What is the evidence thae3.m zq0p-7(:fwn dc. kpxly )4dbgtnt sound travels as a wave?

What is the evidence that sound is a form of enef1 tn3g4i(: cye67yubmt /bpsrgy?

Children sometimes play with a homemade “telephone” by attaching a string t 2myx /hxpnh2o,v: .dz5eh ,ako the bottoms of two paper cups. When the string is stretched and a child speaksazp/h 2yh,xxko medh .,v5n:2 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 air into water, do you expect taf4uf39cw;dg4 nxnkt .r,m7q he frequency or wavelength to chgk; udm n wf4tnaf, 7x94qr3.cange?

What evidence can you give that the speed of sound in air does not depend sige:ba6hxd*q e,rkro/ 6 nifir xhe,kad* 6/boe6rq :cantly on frequency?

The voice of a person who has inhaled helium souni6s;v84qpw nef bs wb v(a19nj) 5 lg)emma4n/ds very high-pitched. Why?

How will the air temperature in a room affect the pitch y,+ p)h unkvllh+7 e4-li)vvc of organ pipes?

Explain how a tube might be used as a filter to reduce the dy1. z-lwlj)uzsg)0n1vmg u) amplitude of sounds in various frequency ranges. (An example is )l1v1u ls0g- nmy)w).zz jgdua car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together h5)-j46a f1j vyf 7yuu5vsj bras you move up thej- u6 1yb5h)v4y sjf5vuj ra7f fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear6cpn.d /dv,8g- fkscq it but cannot see it. When it emerges and you do see it, itsg-c 6,dpcqksfv8/ d.n sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interf d) l,wwu sob.txk:uwej94o)np r q1 sh+-4im.erence in space,” whereas beats can be said to be due to “interferencel.dous.w)o-)p1wkq uhi:ebxs r,w9+4 t nmj4 in time.” Explain.

In Fig. 12–16, if the frequency of thhtbyw:jfvo:d n n+459 a1p4hye speakers were lowered, would the points D and C (where destructive and constructive interference occur yhd nhaw94:nto+ fj vpy41:5b) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas withul(+n5;b3idjeszc- 6x0cryl 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 devi i ys(xulnzj56 cb-el d3;+c0rce 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(2 i4cm:a/ckz(uds0v 4 wigzr–31. Each wave can be thought of as a superposition of two sound waves with slightly different dz2s0/ irca(:c(4 kzguw v4i mfrequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler skk1dnd i 2:1os 4swnt7n 1*ngxhift if the source and observer move in the same direction, with the same velocity? Explan :wgi1onn1kt7k 14d *s2d nsxin.

If a wind is blowing, will this altehxt/agyd* iqs ;(t7 r2r the frequency of the sound heard by a person at rest with respect to the s( i/a2xr7ttg*;d yshqource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a chims9nrtzj h )h.7es1 4xld in motion on a swing. A monitor is blowing a whistle in 1jsn9emht.rz7) sh x4front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thezx; ol2 b9bvx1 length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. 9bo1xvbl zx2;Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shipb(r.iz17 b(km9 bw- m fgc6oes just below 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 of1g.sizk7b(b 9c6 wbmemr(- 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 iu- weh6mhupb: xt*grvf/n ,66 n 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 boa1j b2mgs2 v ev6igj795,gdrht t is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) sm vge 716ggj2jv,ht 2drb5i9 by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. lbr ;9 9/ rf3vvlp it(p6ivoa-The splash it makes when striking the water below iv99-il/pf;lvir a6tp(3ro vbs heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stolh 3o6i7t;x xhne strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far al;xho3 t7xh 6iway did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile ofr+n2z gq1y* /joeo)v:sz 6ljf distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (ajv+ sfn2:lj/o1oze gr) 6yz*q ) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level ofzm.( n4an qlf-1d z:wk 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 soua7abu 8o 5eknq5g63 bwka5)l,eb2pkdnd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta6, gw+dw 37i/ 05 qbsqdmaqelaneously at a certain place, what will be the sd76 e a,amw q0g5q /+iqlbds3wound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cerfb,n3f9u x0 hmtain distance from an airplane with four equally noisy jet engines is experiencing a sound levelbhf0u3 ,mfx n9 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 s- bo c+ 3nf*mmarx:l2hignal-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 backgroundam-+:* o2 mxnc lrbf3h noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a hjzack;fcm8no9x3u . icr*p8g b; +p5person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphe9*hb i3ca pcjz;m5 g8.f8nxckop+ ; urre 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 aju b*k8/ hb0v7lyz(s it d)qvdq+e 5xz y;y5s*n 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, whi:e;mvj-qp 2 z eyoz,s*le the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in tur ;oyz e2 vq-:epj*zms,n 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 1d; bv:n./wx m 6jl:uzl30 dB when placed 2.8 m in front of a loudspeaker on the stage. v;:jlldb6w xm/.zu n:
(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.m 8pk z+8zapb7 What is the ratio of the amplitudes of two sounds whose levels differ by ap8m k7b+p 8zzthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tri:ilvus )dzg/qj/-wtdh *ni*79p4 )y (a lvm efpled, (a) by what factor will the intensity increase? Increase by a factor -en uqi4f)dali /gl)dmvt/ 9 7* hs(zwyj:*vpof    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the6mlw(t6lvy xpf8jj gs s k)3m7;w2anuz0hi 09 frequency of the other. What ji;9ktu 7yfwszgl ) m6nx(3 l0 vs2pjh6m8a0wis the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspond)g2em9f 8dcj xs to a displacement amplitude of vibrating air2jx )mf98egd c molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as 8tzrju6j2n6lt-k o o )a 100-Hz tone that has a 50-dB sound level? (Seenjoto k- 6ur8ljz)t6 2 Fig. 12–6.)    dB

What are the lowest and highest fva8zt3 4i8 aztzj ( p/v0r9quprequencies that an ear can detect when the sound level/pp tqz8 8a9(3u4zt zavv i0jr is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a h7y-f 0(+ebluy, xs noeuge range of sound levels. What is the ratisfe-xeyl+, n0(u 7y boo 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 of 440 Hz. The05jf 9 ggqg4au length of the vibrating portion is 32 cm, and it has a mass of 0. gug45j0 gqaf935 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audibp1kk5x/fl ; bjf g ncqp(j pb-g4/ z3y9t;fhx7le overtones if tp k;cb yz 79p/3kn1jxfg5pbhf4 ; x(/lqgtfj-he 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 yo9 dx tf3tta,n9u expect from blowing across the top of an empty soda bottle that is fd,9nt9tat3x 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 pipe)kofi .2f oy 6jtkq2e96 woo9ys spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ)f2o2fk t.9j6owo9 6oiqy keyired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency 1m2e,lz i)bs yof 540 Hz as its third harmonic. What will be its fundamenby ze1l)2 mi,stal frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above midg-a3xr x5u2nfh 2agc+dle C (330 H+3ua2-2f5 hx caxgrgnz).
(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 organ pip8cv, fl 2/ we2rq4ynjye that emits middle C (262 Hz) when the t8refcq2w2l , 4y/j nyvemperature 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 a09jqv u: tqr.m8tr eb:t 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 Exampl*q8e ih bv0r.te 12–10 should the hole be that musqrh80ev itb*. t be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hzed:r;d.df4ys3n m e y., but not at an fe3sne:y4 d.d r.y;dmy other frequencies in between. (a) Show 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 at both ends. It r q01c d*isyn )pd +vyq)lr3tn2esonates at two successive harmcq)iv2dndn+ylpqs r t)1y 3*0onics of frequencies 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 y 5cooa- b:mxg1zn0vd 9d t5z-$^{\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 range for a 2..colfe( ,/ c-sdijz y*14-m-long organ pipe at(fcsioz /ej *-c,d.yl 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opentd-, qpxfu/*w to the outside and is closed at the other end by thwt/u* ,fp-xqd e eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryt6jga:6ep( sping to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is ts6 :pe (ta6jpghe other string? ±    Hz

  What is the beat frequency if middl5wf q2bhp j(3,xhs,xge 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 kHb .q +sk/rv* *n1x+ vcjh7biaez, 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 frevc1kh*.jr+bb av 7x isnq+*e /quency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunixr)k76+ygs pg3: s njdng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stpxkjn:+ y)g7d 3gsrs6 ring? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in op:gp16r ba -my nnz.dov4-o m: t2/ngone string is then decreased by 2.0%. What will be the beat frequency heapbd 1n2:-o ng:.ty nopvm6 /- zgr4maord when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutesyc4jmq .d9h(j : v5b ys-)rmig each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0 q:. b5vims dmj-9jy) hcg(ry 4$^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencqkglf; g0k8( my 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 f8l0;gkq(mgk 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 person stands 3.00 m fm k0 ha+ v3xs*r)7m08n6 boou+rcn hscrom one speaker and 3. xakmhbhm8+o)scn06*r o un 3c0s7r v+50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be xlw51iv8of mns8 8.bxvibrating 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 bev15mxx 8i.8solnw fb8 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 2.8vp;/ llk; ,5 fnr jxl c5lw1by5f p)t1jam8iy76 m in air. How many beats per5pj)w;v j 1l5 8l8k5r/ pybinlfytm 1;,laxfc second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ ngd)aqisz tm6 9r1+e,ency of a certain fire engine’s siren is 1550 Hz when at rest. What frd1 zmsr aei)69,gt +nqequency 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 x iznb83m nt:j,yv 26erw1 jk8do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed8 t1bje mv 3krw, nizy:nj628x of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you at 12ltt(k8m; lt4b 1vlg a5 m/s versus you moving towa4tmvlg2b ta;t (1lk8l rd 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 wi1k 3*vsy :okcmth the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the h*ckm3o:kv sy1orns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anllp9 l1m ;c*mvhkq7+zd receives them returned from an object moving directly away from it at 25 m/s What is the rece; l 19z q+vkplm*h7clmived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/6)hldavlis , +z7shrb,)n ac- s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thevi6h7czhdl sana,sl+) br -,) bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatq )2;skmk6yia 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 approackq6a;s ik) 2myhed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spee4zu2al.j9dth w;/ mnu ds. 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 blo ha zdm.ut/2u;l 49jnwod is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic,ijg 4ul9a1vvsv jje et k0,x)d7k)1n 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 soqwa.kmzz9vyu 04ar- 87wal d2 sp.)jyund of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who ar0.w7kayvjlzaud 9q - 8zpm)4y2 .wasre 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 spech ks60b7dw:lhb/ kj0ed 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 :be05mu(bnm2zx8rv xt/t )jo310 m/s (a) What is the anx5mb8/tb 0 tvjnu2z(:)ero mxgle 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 where tyncu 3xdkxa i((+x1ew61:o x ehe speed of sound is only about 35 mxx 6cx1 e3( k ynado(+iuwx:1e/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 sa;yptep b/4 c5trikes the ocean. Determine the shock wave angle 4/btc5 eappy;it 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 utg;z( - c.r j5hpgrd:$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead nnko)c;wr0yv0 dj03 band see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you heajk w0n;y rbvcnd o00)3r 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 thas2xrx 8 pkph y.ye2p6/t sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fyxppr6hkx.2ye8/ ps 2 resh water)?    s

  Approximately how manl2c.b sf g;xx4y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ah-./ 0ehz s8 sw7+h(r fqsqulb sewer pipe symphony. It consists of many plastic pipes of varios7- szh(w urbh+8f e /sq.hlq0us 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 per +zhjb lb-vq2;son makes a sound close to the threshold of human hearin-zb j;hl2vbq +g (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an q t2aya w;pao89-9cwj 82-dB sound and an 87-dB sound are heard simultaneouslyoy28wt;c9 9wpq -aaaj?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh 0b/t79 .mnrmu ctpq)yat is the acoustic power output (W) of thnq byrc t7 upm0/)9m.te speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output droprju/4o j1vf +ns by 10 dB at 15 jro+ nvj1fu/4 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft fm5kdwgv*v8 2h2qh ine e.;1atypically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective 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 .812wke5v* g2a i vmfqdhh;enengine?    W

  In audio and communications systems, the if r mt329gsd4 dv(in0gain, $\beta$ 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 tunvenggl-y:j 1 z9 vs+l:/: nopred to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wiqfu*t(4 duc l3pbuiz u;jg(26th a fundamental frequencyu2jdt3;z4 q*plgf i cu(uu6(b 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 vibration above a vertical open tube filled with wab.j-m ,2ys4yp n qc8piter (Fig. 12–35). The wc, yp2 -b.sp8mjq 4inyater 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. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g inlwgbi3y3lq9)i33m ys 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 tyl3 yn m9i3wq3)i 3glbhe tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full logl7hdur d0rq+ebxfb7:93d 9 sop ($\frac{1}{2}\lambda$) 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 souv um 1f0a1)(ajkrz-d urces. The (dju)-f 1 0a1 zmvuarksound is loudest at points equidistant 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.j90aghrm0lmdx a4 6 2o The conductor on the stationary train hears a 3.0-Hz beat fr4 xoa l6mh2dr9ga 00jmequency 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 you6s 8hpzaq 7x8tzvav;, is 538 Hz. After it passes you, its frequency is measured as 486 Hs ;,zvptzv6q7a 88ahxz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the (.1/v+z:5e6vjvcj ; f nidcnjryi n /bspeed 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 (frequency halved) as it 1+nnj6/nj/;bdicj ic(vr y:f vve .z5 goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produecz.-jghb3t*wv0 f6u+ee g+y oqg( 8yce a beat frequency of 11 Hz. The shorter one is 2.40 m long. H8we+*q. c0 j(yg6-zuvgfeoht eb3g+yow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pa (njdt gln/ y6i0u7l1dst 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 speaker d0d7 6n(iugl1 /ytjnls, 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 0.32hv o a; g+t-mpozvgk2doy xj-9(1mo.2 m/s what beat frequency would you expect if 5.50-MHz ultrasound jxo.d2k;z g9-t-m1yogov2(o h a+ pvmwaves 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 while2 oj a3dz *ifh 6(fhaqydy)r7oc(d,r3 the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. yz3a) ic6fqhd fyo2*7r,hrdjoa 3 d( (What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mode;w4p i/gre8 y(rfk) th. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far p /w;84(edr)fkeyirgaway can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig 4mk5qg *jpaf+ sff5h7. 12–38) 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 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 shaf hs5f74+5fkqm g *jparp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can b8sapgzt. os:n n0dk a+b:n3k cv4:/bce compromised by the presence of standing 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. Calcna4 g 0nczbd :s: /pnt avb8k3o.:cs+kulate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alpvrq s zq+7)+xe i7 4)vyfcl+guminum rod held in the hand near the rod’s midpoint. Thz7lprq+4q7)g v+c+fs)ey vi xe rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(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 x ;1v zbg*gom)reao iqc fspp:)05s(7a frequency of abopoc50)v*xe7(gm; zifrb : op )assq1gut 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 the groudv*z:l e ;4tbvht)s7snd hears the sonic boom 1.5 min after the plane passes dir )hvtt4d le*v;b7:ssz ectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 -rp*zag lw)p3s(9wuj2gi wc0 $^{\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