What is the evidence thpd.e dur5yto .5vp 1(t4zxgg9at sound travels as a wave?

What is the evidence that sound is a forxi6,z1b bk1rjr tl7c,dnn9 4d m of energy?

Children sometimes play with a homemade “telep9zz ;qh+ss;/opaj m)/ waj,nxhone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from oneohzn;)/ p+ja azs m;q/sx jw,9 cup to the other.

When a sound wave passes from ai.ib ztjgnpn y,:-q)u-r into water, do you expect the frequency or wavez.:b p-,nj y-qtui)gnlength to change?

What evidence can you give that the sp9)yqf 7d9:2fn0sow) ,zpfzvo x:tu jyeed of sound in air does not depend significant:,y)0:ft7xov dwpyosz9 nj9zf 2 qf u)ly on frequency?

The voice of a person who has inhaled helium sounds very high-pit ,xvdrpkc,y,iq5 p -k0ched. Why?

How will the air templ9ba: w3 w*mdqerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to rucg:j12u 5mhe y1g 6preduce the amplitude of sounds in variousrgm jc5 :g611pue2huy frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1;so8j2 xu gvhgj0,m 6l2–30) spaced closer together as you move up the fing0o2u jsh mj v;,x8gl6gerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it 2jlget4 y5ypaab+:t.but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. ey52t:agtly +pjab .4Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bec+vt8bbew6c 1x o fl.2 due to “interference in space,” whereas beats can be said to be due to “interference in time.”8 wxt6lf+.b e1cvco2b Explain.

In Fig. 12–16, if the frequency of the speakers32b(e .ixk k,ux5 u6o,xm imly were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or clmkix5ybu2ml( x, 63xo.i,u ke oser together?

Traditional methods of protecting the zm1fbkz1 31iy 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 ambient1kb11 3yzfim z noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sog(e)4wn d(uh , tmz7guperposition of two sound waves with slightly different frequen) g( 7unzohte ,w(dgm4cies, 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 souggau6cr+ qc6rm 6az:4rce and observer move in the same direction, with the samcm4 c66r: uagq r+zga6e velocity? Explain.

If a wind is blowing, will this alt9c)gf rter /o*8jcmpn;y/z4ner the frequency of the sound heard by a person at )n* pjr;9ofz/ygct4 mcern8/ rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows vfw;vm ./lve* sarious positions 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* e.svf ;mvlw/ frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakq* d:3t7 dbh p*ujhg r71chdy)e by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the 7hhu:3*dph)t ddy7qcgr1*jb lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shu9 j1u+zak o.yip just below the waterline. He hears the echo of the sound refl9zok. +1aju yuected 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 not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ixl xi93offin) t:6w jw,i0+g vn 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 p8f,; dhgm z0j9 ootzca6pi+f( s3j*dof tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km awm ,a(jc ifs3t;o p6fdozd jh0g 9p+z8*ay (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 splashcod; h8d:jcsg-khv dxnf.6x:b v 09p/ it makes when striking the water below is- xd.f : gkh/ b9d;chx0no6dpvv jc:8s heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gr7e(d53aqgb v 3f qxoe3ound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and th3(doe q g f3b7e5vaqx3ey 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 distaxd .b+o8bsf . wxr7a5gnce by the “5-second rule” for estimating the distance from a lightning strike ifd o. frxwg b8sx+7a.5b the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensit3w6x; d9k2 rfqzfmx9zy of a sound 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 wh(-n nnmeyx2+ vose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produc/2 ob2jktz07et wjdd3e a sound level of 95 dB when fired simultaneously at a certain place, what will be theebtd2k td/0j 7z2o3jw sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jenz t5(e8 lteskov tw5v :tf;3)t engines is experiencing a sound level bordering on pain, 120 dB. What sound level wo k (st t:ow53e;)nf zvvtl58etuld 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 uw/aqq v:x/ v 9-u4dcaratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sdxv-//u :qvwu4ac a q9ignal and 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 converss ; 1mb,bi,kre2dq5 flation. Use Table 12–2. Assumebb,fi1rm;kes2,5 dql the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardsg lcxi-u;pz /ya3 .v*rum 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, whirryfup2pw 9)xi k)(q (le the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each q((f2uwk)p9 ry pi)rx 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 r (kcocx9wtdj-k6y0v .egistered 130 dB when placed 2.8 m in front of a loudspeaker on the stag-v tc60wo d(9k.yjkxce.
(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 typiwgy1wvs 12)nu 4vhlkeqyb2i a4, a*/acally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffe )yqe4hlabwvna*isw 1 2 vuk1y,ag/24r by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the iua e2uxx8 1i 3k7lu5lhntensity increase? Increase by a fiu l87uu3125xl khxaeactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalain-8f)4o lt8 e9 vnm3mssa9y nkk c2: displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities? -nvsy9 e mnsk83ln)c4 ma8afoi:9 2kt  

  What would be the sound level (in dB) of a sound wave in air th8x7p :h ;kkp+uqp1wx kat corresponds to a displac:8qkp+xwp7 u;kx pkh 1ement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soundrh,8k;:4uh l0g ijkzk 7u)arm level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sez0i: k r 7juu8kg) k;hr4lahm,e Fig. 12–6.)    dB

What are the lowest and highest frequetu if2c 2 c*k6ft:2h ld urzpk;33tx1tncies that an ear can detect when the sound level is 30c lt* k12t2pt fiu3hc6;t3kdz: r2 xuf dB? (See Fig. 12–6.)

  Your auditory system can accommodateta9 jcl6hfbmrez21 1, a huge range of sound levels. What is the ratio of highes c lmzj6he,r 2b911fatt 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 of 440 Hz. The lengtsc,gi1qya0s,5t;uit*ai4 gj/ ra 6udh of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Usadqciii,1 gaya564u t0,tjsgu ; */rnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thre2+obbyvh9t pzo4zdads 17l- 1 e audible overtones if theo 1zblvy7 zs1dab4h9+ 2o-dt p 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 bleg2 /cq ytiwfcn(;1o. owing across the top of an empty soda bottle that is 18 cm deep;1n.c c oyewqf2ti g/(, 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 c -3l rum:yh4 )7p aqixyuru32pipes spanning the range of human hearing (20 Hz to 20 kHz), what would u -r 3hyixcy 7)rapu:ql423mube the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third hsad d.5l)9lz;kbq t+marmonic. What will be its fundamental frequency if it is finger bas 5 d9tmz;q)l.dlk+ed at a length of only 60% of its original length?   Hz

  An unfingered guitar stripi d2o q(hk+m6r/y36kxdn* uong is 0.73 m long and is tuned to play E above middle C (330 Hz)*/n mo3dy (6 u xk+ikq2rpdho6.
(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 openey 2j gzi)4om7 organ pipe that emits middle C (262 Hz) when 2 z7ioe)jg4m ythe temperature 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 20eyrcxd sx0,,m v53fm w ()gl-k $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece oo7)t0a1/g9vycn bt n df the flute in Example 12–10 should the hole be that dgo 1btyvc/97tnn)a 0must 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 resonate at 264 Hz, 440 Hz, and 615wxj+*m*nkq d 6 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed p+mn 5*dk* jwxqipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long sk gk1,;h ,zlza)qo4 his open at both ends. It resonates at two successive harmonics of frequencies 275 Hs14,olhhz ;k,qkazg )z 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 9 ez66eu.xk yh$^{\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 a6bei+/ bk)5zq)r rjieke p*/mre present within the audible range for a 2.14-m-long organ pipe i r)epqmzr6/k ek jb* )/ie5b+at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm longypoyk. qg i,)ps 3h+x9. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) o,).s93x +qp kig pyhyof 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 wheq72 k q9/isloan0md z(:p1 swft)2qif n trying to adjust two strings, one off (1 )fqzn 0/2qks7 :iido9ap wl2tmqs which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle Cp;of6: or -tma gh,) nypm woelqw,265 (262 Hz) 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 X) opera//9v b vati6nftes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fivf69 t//b vnarequency 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 fork k,gfd enli lsygd;6imu0;49c bt 0j,(and 9 beats/s when mys(d,9;ck4gnf 6el jidl0g, i tu;b 0sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one sd co .)x2chw,o8 u1ihktring is then decreased by 2.0%. What will be the beat frequcud1w ),h2ioh8xck o.ency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard e7:u*s.vd / zp7d7sumyiny0sif two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 2 ydss7ydnu7 msie:.puzv0 *7/5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequen5m -.lc rgnid.cy 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 freq5mg .dlr-inc.uencies 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 stands 3.00 m from one speaker and his1gwcoj*/0*bc i0g 3.cjihwi/ob00*c g1g s*50 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 132 Hz, but a piano tunie n rj5 660r79gu*xc amilfp5er hears th5 a ml7j 6f6rgerpi*xinu0c59ree 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 2.64 m and 2.76 m in air. How many beak5;bt x t+or,8ysy3au ts per second will be heard? (Assume T = 20y t5 yxua,s8;+3 btkor $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hh(x, 2b l4fmd1jn rld(z when at rest. Whjdl l (mh nbr1(,xfd42at frequency 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 frequency do you detect if a fire engifq v/313cknaf ne whose siren emits at 1550 Hz moves at a speed v3f q3c1ka/fnof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if az7il z2w1r)4 vzsl uf- 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are th 7zr- l4)vuw2slz1zfi e 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. Whuli)dbc buv9 a6w8naoq.dl 67*ktl mj,su 7+5en one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the freque)anl 7d l,5.udav6 q ckjubi8o6*m +sulb7wt9ncy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends yez/bioqd 4klo/ b7k)(iqz:/w r,,vlout ultrasonic sound 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 frequd,:k/zl/oq kqli/rw ye(bvi,ob4z) 7 ency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of. bp;n:dtduq,0- ,cz e5c g uwx15hedu 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the ba5 gud q- d zuuenhxed b,p0.1:c,5w;ctt hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a 60 d k:b,n)8 cu5h3kbi/dk oz qprfkh1tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed pk ,q01 3fo/6kkh5k8bb:)riczdduhn of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves toev0 vzkwje6g*v ;j;u* 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 is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awayw z*v;0evek;v gj6uj* from the sound source?   Hz

  The Doppler effect using ultrasonic waves of w.pz k,p0 s yw*eg,.lml6ojm7 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 s i sd6ssa aox,x5/8e8j0umja9ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequ5x86e9x/ mos a 0ujjida8as,sency 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 modd n*uev9 j9g*(ofp7r jju8n0ving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound ish4m, ba9s.v4x6 bmk pivo0,af 310 m/s (a) What is the angle the sha6kbx9.sm,4 fbm ai vhvo,0 p4ock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosp,x j w7+k;p6jwsdnyob c:8k2v/rrt. qhere of a planet where the speed of sound is only abkjkdon6 twsr/y.7qj 2 +wp:8bv;,r x cout 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 - gtp +bfo.ol*m/s strikes the ocean. Determine the shock wave angle it pl +ot-b f.op*groduces
(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 cqnc )9z9 2)s.fbeuch$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overh1d/ 19:jktaxk6ztg) d hgsu2aead and see a plane exactly 1.5 km above the ground flying faster t:j/tkh6 12 )g dxd astzu19gkahan 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 20,0vpx,kui--5cq q 9dh2q+g kat 200-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 2cg2qq vuk9d+,ip x2 h-k5qt-a00 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human-6 z hkrh*e:14rfxw wt audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dis n*h1jwke;l2 */epqn kplay called a sewer pipe symphony. It consists of many plastic pipes of various lengthnq ew/2ek1jkp*n*hl; s, 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 ma /7vpuh7ot-zv kes a sound close to the threshold of human hearing (0 dB). What will bo7vv/-p 7 zuthe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when a;mogc xjt:hg;/a j 3p/n 82-dB sound and an 87-dB sound are heardj ah/ j:gxcgt;m op/;3 simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh*h6tb)+hvqo t at is the acoustic power output (W) of the speaker, assumibh6hq t*o+tv) ng it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output ahlyw.4f:ez( a-pcf- ft 1000 Hz. The power output drops by 10 dB at 1z(l4 fe-w-fya.p:c h f5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aio 7db1t06cw,bgm z, ;xcm6 wvkrcraft typically 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 rbzk 6,bxmwcvg7d mw,o ;0c t16adius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, th. z)w f )h:cz +3mafu59ibtelfe 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 tun3gll *zxu q ogv)j,dkj8 yq/)5ed to 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 c yr*4j;/o1,ibzi+qls a4fek cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit le,*fe4byrk;so c+q zl4i/i1 aj ngth 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 filled 4cxuii:o9)scwith water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the t94 :s)u cioxicube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tu/wvnwu6.5 ep 0t k-jdeat,pt+ be that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce j/,wken-0pt w.d6epatvt+ 5u resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full lox6nlu2m -6hdu1w tje1op ($\frac{1}{2}\lambda$) 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 co s 1jqa1sc*z)lming 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)szqj l* a11sc 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 station(ta2+ q3ypcyp s .pv3xary. The conductor on the stationa(ptav3p2yqs.c3y +x pry train hears 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 whistle as it approaches you is 538 Hz8dfwm) rf8ic1 . After it passes you, its frequency is measured as 486 Hz. How fast was the train movir8ic1fm8 wf d)ng (assume constant velocity)?    m/s

  At a race track, you can esti3lw c 0cu0wpa+09pj0nu q ebkml3+p6 imate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Supp m+0uup0bp3wj lcc9p 0laew +q0 kin36ose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce ad.p7g gfazevx 8g7vkh5ukjw /3l 1;g8 beat frequency of 11 Hz. The shorter one is 2.40 m l787 /axh8wuz jfk;g 3 51gkgvveg. dlpong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta ppt p d;8-gwal5 ;v+tewt(2eetionary 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 passed him, atlege;8;td5 etw (-v awp+ p2pt C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what ./f /gd( axvzvkzet.-beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected f k.xzgz/ta(vv/ fed-.rom 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 a7sgl cv035 rv:ut;gy m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave dev t5 0u:rlacyg37vs ;gtected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it 5ux n3;-1r+q wiy rbctapproaches a moth. The pulses are a nirwcb3;1xut+ 5yr -qpproximately 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) wasbie*j(h23n qm0p1m2 6sl d+ xvlfxyn7 once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, *7 vjnhmlxms0xq(6 pen yi+1 2d f3lb2long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F 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 stereofj8.yy;0 foc2zl qv3 h listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of8.yylj0;z qo2vc fh3 f 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, slender al4 -b+/5*izu* aacgfa3cn( eq0kx kflguminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,ffaaalbzc*u0 / 5 qggkx-+(ik3cn*e4
(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 hearingtv q)b82tfxq zxu3/,a for the human ear at a frequency of about 1000 Hz is 2af/,utz)x b8qt x vq3$I_0$ = $1 \times10^{12 } W / m^2$ 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 onxk p3*zzu4c.y the ground hears the sonic boom 1.5 min af k3p4yz*zcux. ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 m3dn tg d( gniu6w.3um,m*:ti$^{\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