What is the evidence that z78z+ nb26j52oqj23kxp4l wyy g efc xorn 0,xsound travels as a wave?

What is the evidence tfn8bhkt ue0;-(ib6p ahat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to th; 2duzi*+o1 k7uqx gkhe 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 wave2 71gu h*odk+ziu;kqx travels from one cup to the other.

When a sound wave passes frlk (7llw3g( ei +r.g.ipmhqb,om air into water, do you expect the frequency or wavelength to g i lk bw((.3lepih7l,rg+.mqchange?

What evidence can you give that the speed of sox t3:vuige3en o,e ;8xund in air does not depend significantly on fx e,e3ng:8ieox;v 3u trequency?

The voice of a person who has inhal d f*lyzbq -+mt86o8xeed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ckvjt87 )37u 9fw9zcnkpx kc) organ pipes?

Explain how a tube might be used as a filter to reduce the au.m*lq(ho q e2mplitude of sounds in various frequency ranges. (An example islm uo.(*hq2q e a car muffler.)

Why are the frets on a guitar (Fiwck-hzw +7u-ihz/ m,eg. 12–30) spaced closer together as you move up the fingerboarzzum-+k ,i/ch- hw ew7d toward the bridge?

A noisy truck approaches you from behind a building. In 0ry p.8wi3y-qe/boyoo3vrh : itially you hear it 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. Explain. [Hint: See Se3/y.8y:rboh yow- ie p 03rqvoction 11–15 on diffraction.]

Standing waves can be said to be due to “interferovv0 sf*h(o r3zt x7k/ence in space,” whereas beats can be said to be due to “interferef*/ rktooh7vv z0 x(s3nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the m2vg;vo4qb n4/q al.g points D and C (where destructive and constructive ib lmg;nqao4.2/4 vvqg nterference occur) move farther apart or closer together?

Traditional methods a88rv/ y2*brm i7oo1ml240h ywa s wqf-rf kg5of protecting 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 oh7w8gqamk -82 *ar 2 vy0ys4mlobfi1 r5fwr/reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12zn(red,9c /ykj y+x ,zi/d3r3u cfa q* bow;*e–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whiy*ci ,e9/3jwb* re/;3 qkudz r(xy ,d+z afnocch 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 obs0o 2cym *lkjohuo/ +nnk84,vyerver move in the same direction, with the same velocity? Expl0 8ncymvk o yknu*2oh4l,+j o/ain.

If a wind is blowing, will this alter the frequency of the sound heard b sz+s r:b(cl.f(s5r mqnyl(:sy a person at rest with respect to the source? Is the wavelength or velocity changed?l.s s( fbqmy s+(n z(cslr::5r

Figure 12–32 shows varip gc/o jvh90 aui3a-3rous positions of a child in motion on a swing. A monitor is blowing a whistle in front of the chh9j 3coap 0v-/3ra iguild on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of he5q9dek vd675 o4etx0frwqbd4ml h6.ur shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutqurb5hvt9546me 0f6kxl 4d o.q dew 7ding. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship ju+j8m5 myf)u lcst below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 8+)cylmfj um5 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 inhle-tidno o2p.5 va2. 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 of tu0*j 2 nb*xm9h)7ypnpvtnf 4hjna 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 ty 0hbft*2* xv) pnpnnjm947hjhe backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top8)llg 3hx rpu6 of a cliff. The splash it makes when striking the water below is heard 3.5 s lgh 3lul6r p8)xater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strnm 8xfpk t1n-9ike 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 they are 1.1 s apart. How far away did the ipm9-nktf8 1x nmpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance b3is-yvgl chl)94ocz 9y the “5-second rule” for estimating the distance from a lightzgov -i4lc cy9l9)hs 3ning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 j 9u*ag y/uo1k /tx)yo:(m)d ki*zydk dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level d*ycp8(c 2vmushz)y2wsr .t 9ymil,of 2a3a6of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leax3v9raojt-; .ra2 jq vel of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’3 9a-ot vx2jara rqj;.s.]    dB

  A person standing a certain distance from aeacd5:gh3 kv/;wiw1p wg07 b bn airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level dpibv;ewa75g1g h wbc/k:w03would 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 ratio of 58 dB, -h e/r ,ylgur9y q:t;vwhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac:r;, hleyrv t-9/gq yuh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from r)5z3*k (jnn h7tn +2 zh +a)pskznbvja person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uninnv*3+k7zap 2th)jj5(b s)+ nk hzrnzformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum who. 0 c sn5 j5 i8molkrim-6 tnwx)pe26elxv/pt.se 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 *c).92 adifiujzccgx (t86yy 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 connectefc.jgc)9y (a 2t zy*cid 6u8xid 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 registbzyp/h+/fu i 2rg2 b0*stcr) 5f*eqc gered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. e 2bhfi qb/ uc+05/trzgcs*r2fy)*pg
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What isrec*jw;h)ycif/)q s - the ratio of the amplitudes of twoyrc;))/fhe wqisc j *- 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 z6l lhbyu ::4xfactor will the intensit:y4ll :hb ux6zy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tgf*3yzq wp5e 7ex8stu fu) k82wice the frequency of the other. What is the ratio of their int 5 wetff2p*uk3q 8u sx8e7yzg)ensities?   

  What would be the sound level (in dB) of aju5ne+. o,p3z) hc 9;wym,vxj0ts wrl sound wave in air that corresponds to a disp )+5scu hvxrj.te;y3zo0nm ,wwpj,9llacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz ton)*b*8 .ygrch uq6czm/.ssxux0 er dgfk+3+pbe that has a 50-dB sound lgc*f b+xqr) .ry.0 x+dp csh6*sg z3uk8/ebumevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when;pvpv k,7lp7 d the sound level is p v klvdp7,7p;30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangepxd iml*y4o) 2b2hbu0 of sound levels. What is the ratio of highest to)ibdbuh2lx4p 2m y0o * 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 fundamentalhq9o rw.wtg 69 frequency 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 q9htw9worg6 . string be placed?    N

  An organ pipe is 112 cm long. What a7mk) fg-rg,,ju,: zllrt ke(ure the fundamental and first three audible overtones if the pipeeurkzul,:gj -)r,k gf t7( ml, 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 frequen)p5g al+y:vl pcy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assuma 5g+:yl)lppv ed 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 pa 0 k-db(;;x/is:hp diax xj0hipe organ with open-tube pipes spanning the range of human hear/si(;hd a:-p a;x0bhdx0xkji ing (20 Hz to 20 kHz), what would be 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 harmonic. Whm1*.u oopdzbr/sff1 ;9 ml4asat will be1/pd mmzsur4alf* ;oo 1bf9.s its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar gi 9 *tvo(aq4mg2l7isstring is 0.73 m long and is tuned to play E above middle C (330 Hzi*4q(9g mai glvo2s7t ).
(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 or7:rkzs i6su;jgan pipe that emits middle C (262 Hz) whenjuzr 7k: is;s6 the 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 atrj/7n* pijvk( 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 12–10 should the hole be / gjk(iowot.) /3fr0zl1hme fthat must be uncovered to play D above mid3z)fir/loh t kf/ jgme.1(0wodle 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 616 Hz, bur-u dgq.l- / iangb:7mt not at any other frequencies in between. (a) Show /q :m. urdlibgg-a -n7why 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.5- 1hb1asyycrbvh9e2 It resonates at two successive harmonics of f1 vc 1yhb hse-9ryba25requencies 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 n17u q 1ro(wvo$^{\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 ryxly uqf lq, ;ofq4;,2ange for a 2.14-m-long organ pipe at2o;yqfy,;4fu l,ql x q 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelx 1( ff9kyufi23k9ng cy 2.5 cm long. It is open to the outside and 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 gg9kc( iy ffnxuf9231kraph 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 two strtvfh n0guk 2* n85wr9tings, one of w59g8f uwtk *2n0vrt hnhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequenvd( v zi)8rb,p3abnnird2p -(cy 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 23.5n7 pnq.2 fp n/rqcei av6ke(20 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of ck2/q.n(fnv aepne 6pq2i0r 7brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork anddn 2diks9j1/b u5 ytai54.v gd 9 bea4ik5j guday sd9.1nv5 dbti2/ts/s when sounded 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 H*o1 ,pkn qz; +)s4z86r faboadbv8rl jz. The tension in one strin ,j +fzq nb6a )zosd8o8;k*vlra1pbr4g is then decreased by 2.0%. What will be 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 flut, d06xqepqcq/ni)d.* ow 1haz7w tzo,es each try to play middle C (262 Hz), but one is at 5. athczoni6,pqe o . w*,107wzq/ dqx)d0°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 ;9e w xvnrj56cs4m2sdHz; 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 frequencies are possible when A and C anc9 426rv;s5m dewx sjre 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 stj9+c2z 4ckb8(f go ,u ytu6mbwands 3.00 m from one speaker and 3.50 m from the ot 9, byj(uw 8k6ozgb4tm+ cfuc2her.
(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 +o kaia ,d7u3l)v bh*b132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If )+3odb7ki, ba *lu vhaone 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 .tb;8mf:axjm7 r ju xf-g:+vym and 2.76 m in air. How many beats perbm;-j 8x+ay:utgr f: m vf.x7j second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a hl05u 02s 8oteet.d3v 1gx.my : sxxcscertain fire engine’s siren is 1550 Hz when at rest. What frequency3hcg1 . yo 0xte u2xxv85.es0sdslt:m 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 freme*lnk)35ez 9ks, fpj e1ltu8quency do you detect if a fire engine whose siren emits at 1550 Hz mo m,9kse)j 5t1* nl u3pfzee8lkves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i;on0npr5u sh oxgd9ms g5j7q/qn ))b5s moving toward you at 15 m/s versus you movinr5 ng 5q;pbhqmu s))ons0xgj9odn5 /7g toward it 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 sam 2:z,ed8kumtyta/4,8em m nv ye single frequency horn. When one is at rest and the other is moving towardt d,v yku8t84en , emm/m:2yaz the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 501n1qlu:vcz: og pw:s-1xf b4 hao7,pt .0 kHz and receives them returned from an object moving direch 7nb,-:swop: oxl 4za1q vct11g uf:ptly 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 emits2i8 x8mm)fss i an ultrasonic sound wave with 2mi)x f8 mssi8frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played oz5m rh5*h-nc fn 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 approachem hcf*rz-55nhd the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spee ews7bcj:/xgr*1 qtz)ds. Suppose the device emits sound at 3.5 MHz, and the speed of sou /1qb:j *s7)xz gwrctend in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyv b t luj0uz4da 8:7vok9v-7wn $2.25 \times10^{ 6}$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 emitvw(i 7ti v0b2ys sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are locat7(v biw 2yvt0ied, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land5vn3acfp5od g xkhy0:tn: 27w 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 lf o1*;6a gbkawhere the speed of sound is 310 m/s (a) What is the angle the kgf*laob1 ;a6shock 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 atmosphere of a planet where the speed of sohvokle d:pzu5yb * 1so 81n:44k xcdy*und is only about 35 m/s s4 *1d ecy1k::h4zpnyxdvou blo*5k 8
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes t*ssasitoj6, t-/p2od0m-fl r he ocean. Determine the shock wave angle it prodt *6t/mljop0- ois ssrf-2da ,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 * of.(q8br8xq yqxvu-$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead2.hgs.zpxymv*1ub n iv 8q.x 0 and see a plane exactly 1.5 km above the ground flying faster than the speed o.sbzx2 1y x.uvv*.pm gn0qih 8f 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 20,0a vkkm) o:+c:kjvk 5e000-Hz sound pulses downward from the bottom of the boat, and then detectsk o0 5m:vka :e)jk+cvk echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human ao+) xa,12ml+w;jewe3 uj*1 vspn ugswudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It coy rw0pe0hpa*1nsists of many plastic pipes of various lengths, which are open onewhp 010* arpy 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 soundnt 2l ;q ia0+wxd0n;hq close to the threshold of human hearing (0 dB). What will be the souqn id 2w ;00ht+q;lxnand level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB x lmlgc:5ezs1. pk g(*sound and an 87-dB sound are heard simuecm s:.g(*z1g pxkl l5ltaneously?    dB

  The sound level 12.0 m from a lo;mf h fv 0:9riuhxg/vhbs5 5g.l7)qxuudspeaker, placed in the open, is 105 dB. What is the acoustic powefvh/ i 9l0gh.fgx m5s; )uruxvq75 bh:r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 (8- u2 gxe2j6hrjupep Hz. The power output drops by 10 dB at 15(2puegpj- 6erh28xju kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wea-/foi,5 wdz1si738vy5lgn 5phz t aksr protective devices over their ears. Assume that the sound level of a jet airplane engine, a d 5g1hn3v5fo5,i8p z/tlawy -7ks sizt a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communication67 f,n-xv h/zx7 v.nhjl8p0f eo5yme ms systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tomog(qtw,y)2re oj-i/ 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 fundam(t(b7e.,p cyirq / dxrental fr((,r/tq .rx7yep cbi dequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vtq-/42 v3 z f5kxskmezibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonav t2/ 5sekz-z34x qkmfte 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 strin:c*hvexi g : z *d++;bvtmomp5g of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tmo vdmx+h5 gti b+;*zcv*e:p :ube?    $ \times10^{ 2}$ N

A highway overpass was observed to resona t;oh7zp.(bzskn p,xq7 3kdxu v .xv:-te 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 -*wmm ;j we;kvfrom 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 f j;;kw m*emvw-inds 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 stationary. The conductor 8q:gebqejib,t7n*y8 ixz7vb9-zg2 oon the stationary train hears a 3nx qb8q7ez8,7g t -izoy 2 bevb*gi:9j.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 Hz. Afteylb+k6a 45 dbs fnsc1s/vs,*vr it passes you, its frequency 1sfs+s l6v aks*dcbv5 b n4,y/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 cars just by listening to th-vu*fc8 k/ h/udqsv ddfw4d:48s k(osc6lcy/ e differe8fdw:qyuvcuodd cvd46sc/lh* / (k s- /f4 8sknce 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 fast is it going?    m/s

  Two open organ pipes, s 7i)2 *znbws9v m;haad9bkv/ vounding together, produce a beat frequency of 11 Hz. The shorter one is wb v a) d;29bvs7ihmavz*k /9n2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends ob3vv*jb kfg6bnm2 o *8 dk/6oyf 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 observerk o6d82gvbko6/*b*bn3mv yfj 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, at C?

  If the velocity of blood flow in the aorta is normally about 0.:*ku 75 yvi.t5(dcy kjmxqrz8 32 m/s what beat frequency would cu(d k5jrv 5mt:xzkq 87*.yi yyou expect if 5.50-MHz ultrasound waves 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 is flying to2-i*,.l s1zpf 0 ypx)x oufy9i ,lqyeoward 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 reflects off,*ls1 u p yilyx 2ioz-eo)0,9yx.fqpf the moth?    kHz

  A bat emits a series of hihxm1 u(ydm7u1 gh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one c m hu1x7m(d1yuhirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once us*p 6.mch r7qinch.miy42ba.m7 (skkaed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be b(r k7i7..imhc26m4ca.s amhp ybnq * klown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the pres 0l4q+8ogz /f tv(ucntence of standing waves, which can cause au nzt (tv/8cl4 0goq+fcoustic “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, onv 20v62 nff .+y9amkcx,velslender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with vffx+.6ok2nnm 0, vay clv2e9 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 hearing for the human ear lci* b52lw0azm8ttq7 at a frequency of about 1l *a0bt5c7tm 2zlwi8q 000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the 7x( b(p-ibekavwz 5zh 8o f19lsonic boom 1.5 min after the plane pp5 ab 8zohzl i(w(fv97ek1 bx-asses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is tgo 2mt:e1 0g. foeunj( gsu)rnx1 7/h15 $^{\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