What is the evidence that sound travels as a wavn b7h4 bl*j2obe?

What is the evidence that sound is a f9q;5wc .ncf1j w*gp igorm of energy?

Children sometimes play with a homema.cu l.g*jn9ew de “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave trn.lj g*9cwe .uavels from one cup to the other.

When a sound wave passes from air into +uvem -8ucmh:p:f 5jmwater, do you expect the frequency or wavelength to chaf up+:m:-jcmhe8 5v umnge?

What evidence can you give that th)vvr 6pd1to+ i bq t((p.)nlzhe speed of sound in air does not depend significantly op (r (.qidh6)b1l)zvttp n+von frequency?

The voice of a persofzpcvb+o /2 hlyd,d,yd +i)/wn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affej7j(n nx h u) tn10bmhbr4p69iy u2yl5ct the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun)2u8cf :pms0j/ twyzyds in various frequency ranges. (An exam/:s) tm2cy80 zj fwuypple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up l :gmh;lux5n9) d3hva the fid;hnmv39agh)xull :5 ngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initiallh(0vri g . q0 5w sggn s:(tiaz8c2k*kxwmdh:.y 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 Section 11–15 sg0 gwv k.2dzmr 5hi(nc:i a t 0x8s*h.qg:(kwon diffraction.]

Standing waves can be said to be due to “interference in space,” w3s .bkzk++ n7rq)awpwhereas beats can be said to bbr+ a.swq+k37 )pw knze due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers s5+lb.g* n ljo8+bzxy were lowered, would the points D and C (where destructive and constructive interference ocbgsn+j5 8z.l l+*xbyocur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with -q9ieoj 2w4.ted8 leb very high noise levels have consisted mainl t4 -iwqed.2leo8bj 9ey of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown infn )-z/z;* gg8gq(n9yfmfyx0,e xvl q Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component fl/(x9z zf*ymvyeqf )8gqnn ,gx0 ;f-grequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dizh dp nft;;o,t /nx:hny1 cyk83b; 8fcrection, with the same vel:38dt /;,ofnc;nhfk b zy1 nhy x;pct8ocity? Explain.

If a wind is blowing, will this alter the freqvv d*i7kwk l,+uency of the sound heard by a person at rest wk7vi*vwk,d +lith respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows vz ok*h+p;qmh/*i z 0mlarious 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 frequency for the sound of the *hzk /+ 0;ipmohlqmz*whistle? Explain your reasoning.

  A hiker determines t,vwe3c08:vv /yha zf hm+ st4fhjg./hhe length of a lake by listening for the echo of her shout reflected by ashthfcm/wf4g .jv: ha 3y8vv+/h0e z, cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belo-ab ge3,zj6w)to +5lb7zb fkfw the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not varyoa kt-zw75ffb,z+gl6 e )b3jb significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ai npzj5j+)s :y3ctwk4z * g2ka1rl,jy or 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 tnewavce 2enb ()2 75)ubvn8e kap6 e6is drifting just above a school of tuna on a foggy day. Win7bu)ewb()6ec2an n2v e p8 56aekvetthout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of an -bme3pyaol 54obs6fl n6 -5k cliff. The splash it makes when striking the water below is heard 3.5 s later-b6omklop5 3b5e 4ysnn-6al f . How high is the cliff?    m

  A person, with his ear to the ground, sees auq0 c ajr;,e8)ts/e xz huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the 8ze taqsj ,/ux; 0er)cother 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 p g6guykh3v b jw-3ci,v. ah84one mile of distance by the “5-second rule” for estimating the d3jh-ku4i6cwghvp. 8gvyb 3,aistance 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 levela5 7k oq3e6yaxm)n jz-s i+8fut9imtzr:7l e/ 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 sa j 4s+;rm8 (qs4wnvw-j)bxh p+sj lj-ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simu8zm5a-suyq cj x2v5femq )v0+ltaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]5 ysz5j+8 xq umeacv0-2mq )vf    dB

  A person standing a certain distance from an airplane with four equally noisxb8 3ooe:lz5+ )ppvuebb4+o sy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add int 8:sx4 +bbv5o3o )uoe+plp bezensities, not dB’s.]    dB

  A cassette player is said to haveg-;x vdn0v- f88vemca ;b (ocb a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the bacmv o;-8a(b08 g-ceb;fndvvcx kground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conv 4bykn-;qrhy 5ckl;w pn 9zz;6ersation. Use Table 12–2. Assuykqlp;b;n49c-n ; 65krzw z hyme 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 eardrum y )6lfhumw;)xlan( 7x 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 iema*/t 3ot6-x4* e2dk:trn gdbw/ edrs rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decidgo2xd-wdn r a m*k:t/*3r4be/e et6tbels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 13 2 c0ha0trtj+l-h3ve x0 dB when placed 2.8 m in front of a loudspeaker on the stttlv +2 x a-j030hhrceage.
(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 typs)g)e5qzhc/ pa4 up:zically detect a difference in sound level of 2.0 dB. What is the ratio of the amplituduq:zzs)5h) cg/e4p a pes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is 1e bdd/v )nrt)tripled, (a) by what factor will the intensity 1envd)dr /b)tincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have es kv;8a 70ca7;g1ggnuhxi6xwu s7b 3zqual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intcx 10 x3s 6g7hgbus ;u7k;zwia7vn ag8ensities?   

  What would be the sound lewnf7:/z6t ofa vel (in dB) of a sound wave in air that corresponds to a displa:tofna 6fw/ 7zcement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lesc wsjzwj)707rhlvu+; n-9 t bvel to seem as loud as a 100-Hz tone that has;n7-7s 9+lj tsw )vzuc0bhjrw a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sounyr - 7;h1ktew3h1 kdeyd level 7r eey y; dkh3k-w11this 30 dB? (See Fig. 12–6.)

  Your auditory system car f-xkkd2s 7i4 au7+wfn accommodate a huge range of sound levels. What is the ratio2+wa fis ukk -rdfx747 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 frequency f/71 b0fw mn1ch vk+n xc(hk+aof 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 placed+(nhn/ fakkbhv7xmw1cc 10f +?    N

  An organ pipe is 112 cmsd139(mu* (tgfj :xcerek j;m long. What are the fundamental and first three audible ovee(9ujfsd3g;* etx j (k:mcm 1rrtones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing gucsr n 6jf-7m1n2be-across the top of an empty soda bottle that is 18 cm se7r1nmf- n-u6g jcb2deep, 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 alcc 6-r 7af *ummh3n)open-tube pipes spanning the range of human hearing (20 Hz to 2h um63rlnc fca7-am)* 0 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 19p 0mx)qyhr 0oc .;qd gukj6fhas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length o1uqjq06.9phf mcgx0dy;k) orf only 60% of its original length?   Hz

  An unfingered guitar string it2v yf0yiy. f(s 0.73 m long and is tuned to play E above middle C (330 Hz). t 0.iyyy(ff2 v
(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 annvv6 5bj;n1gl open organ pipe that emits middle C (262 Hz) when the temperature ;g5n6vnb 1lvjis 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 20 s3/; t-by7o 1n aihidr$^{\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 sh0/ ye;,0szs9r ae6 stb:i h; hmeqq;eiould the hole be that must be uncovered to play D abe;s6bzrh:ymq ti ; s,9/q iah 00e;seeove 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 Hp0av7wcorw 36 z, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) w0 7rovw3 a6cpShow why 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 aa6t/pv7j 9 xikf pb4 dya;g/z,t both ends. It resonates at two successive harmonics of frequencies 275 Hz and t b;pj7/y6 9 fvzix4pgk,ada /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 td3g58r5vg 6nfscq0.oklq :5 o*dnnx $^{\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 w1zs /8ou edv+yet*z/dithin the audible range for a 2.14-m-long organ pipe at 20 e* zds// otzy8e1vu+d$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thr z*sgrm.92xrfas:l+ e outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the sgr 2ma.zr* +:fss9rlx tanding 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 two strings, one ux k6mpg0yeoudo *6so6, i6 (yof which is sounding 440 Hz. 6( uk6o *yipdoosm, 6ey6gxu0How far off in frequency is the other string? ±    Hz

  What is the beat frequenqnk/ka,scqw /hj6+c ln2) y4ccy 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 anothka 3 2a6ggy/34b/cej,:7s pclls;h(d q joo wcer (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, 3,cjgas:7 oyl4 b oc6deq l/;2/ kpgc3hjs (wabut a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4x1y a7k.ei,2 vm wgfe 1flym7) beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your k 27 il.,f)gfy7meeyvm a1w1x reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oncy/f (nh6iy: je string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1y:cfhj6 y/n (i3.]    Hz

  How many beats will be heard if two identical flutes each try to play mido* klt39kr0 qdnp5a2 tdle C (262 Hz), but one katk3 l205noptr qd9*is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; wh .u3l9ff.b*ot 6xxp sv.v xpsb6iwz5: /uz8xyen A and B are sounded together, a beat fr: .p/ 3 u8xtpf*xbui5zly .z9o6 fs6xsx.b wvvequency 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 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 person7nt 33opurh*l stands 3.00 m from one speaker and 3.n3 *t7p ulo3rh50 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 betiq7ue qsa10n 82ta; u vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s702u; qauq1e s a8ttin 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 msbc*zbb1)yx f55 ly i* in air. How many beats per se f s5bicyyx1z* b*bl5)cond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cu.eq be5q(g db9ui;y 57bqek-; bvvb7ertain fire engine’s siren is 1550 Hz when at rest. What frequency doe;b5d;(.7 vubi e- qvqe5k ybu97bgqb 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 engine t8.7yt 2hz dpowhose siret7 p8ot d.yh2zn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a m6us5 vhd)doejs/;u :6ee6zh2000-Hz source is moving toward you at 15e edu)v5s: zm6s/6oj 6hu ;hde m/s versus you moving 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 same single frequency h7 a73 /k9ixvh)ttju2-r*a)yydf g hthorn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fr uh2j f7)htyt -a/d37ya rg)h9 *xvtkiequency 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 50.t1i8gd2 updefj bm*ngu+ d7h. n7ac) -0 kHz and receives them returnet 78npc+) .gdhbejni-2umd 1 fu da7*gd from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits andgs qk9h59m-k ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in k-9hkg9q m5 sdthe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler : 4to*pi.,vmk,mcs wp experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical to,4* vi.p,k pm:cstm wuba 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 waves to measure blood-flow speeds.z ixn:ic2wa1 d f)b6j3 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:d6 2 b zca1ij3niwx)f from the sound source?   Hz

  The Doppler effect using ultrasonic wavopdx-jiteq s /p)ff.2iih1/ j,b ra6:es of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz./zflyo/ju 5o;s; oi y6 When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at /yol6;fz j os;o5ui/yrest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if itsa i kjn2my8yo*(vvs*2hh i .c4 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/sv,iv0ld.vg6 s*z p7e g (a) What is the angle the shock wave makes with the direction of the airplane’s moti706 dp,s v*zvveg .lgion?    $^{\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 sound i+e2; urwwip a3kkua26 x:khb.s only about 35 m/s w3iwa;6p 2uhukb+: erx2a. kk
(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 ix: 8-axsl4ido qyd5500 m/s strikes the ocean. Determine the shock wave angle it pr q45i xy:o85idlsx-da oduces
(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 c6w3p+/iw;mp: ymhik $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 10snz0gug y rl 5osfd5 f-e1xfz/dw: +i :v9a:s.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizont9+y/zf-0:a sxsgso0d : 5nwiu f 51flg:dezrval 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 senilvykw)q5zhc() q j /6;wbbc9ds 20,000-Hz sound pulses downward from the botv(6)9h i lywkqc b cqj)zbw/;5tom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many oc6v9v5p. /u lwqnifu .xtaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists oki7;n6ety6ho -br; qte f94kvkmcnn-( jq p(3f many plastic pipes of var -or (n 6b7-v3qt4nki kpce9kh;e;t(jyfn q6mious 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 threshr- mz9al2nq fivf )4etcmvbj1n56 v 9 10trzy1old of human hearing (0 dB). What will be the souf1t29aie lf1m 4y-5v6mvc tbjn) q0nzrrvz19 nd level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8klj6i tpsd0; s9 *yi*7 3rjqk2rg0omj 2-dB sound and an 87-dB sound are hearddk y3*r0iimt6jqkgp *9oj;lsjs 0 r27 simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1.iyd;(:igr2 s7kj9 r ftzj-is05 dB. What is the acoustic power outpusiysj r ;i.g7kf9 tjz2:( ird-t (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 1c90 5gnc 15y)a yzk2b qv4ruep50 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is t2cvypq5 beay 0 ru5k4g1)c9nzhe power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prot8nvfhbi*h61 bective 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 earbh vinbfh 1*86 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 systemsur,fe-t6 +ozcvrhn1.ck;j r ., 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 tpvyjn z7r90 -1dcgw ;ttd)i)oo 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 violidh9c 9 b,rhjq-4xyl2b n is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length oc9hyxbb-jqd 2 hlr4,9f $6.1 \times10^{-4 }$ 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 (8w qg 6t/bficfilled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the abw/f(gic6qt8 ir in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is)by 9b 1 ;gobfod)6zie 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 harmoni9oo6b1ifdbygzb) ;e )c in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resf 3ot0cbn, x1t.vi cya87m -ahonate 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 500–100(vn/9j / zetnky;jb.w0-Hz range coming from two sources. The sound is loudest at points equid(t/e;jwnz y .bj /k9vnistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 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 con8ar h(npfwhims (u,9e6k ifkw2.)vd6 ductor on the stationary train hears a 3.0-Hz beat.whai26 sk( 9muk 8, ni(6wrd epfhv)f frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trainys .a,fn/z7jwx kcdu)n*r i. ( whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (ass,a / fk7yj.cnsiwr()nxdzu. *ume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to thegbf 7ml(5uqsdq+ hha1/2 br3r difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halveq3/5r 7g 1hqsh(blm+ fbrad2ud) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat fre1np,*qbd e+k1p rhp w:quency of 11 Hz. The shorter one is 2.40 m long. How loe ,:rb1*hpk1 pn pdq+wng is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mov5m,0bg4nhmqa es past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him,,bq4m5 g hna0m at C?

  If the velocity of bl+ue 4;o(oxgnrood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves traver( ogneo ;+4xul with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed i3zr jdcm7ty)., vw j3yxt)7jqk6 pw;6.5 m/s while the moth is flying toward the bat at speedt.jc) ;t 37ykw7wqrijz mdp3j x6,v)y 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 the moth?    kHz

  A bat emits a series of high frequency soeg )c npv 3h -w9zb+bqv;w*)jpund 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 th9 z)ej* b; v-nwbqpg hw+c)pv3e bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oncugp,z)8of 7ek0 tfx6 ve used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be bl uk0,t768ze)gfvf oxpown 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 presence of stand/s hs/bl8 w/p6jbumm;ing waves, which can cause acoustic “dead spots” at the lo mhs/sb6juwl pm// b8;cations 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 oxdkey+ulw+e+v2 n.( a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked (ye+ .e2xw+ k n+vuldowith 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 atngv10jyd,am0 vao(jt-jh/l * a frequency of abounyjj*aj 0avlg(1v-ho dt/,0 mt 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on tf c0e8k*rh7g5g:xd gzhe ground hears the sonic boom 1.5 min after the plane passes directly o g8e:dz0gr5k 7xf gch*verhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15q v(;r ou8ewc v)ccn.u49:xz d $^{\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