What is the evidence that soumg o96ss)rf1mnxm+fsmwh;2 8nd travels as a wave?

What is the evidence that sound is a form of en2ku ajjgo56w *ergy?

Children sometimes play with a homemade “telephone” by attaching a0 z zbzvgu.6 iaxio)0yf/3b,a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound canbyvb,a)o iu/zaxf 0.6z iz30g 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 expe2fjus7)ph2 i e*qh6 azct the frequency or wavelength to a h2*2jipf6s7zq h)uechange?

What evidence can you give vfy09u7tiz4zt )of t +that the speed of sound in air does not depend significa i79t)ufo4zt y0vf tz+ntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. n27bx1ly fs+a h)1gy 73mijar-d qa v-Why?

How will the air temperature0fb n/gn-hly+,cj 5. fscohk6l:m+cs in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce th. zutjl 3 x7.u3 fm7jvasg3a6(q nng2ke amplitude of sounds in various frequency ranges. (An example is a q3fltn j37ua7axz mjks..(ug3nv g26 car muffler.)

Why are the frets on a guit9*lb m8*n vq hpvstnhc;p+;1iar (Fig. 12–30) spaced closer together as you move up the fingerboard toward c +b*hnhsnp18p vt*vi lm;q 9;the bridge?

A noisy truck approaches you from behind a bu :t6afs-*rlbi ilding. Initially you hear it but c al-6is ftb:*rannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interf;ay 1lyht sr;1p *av/5 k5bnfnerence in space,” whereas beats can be said to be due to “inta5tyy*lvsh b n;k1rf p1; an5/erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points jue/r 46avxj1jqh,i a ps-2 h6D and C (where destruqr6ij1 2u s-aj/4,6 hhpveaj xctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the87m gx0e )z)+)fmmx k(l)rz jtmu;( si:lwkyq 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 could7k)0wksjy:uxlrmm(meg+) fqzt(il ; zm)x)8 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 q7b3+3x*o x vbay)vqr(l-c) f (gvbyna superp yn+b ovfaly7q( (3vxv*g)bxq-r) c3 bosition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in t;i-ww z-gk )njhe same direction, with the same vew--;)nj kwgzilocity? Explain.

If a wind is blowing, will this alter the frequency of t)vo2k8dqk;x(v +e+8skn ko vjhe sound heard by a person at rest with resekjk+v8sd qkk8o )vnv +;o(x 2pect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child ia-0ri tr3 z4;aj*mdejn 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 the whistle? Explain your reasoninga 30zr 4ida;m jej*-tr.

  A hiker determines the length of a lake by listening for4 2f0wvyz4 awg 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 t aw4g 0zw2yfv4he lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wathq plo d 4jo(+j,09k t7xf(wjnerline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. h7 n wj tj0 +x(9qofol(j4dkp,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 in air a-tvv) e 6gqypcnf7x,- 3vlxj9 t 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 schmohyb),aogw jo)(z7 / ool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the bhy/7),a ozo( o gbwm)jackfire 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 mx6ieu16la cr4akes when striking the water below is heau1 l6x aeir46crd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, ser9bz- jzai 7;wes a huge stone strike the concrete pavement. A moment later two sounds are heard from;wbzzjr a9 7i- 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 error made over one mile of distance by thfa*fd02*ta/v d itji,e “5-second rule” for estimating the distai2*a,ad/*dfvi 0 tftjnce from 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 leven / qcxohjes *i7/*dtoy3nd)7l 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 whose /rgh8y(:vy1 gxk cg/ eintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at)m8ybzi n7x hq:d)e 6tojvv2. a certain place,dv o2.t z6byiqj:)7mevh)8 nx what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an a3g qqpvj:q8f ;irplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dBj3:qvq8g p f;q. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to havecj0u;)hfa 3 (/v pjm/lv bmsz 4+*kfqy a signal-to-noise ratio of 58 dB, whereas for a CD playeu(/ )fpb+mkavjl v yf;3/ j0qm4s zc*hr 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 soyk hc.e18cyvb h3fj0(q k+nr- und from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. +qnv8 jh0hb3c r(key1kfc y.-$\approx$    $ \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 strikee8l -n 1o w a:w-8(xr,ozbkcbys an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is r-k g*ng2 5nhgjated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker co *gjg2-hn5 kgnnnected 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 registe.0rf4o-y;5xf.sx o.t-5 b fcp cnrwpgred 130 dB when placed 2.8 m in front of a f yp. tfg.-.5-xwx4r 0s5p f ;nboroccloudspeaker 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 detect a diffe9/u;be g 6cymprence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [c/ ;9 6yebmupgHint: See Section 11–9.]$\approx$   

  If the amplitude of asj ezbig27 +mt aptuf ,qjbox :+t:.(+ sound wave is tripled, (a) by what factor will the intensity increase? Increase gjbsmpx :to +.+jt+t,bf qa:27(eu ziby a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceme.ofk +yw 0-ibent amplitudes, but one has twice the frequency of the other. ob -fy0i +wke.What is the ratio of their intensities?   

  What would be the sound level (in dB) of a su0 +ohbuh/v3)ze 2uwoound wave in air that corresponds to a displacement amplitude of vibrating air molebow2h)u30 vezh/u o+ucules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100cyo4mw2 a9-e d-Hz tone that h92dcao- m4wyeas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest fr4ucbdyfubz g ;1*/vr *equencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–4* gz1*fubvcd/ b;ru y6.)

  Your auditory system can accommodate a huge range of .,uk7)vw0-a/cm;gp im4b gvftg mqt + am,w0x sound levels. What is the rab gu/q aaxmkm, w0,g)v4;c pgmtw.-f0t m +vi7tio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequkykhh+s (/ 6zk9j :wju9x.8nklu w sz1ency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placej9 s+ 9k sh(ywnz1.jl6 :uk/xzwu8kkh d?    N

  An organ pipe is 112 cm long. What are the fundahv.k1 1rha -hr+ 5ph+bseqi p1mental and first three audible overtones if the p1hb15+ qvh ip hrhp-e +s.kr1aipe 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:fc*+tg zel*l7/3mpufg o 4kt from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed itk*zl mt:*e gol7c4fpu3/f+ gt 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 pipeq; okd kz7w+od5op30p4u )qco organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of tu +0z7 4oqo)d5dpo3 kpo;q wkche lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540a *f,r dbstg yl8tf;z+i3m *o2 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onb*z2 sg* ld,3ta t+imf rfo;y8ly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long anm;6l akspxf )3cza1*pd is tuned to play E above middle C (330 Hz)3* 6sl)x1cpm pzka; fa.
(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 organza+c6 uc.-n92axc jej pipe that emits middle C (262 Hz) when the temperature is 26 +-cxue an.c2jacz9j1 $^{\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 ath bp3j c,2vzkr9ubqtae:4:k sc,5s7s 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 Example 12–1 r*k aqnkxvd *k975/rd0 should the hole be that must be uncovered to play Da 9*xk7r/dndkk *r5qv 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 resonoyanbp(i/jvj l.5;u9d04 4p 6flwe onate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wh; eyiobnu.njlw lfj0/ (5 4pvd p94a6oy this is 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 m long is open at both ends. It resonatfoi 6htgr1idi ap3 9a9 -r97bhes at two successive harmonics of frequencies 275 Hz ata6rrhp-3id 19i9hg b7oifa 9nd 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 9we(obu:*ctn4d: i n r$^{\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 with)t vj2 u :q l)pph1kbyxo.5 b7.tmfp nn9v1j;win the audible range for a 2.14-m-long organ pipe at 20 7 kt:yf9m);.nbjpt) 1 pbpv52ljn .o vuh1wqx$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm3: 2kr 8g5jeb n5hxwjm long. It is open to the outside and is: jeh rmwgknx585j2b3 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 Fig. 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 ty1)fielgo5d-b)d0,45 d mi pd+qggt lwo strings, one of whicheo )l-ddig0typ if l5gq5+1gdb 4md,) is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fre 3oe+up) jrupd14 4n- eypj5unquency if middle C (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 (branzhx4 w7kyni cf3, lm4mh 6no9/d 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 simultanho ifz ncwl /k39x74h6,4mnmyeously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound,j,h urqur51c0bp r: .oa nej/ed with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whatj,b1/ca0u :rrjp, orh5.qeun is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same 88/c k.p7uzwg.z x lpahtk6t: frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be 7ctt .g 8p68zwkzk .lh u:apx/the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try t: /oxdm s0k m ohk507vbqw5u0zo play middle C (262 Hz), but one is at 5.0°C and the ot0xmuovzo 5k :/075dkmwb0 sqh her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a d6s-v) vxb8abfrequency 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 vb8 v6bx-)asd. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m dg,pbje ,kfefd/8,djs9 lj 5)apart. A person stands 3.00 m from one speaker and 3.50 m from the of8b,)9 gjkld/dsfj5 e p,,edjther.
(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 supposebnb y5l-br3o9d to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If oney9o 5b-b3rnlb 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 wavelengthsss0qb+ as)0td i;g(dh)g2cmw 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assh0ss mw;tsq)+bci)0 g( g2dad ume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of ar nmp2yj o.xh 2ua6kg-s1jf*5 certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect26 *nmr-fxg1u jo .5jkp2yah s 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. Wha6epkn 1m mtg.6t frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at pt n.g1ke6 m6ma speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving tyx.lq2t 2tv 6foward you at 15 m/s versus you moving toward ittvtq f.y2 6lx2 at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same sjuk bc/xvkk,7:oh 7h ,t:4wmb ingle 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 beat frequency ktbx7 4wu ,hv bcoj:k7:hkm/,of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrad:*e*jglke2 zfho) n,sonic sound waves at 50.0 kHz and receives them returned from an object moving directly away ,geoekf*2nl)z d j*:h from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed okel2 06 4duvdm : x7 )yg*qogbyrz3:mlf 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectqgyzy:b64d el2rolmkm3vx d7:u *0g )ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentse: a9 mt9pyp; ..domqh30zn jgvti p2-, a tuba was played on a moving flat train car at a frequency of 75 Hz pgdenjzapi pvh.: 99t0-m t2;mq.y o3, 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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound j3qc*ej5mz6 s 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 is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound 6qczsem3 5jj *source?   Hz

  The Doppler effect using ultrasonic waves of freqr ssc +d(4ie*quency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. so)nf2of9 qbsn )f)+ eWhen the wind velocity is 12 m/s from the north, what frequency will observers hear who ar 9ns fse)o+fo)nbq)2fe 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 momjh rapy2 m7qdcvspok rr2 )+* 6k.e.3)5vskoving 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 is 310 m/s (a) etl. fwb7wv )/What is the angle the shock wave makes with the direction of thb7.wel) tvwf /e airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pt3s0)st 1 v;;ljrfjxx3sikg +lanet where the speed of sound is only about 35 m t0s;sgl;txj k)vi+x33js 1fr/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 85 ck.mfjap;*5s *+p ux85:bdzc n5czgm00 m/s strikes the ocean. Determine the shock wave angle it p f:njp.m ukc55x pa *ccs8;*zb+ gmzd5roduces
(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 way 6wuwprqdb k .1xg 1bzl7,,11b cw2$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ovkdaqf c5 lqvdu6 7/1d1,ncpyt;g1m 8g erhead 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 hanup7d6acgc 1 qk18vyf ;1,/5mlqtgdd s 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 20,000-Hz sound pulses downward frt di3mh:w 4()rl v*shdee m+y(om the bottom of the boat, and then detects echoes. If the eywd4(:m* h(trmidh)s3el +vmaximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oqcu9kyx3:ubgkx t, ;qk700c sctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calle fuo,z1yh4l0 td a sewer pipe symphony. It consists of many plastic pipes of variou4z 1h ou,tly0fs 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 o:a+jbfs)5lasr 0zij7f human hearing (0 dB). What will be the sound le ):0jzs +f asbj5a7rilvel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dBaowt8cw ;y7p8c ,lg/7ujkx r 8 sound are heaw ,8a rlo; /8wj8uxgt7ycp7c krd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whaty c)5cg5tt/g v is the acoustic power outt5gc t5 v/cgy)put (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output da nij76uh4beasm;) rocu:p /m 34 pe8xrops by 10 dB a/su4b ie 67mrceh38n )maoaup ;xpj4:t 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weaj yo zdipx2gen6 y0c),8htr..r protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, i,pj.ctd ex2 .8n 6rg0hyiy)ozs 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sr3 z ox7ri3zg4ystems, 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 :x9exuq cc8f (is tuned 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 cm long between fixed points with a fundame-u t zawjpacchj835l25h u93cntal frequency of 440 Hz and a mass per unit 3 tcja9a2jch hcz5l3p8u5u - wlength 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 with waterp-lmb-t f ;s8r (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the pmtlr ;s-8bf-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 sn- xgxqt7 0q1ftring of mass 2.10 g is near a tube that is open at one end and also 75q- gq7f1xxtn0 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tcg, 4 a3ku 2b8qkzi.pvo 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 two sources.-pa0:8qu csbx a/xj:b The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the aax-: pu:j/bx bqs 80cperson 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 i 4iq/nsq5 kl6qs stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What i4ln ks6/q 5qqis the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Afte( 48y yk*vjq.+gourv wr it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant ve+yyv v8.(w k *rqgo4ujlocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dihuk k+6dj f83.ujc9qc pm.hp+fference 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 the straightaway. How fa8hd+kk9ppu 6hcfj.q mu3j+c . st is it going?    m/s

  Two open organ pipes, sounding together, produh(yqtty(s ( ;kn+ xr9ece a beat frequency of 11 Hz. The shorter one is 2.40 m longqnxyr;(9hy +e ((k tts. How long is the other?    m

Two loudspeakers are at oph 0 laf9 ()yt0h5dnlapposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speake95 nlath)pfyad00l h( rs, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0b*-e1gf/ipyw t, xw*j.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wav/b j,*x g*wyfe- ipw1tes were directed along 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 indrezr7h*8ou(-o 8;ql eak)is flying toward the bat at speed 5 m/s The bat emits a so qi8z7d; u(h8rak-r eeno*lo )und wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a, iw 2* 5kvzdibtz0hy7 moth. The pulset, dh kz*yv0izb75wi2s 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 echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used wnuty84y4kpn7 y *th7to 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 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 clo 4yk7nup78y ty*t4hn wse to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by thmk g02p u8qp-ge presence of standing waves, which can ca k-g8puqg pm02use 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 lojhi/( j*j- ppong, 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 c(i- hj*/pjpjo an be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear aiukbinx byg js+0/3 ui0p8t 1*t a frequency of about 100bj+x0t1p yi/siu 38*n k0iu gb0 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the grounnrm .y.ghcrxr cx 2g54eozgc(u36 :*nd hears the sonic boom 1.5 min after the plane passes directly overhead. What ig(y: 5uxzng2h*n.x4g3rorc 6e. ccm rs the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat istu,1glh /f5zak-b; vf 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