What is the evidence that sound travels as a w:*gv1zd2eh z (sqqjp .5qc.ywave?

What is the evidence th+hq 9cqhic)8cj/e o0 3f-0.+ tgx nehxl tagz:at sound is a form of energy?

Children sometimes play with a hoa5zcf+*0*t( b (yiqc7a tvsetmemade “telephone” by attaching a string to the bottoms of two paper cups. When the striny+qi e5 v*scta07fc*(z tt(abg is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from . b( s3z3kjpqaair into water, do you expect the frequency or wavelengthz(p3qask3bj . to change?

What evidence can you give that the spew1ebw bzo(:*;-gcvq1 a9vr u fed of sound in air does not depend significantly on frequrozbac ;g ubvqw:(-*119 v efwency?

The voice of a person who has inhaled heliumwhefclc (9;u .ab2 fq/ sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch x 1cd:yir suo 0ku 44veq1(mz)of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude l 7v /ix9*v7spx)cwyiof sounds in various frequency ranges. (An example is a 9lyv*)xisw/ cix7 p v7car muffler.)

Why are the frets on a guitar (Fig. 12–30) spacex +sz,h+i2 zaud closer together as you move up the fingerboard toa +i+xhszz,u2 ward the bridge?

A noisy truck approaches you from behind a building. Initially you hear me9 g s1khwf2 o3z2mz3it but cannot see it. When it emerges and you do see it, its sound is s k hemsz32 fzwm1o932guddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be 2a,b *shgy)vizg t4(3 -pw vljsaid to be due to “interference in space,” whereas beats can be said to be due to h4 lpz(- y3sjv)*g,bagwtv 2i“interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wo981euc f 9tccduld the points D and C (where destructive and constructive interference occur)e9cu1ct9 d8fc move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i;u,efj vvh u*l9*ng1 nn areas with very high noise levels ha , *vu19lfn;u*ejngvhve consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave cabad0n)3az8.kx q6 e nan 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 frequencies farther apazadb 6ka qx83e.0nna)rt? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction2yb9xq1iimrjx7keaqr j 9w -4l8s 7*x, with the same4xyr-mix7qwi129ark x*j89qb s7lje velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a kq)j/b lw+ j2cperson at rest with respect tj l/k) jcb+qw2o the source? Is the wavelength or velocity changed?

Figure 12–32 shows variousqxzh2ijf kec x3 beh/p08x7qk)j477z 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 fre jk/kh3zxp e42xjhf 7cxi87)qe b7q0 zquency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listenin1(fj yhmo )pa/ggj)1-e qh8d mg for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s afjfdm1)-h) me/pg j qah1yo(g8ter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below tyh)rf o9x orn3s ja 3b4w3va9;he 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 se;s3h9voary bo)rn3a f94xwj 3 awater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ao6*cj.f k*u.1jce t lmt 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 tunvkh-r +o5nb+sa on a foggy day. Without warning, an engine backfire occurs ov-+kson+ 5br hn 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 ofx31 * ew/i)f7vax d8r v ;uuoaub0vha7 a cliff. The splash it makes when striking the water 7a;fvrvi13e8 x a/b0a )7wvoxuuh*u dbelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, atv )iyq5: f2::vywe.w 9npzvsees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one trw:ayv5 np).fyevv9wtz :2 i:qavels 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 distam161m 6 ngs,nk/y kqs.1.blfkizx :ngnce by the “5-second rule” for estimating the distance fromk,/k nblgn m: .isfxnkm16 1.g6s1 yzq a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of ahxe+- v5gx er1 sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level oe+3;/fa f pyu n3/q:-hszx yczf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 0pd2d 1ms07hwvu;cb ax x /gqfflt-j:1u01t r95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? -vr0;21mpfhxddt xg0sfu0jq7 cl1w :at bu1/[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with:m kznc rhzg: u3wx+*1 four equally noisy jet engines iw h1uxmg : :nz3+rk*zcs 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 intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ra3uvldd.h 1rtukv 9 s88q,r: sktio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitkvs.1v9tu8ksd dur :l3, 8qhries of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outp hzx h5s/6g0jlut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uni/0l5hx6 jzhgs formly 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 sm5v8yty,t 5dcs9a prz6t0m * jtrikes 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 mo9pl,p77wsxxv( q rkm-dest amplifier B is rated at 40 klp,q7xr w -(m 97xvpsW. (a) Estimate the sound level in decibels 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 130 dB when placep69yp6yg ox em6v u18ed 2.8 m in front of a loudspeaker on the stage. 6oep8p9xve yy6mg1u6
(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 typin/:dz t;5cj1is*b q w8nv/ndically detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 1dn* n1bidts 5:i/;vqc8 /wj zn1–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte-,ifypafehpd 8 / f6ffdj.63ensity increasedyf.e6d 6 ,ffifaj/p e-hp3 8f? 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 twice the frexbvukix4lf6e r k 8 ewsz47731quency of the other. What is the ratio of their intensi7xsf3kl78ibk 16zuevx e4 r w4ties?   

  What would be the sound level (in dB) of a sound wave in air that corresponds t;u4 yglt7b ys(o a disublt(4 7ysyg; placement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hqt 4+csq1ypf k q/qg-7ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound lfy4 / gq+ tkqcq-1qsp7evel? (See Fig. 12–6.)    dB

What are the lowest and 2 ls e;nsb:gl+highest frequencies that an ear can detect when the sound eslgns :+2l b;level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levenxv )*7ar9ws)qz c m3hls. What is the ratio of highest to lowest intenr*m) 7c9h )saxv3qwz nsity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 H n ,4n9ai sf+ g*nzioes3 148m2scmbzbz. The length of the vibrating portion is 32 cm, and it has a mass nizns,oib84zsm c1 4*sgnb9f mae2 +3of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamenhqi5v, :hg0eg tal and first three audible overtones if the pipe is 50:egqghv ,hi
(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 a fx rw60 elc2lf9pw6bz) g;d2ecross the top of an empty soda b6)rw l;f6wbpez d ce0 gf22l9xottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube et(/rf 5jgk( bgba u46pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipeb 5u ga6b4rf tekg(j(/s required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hadh3s)m2 -brhlch23p xs a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is finger3 h2b-23 hhclpsmdxr) ed at a length of only 60% of its original length?   Hz

  An unfingered guitar st h( llguh:zo.(ring is 0.73 m long and is tuned to play E above middle Cz.(ohg(lu h :l (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of ankly1,3ydnp f k 240r-bcutfa: open organ pipe that emits middle C (262 Hz) when the temperature ist ab0p:rkf-ycf4l 2ynu,d3 k1 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 6r50i qiv1 d t/+px7k(hzjb vwat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mou)smilbze 2 )3l ye7u.x p)*s*byuz,y* l 9exlythpiece of the flute in Example 12–10 should the hole be thasl.*yu 2be)9 ll,y*xeb xms l3*yez)y p)i7uzt must be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 4c8r*jh6b 99rqqti.e b 40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a close jh*96r8eitqb9 qrcb.d pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.8z r6pg0 fr-qm20 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wh -rr6m2f qzgp0at 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 vgzt/ c8,p 8fv$^{\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 ;/zmspe y6ibv,( gsesm/sxa *x*-s r/within the audible range for a 2.14-m-long organ pipe at 2/mp/ ms/*( s;ssre6gx eax, -zvsyi* b0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. g6pzdz* p*m*p5+: cyfo .4/xte ksabcIt 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 wavesad:*yx6 /*co4p.z c spkb ptm*e+5fz g 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 s.gn1gin ca.w pi* ,anv-)p2mrtrings, one of which is sounding 440 Hz. How far off i,1mp)nwncrp gg - ..naavi2 i*n frequency is the other string? ±    Hz

  What is the beat frequency if( dfmi1lny9*e 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 23x7gig-; i;he jre,l yt+3o. ak.5 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 p,ti;yax; g l.-+jikgeoe7r3h layed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with6 gmj-wqi t-0s a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vi wqg06m-st j-ibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The/;x l t+*p6zlc njvuf1 tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together61u v+;nl/tx lzfcj*p? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle Cj2i rtd *p))rb s:uop:f*q1qn (262 Hz), but one is at 5.0°C andi b:qr:r s1o*))n2 puqdtjpf* the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B wz.g c2tsgxl5o :ju b0kl2ov8)jr74p, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A at4x wjou .kbsjl0v cpo2gzr2l g758:)nd 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 per*9 qbi/joaa2z,a asv4t2 )t uwson stands 3.00 m from one speaker and 3.2 vb4) aj9sqza uaw,ot/ t*2ai50 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.d) c,r/7dsb it+ r9dyjk6dy u to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the freq)cj by6 y +dk7t.9ird/,sr dduuency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m h;,j.xkn+ 1wh )fxtbhkgpd o+ts: a.. in air. How many beats per second will be d ; k:+ o+a,gh1nbktxsxhpjh ..wft).heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequm 9hl 5oma2w72bn kes:ency of a certain fire engine’s siren is 1550 Hz when at rest. What frbm sa2k7n e9 :2hwlom5equency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if;)y(ts hj)8ljhro. zi a fire engine whose siren emits at 1550 Hz moves at a speed oz( ;il)oh hr)8sjtj.yf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is m/ wpmu: ajq2y:oving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same?/j y2p:: qwuam 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 hornxi*x:xem3 +h z).b 5 1uwv mhnfjiyz lv19t/7m. 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 ofh mu.wbx9x1) +fh tiixm5/1vvj:y*3 mze 7zl n 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoibr99ifbcnp0 s6-d; u nic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is th 9biinr6su;pdf9b0 c -e received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward ao*ps/;dg i4r8x 9rjf q wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz; rqsdi/po4j9g8 f xr*. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on r2*g+ljn*h*i g.s. 9;ba y;cuc ixoipa moving flat train car at a frequency of 75 Hz, and a second identical tuba played the r2g* a*.jypnlu.i *cch+i; oix;s9g bsame 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 wavog; otz:wc8/o es to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human t8w; ztocg :o/oissue 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 ulxuu+v73.*r gp;hg +t+itfzm 0 rkmb:zxhgf 73trasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fr 6h:b-lyf ;*zldgosr3equency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observer oy;l:g-dh*r3 6sbzfls hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed a*h-)(0z :0escnlo7uwq ju p oj 4f:wfyp 8u3cmt 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)b8x)x +.roszx What is tx+xx)s8. zbo rhe angle the shock 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 s7 *x zpu i; fkzngzzf:+*.k/twhere the speed of sound is only azz :g x*uf/.k ;k+z7spfiz tn*bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave a5h wnf/ +kmu(c*u2v cgngle itf/uwch+k*g25 u m vn(c produces
(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 icegr0 +dy6 +l-7zzvh$/theta$ 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 exacpvpfght od2i( (.9zu 4tly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boop.th 9opz4d2 gvf((ium, 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 se6j6mr y2 ca;ddnds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which ij;addc 2 yr6m6t 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 audib8 wl,:- e6lvy5igz kb0l8e hjrle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewe m22u3moog.mr r pipe symphony. It consists of many plastic pipes of various le 2mmuomo2 3g.rngths, 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 - +1jg8 vduhpwthreshold of human hearing (0 dB). What will be the sound lev u18 pv+gdhjw-el of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an hpzc8 -1vpw2+e; fg rq87-dB sound are hearp; r1-wg z e+cvqhp28fd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,:z (vm )gz,gysdog,evu;9pm mp47cdrjy 6*b, placed in the open, is 105 dB. What is the acoustic power output (W) o : cgd g p omvmy6z,d9(*b e,)prgs47;umv,zjyf the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is /cew 1(y.*tul5xo* pzf+xc xtfq 5 rv(rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What i(qy. xf t*fuwo 5+zcl5 1(*crx/pvxtes the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective dev8zc dn8 *;ne lw0flg f/iqt5e0ices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a d8*n c 0gl lewdne8/ z5tff0i;qistance of 30 m from a jet airplane engine?    W

  In audio and communications systemsi*yd dk4 /;7zyj8mu 88ghowyo, 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 to a frequency j,fard 8-to5vu j ,4fig;xp ;m1$\frac{1}{2}$ 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 fundaau+y hyevxq2s hf2-+n( ;t*fp mental f; -q2vthpaf+yexh2n +(s y*fu requency 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 vin -bs3p -zb)em4xe4xx bration 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 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. Wmxp )ex3--en4bs 4 bxzhat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar h7ljzebln u .k ,:)v2i z2iy+dj)h5pystring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tensiihkui2, : ellnd+z)hzjpy j 7bv5 .2y)on 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 -o(o1 *a3gu qrk6ec knobserved to 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 sour6 * nz 7zx1wim+ bkyu+6 m8m4efbm3jpjces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, t fbm1yp6 4kwz*zmj+ u 67mij38+mneb xhe 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. ubunxaa6 5) u5/8w iuj sb+wjh.ste+5 The conductor on the stationary tr sj . aw 5ujw+huu+/ e6s5bnxi5)a8butain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 sm)9q /0tzwey Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocie/wzq)t s my90ty)?    m/s

  At a race track, you cdzu/6c)2 ktxvan estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (fr xtzkcud/26v)equency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundinlyrz,2:9ixoeu1k1 a ii/qcvj 3: mt4qg together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. H 11l y3oamj /it:xii4:cer9zq2qvku, ow long is the other?    m

Two loudspeakers are at oppositqd 4 4-f+5 tizvw3ukejqjezsk2qp. ww2 k+ x;5e 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, whatq +5we.d2f-q+kzqt4wji jw s5puz kv3xk2;4e 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, at C?

  If the velocity of blood flow in the aorta is normallyfi mklj d.-h*/dtp*+h ewf ask f,8/i8 about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and ref- s*w8fm.fk / l i+d,dhajt8ef*pikh/lected 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 toward the b p-*lai grot .,+vph4yat 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 pa+*,.ht r-ol iv4gp ythe moth?    kHz

  A bat emits a series of high frequency sou,/ o jpzti :-vgem/z/knd 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 m kpo//zzv:teg/ i, j-from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)hxs8+6hu -a kjvmy,)x - 1qmrt was once 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 blown in such a way that only one of the overtones is resonatin)1xyhm,+- 8- kjsar6m qxvthu g. 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 stanhjg9l jz1i4:t;wme8 gding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamenzg;1 metwl j4:h i8gj9tal 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, sip3nm: ub*xje8w* j y.lender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a litj m :bu*x .yn83je*iwptle 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 at a f3pkz 8 scaw3p5qpnq jd bn)-/:requency of about 1000 5d3p )znpb- wj3kn8/p: s acqqHz 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 grounklzggxt4 984v d hears the sonic boom 1.5 migx4v 8zgt9l4 kn after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat n9:ay 0.x 1ol.sot3zm kx*eayfmzbq*e54 zn5 is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h