gph/xhzikj 01n experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the sameik h*0j 2zgi;h pngx/1 tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound 8egtc3ay2 zc:bwv,: iwaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in huma2atc c8bzgw ,i e3v::yn 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 usingsk-fogce ny--(nyn6f3m h+*pb:jr *g ultrasonic 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 freq.e-hx:0 y k1y muw0/zrt+ uuxruency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, xwu+: 01h.k0uzytrmrx/- eyu
(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 sfhzd6o l1o0jgua- t7/peed 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 m/s (a) What izer7oxar.6y6u9dk x3 xpnstn :f4/*j s the angle the shock wave makes with the direction of the airplane’s motix.:y9tpr 7e3o4 6xf nzujn *rk6/dsaxon?    $^{\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 atm+e ohl.y1zj,z 9ljes b*iz.peco8 x t:cog:23osphere of a planet where the speed of sound is only about 35 m/s 8zbeyoj zpe+osg3j*1.:h z.xc,l:ec 2i 9tl o
(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 strikessinz; o1+h aegnk)-* eyz4o6 jh.cu8w the ocean. Determine the shock wave angle it prodzizh se .ck o6ah j* gou4-yw)e1n8n+;uces
(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 k1* 5gp4q fx(vm lt;gk$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sjpa a(:7xsq:v9cfzx ,ee 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 tvpxs:a,q: c7jz9a fx(raveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pultg c7c8.nmm-pses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed cpm.c 8- mtg7nto work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hum:blqwr me -xl0nix79 ;an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It 6nfa;+7oit iy7;ai+)rtd bll consists of many plasna)7 ;lr6filit ;oa++iytdb7tic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold og6o l0 lql1 fasmq.d i:oj9b(+f human hearing (0 dB). What will be the sound level of 1000 such mosqui9+lag 0f ( .ijqldbl:1o6osm qtoes?    dB

  What is the resultan6 odr3kt, vc28k21oxfgygkd 8t sound level when an 82-dB sound and an 87-dB sound are heard simultanegdvkg63k,82fk2r 8y oxcod1tously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. W dklbm2l;6 9*e3 hpce)8uou txhat is the acoustim8h u2lo6dtu*b pxl e3e;c)k9c power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output sfo1;8.bj 6xs6 krzqkat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? . k;o6szk6 f1xsj8rb q   dB

  Workers around jet aircraft typically wear p27oo nq/v3/ kqkmtl c 56yk9orrotective 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 unprote67/klno kktq2ocq3 ry m/o9v 5cted ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sds .gll 4p,:z.st.n jvystems, 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 to6p/qlc),vuf-g cv 8pf 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 betweu89ma x9-5 giovqmfr0 en fixed points with a fundamental frequency of 440 Hz and a ag9o-x9m0fvm q ri8u5mass 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 open tube fi dlzu)ki-ks3 3lled with water (Fiz3)-d 3k lskuig. 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 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is ne 2+f1gw0u8ja2n6s /emt- ca y cwwhb:nar a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the thirdfgs 1y0/8-6man t2 hcewbwa u:c+j2 nw harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resn8:yfafm-ht 6vi/ w 2zjqr(k2onate 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 tonf-1b-9m.ffde k fl1t nfb98gke in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two s9fg kfl . 1m-ff9efn8 b-btdk1ources. 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 statiok-/x65mvg xm7ta / fiwnary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tra/ f iamxx 6gt-/7v5kwmin?   m/s

  The frequency of a steam train whistle as it approaches you s ji+j/gcca : c)tp2)tis 538 Hz. After it passesptctja) c) i:sg2 /cj+ you, 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 ca -qbrj 8qj7+y rh59gpcrs just by listening 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 goesjy+7pq8-j ch r gb59qr by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, ;*2lcc ;38ugyz1l x oicf/xpuproduce a beat frequency of 11 Hz. The sp x*ol;cc/iu8312cfyzx lg;uhorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends ofua9.2v3a- g4cytn fow 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 the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they .4 fc2u9ty anavwog3-have passed him, at C?

  If the velocity of blood flow in the aorta is dvsv.y*t 55agh s1+ uj- mnoeqn*9k1t normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alon*-otyn 9 5a.tdg*v1jsmvu s51hke +qng the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towayfwdc)cn,./ t mu 1h-krd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave rcy k/tm nw)u. ,f1d-cheflects off the moth?    kHz

  A bat emits a series of high frequency sound y ;; bqqyc*rp.pulses as it approaches a moth. The pulses are approxr ;c.qpy;qyb *imately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used t3m/.f2fwuh) t.jw1jkg8 jd gyo send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The mh.t3 1gww ujfj/yk.f 2gd8j m)ost 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 stern9j2-f gj jt+ah1;ipf eo listening can be compromised by the presence of standin fj;h+pijg- 21 nf9atjg 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 waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendg, b i5twph(90c)bbqp-hh( l her aluminum rod held in the hand near the rod’s midpoinhig0)hbhb,c h 5 t9(w(lpb-qpt. 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-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 hk/wz 9ylzw6o9 ceuels2s( / ,vearing for the human ear at a frequency of about 1000 Hz iz 6/su (v2eo,9/kwcezyl9w lss $I_0$ = $1 \times10^{12 } W / m^2$ 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 observeu x;3 k mdb2f+( blgzq,xna6p8r on the ground hears the sonic boom 1.5 min after the plane passes dmxpx z b,d;8 bgklq3fn(6u +a2irectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboqw ge4(o8kyhk2k.*f oat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h