What is the evidence thatp95j / p.gvmjgtot ;at y 81w1.afr5du sound travels as a wave?

What is the evidence that soaf:/ipi vfoqi9i/ t 5 vy(3w+rund is a form of energy?

Children sometimes play with a homemade “telephone” by attach 5wn*a) f4 xwrp7xfzl-ing a string to the bottoms of two paper pw *az5xr) 7xwf-l fn4cups. 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 travels from one cup to the other.

When a sound wave passes from airavfn.x 1 m81zgxe /j;r+wzv 2l into water, do you expect the frequency or wavelenn1. /v8ar zl+xfw;zje12m vx ggth to change?

What evidence can you give that the speea+(sp*7l o l 3osfzdc;d of sound in air does not depend significantly on frequeno+ 3;a lc s*olzdp7fs(cy?

The voice of a person who has ) -y9 rf.fet qskjd au*r/i)g0inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgxf4u7.;rn y rjan pipes?

Explain how a tube might be used as a filter to reducefcqjz.1 35cmf6iil o , the amplitude of sounds ii.,o1fqf 3ciz lcj65mn various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c(s8nb)dibj0wwz jvz*+ 58 u kuus5 p ll;nkf55loser together as you move up the fingerboard towa vdl)nw; 0jnsu85*up8fl 5 usb5b+wj(zi5 kkzrd the bridge?

A noisy truck approaches you from behind a building. Initially yok8u2aaqi 9l*wz r svoq n5f;wi4*/k(eu hear it but cannot see it. When it emerges and you do see it, its sound is suddenz8ii;u*q 9so r4e/vk25wkf( la*wa nq ly “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 “interferdgla+p3l rstv/ y+- 9vence in space,” whereas beats can be said to by+tl v +g3as-rl/d pv9e due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of t oe.ppuw3v-c3:f pzl4he speakers were lowered, would the points D and Ccl . 3epz-v:p4wufpo 3 (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areaa ;m- dp6zl a)okkr6depai*2 6s with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detec6p6deikomz ark*a 2- )6 d;palts 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 F w( hfxwu((u6tia z2r+ig. 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 frequencies farther ai6xu2r zfwu(hat( +( wpart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the souch p30y,.c 8*uxz jfewrce and observer move in the same direction, with theypj.30xz fhc8u we, c* same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard 5j w;zj1anx ic*-bdu( by a person at rest with respect to tbj(; dzj*wc1 n5u -iaxhe source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monit 2 ,ilakgg5.fq aor2-yo s)c2eor 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 f2- s 2rago.oqikc2a ,gl ey)5of the whistle? Explain your reasoning.

  A hiker determines the length of a lake b,c,ls fu;aexhw. 0m4sy listening for the echo of her shout rec0a u4;.sms,lfh ,wxeflected by a 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 shipwsp)xs0cr jyw j/.,/1mdq:8dl i* vin 7bpp: w just below the waterline. He hears the echo of the sound refjdmpqci 8 dw/s)xjwrp*10sv. 7:,b/lwyn :iplected 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 vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atyxl0agh0 0 /mfm;6 vxsf e/:st 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 s7.gqikezg2;v4c )v tq;mogp- chool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.zvvgemg4i;k2t. qoc-7q) ;g p0 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 a cliff. The spj+r/ i1n6ypn9 u vv/eolash it makes when striking the water below is heard 3./u9p1n/ v neyjriov6+ 5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cv1nf27 sd mwiib13p 7tv/cf. foncrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the f1mbtn ii3wc fp/d1v.7 7vf2s impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent err8 /8 avn4czjrror made over one mile of distance by the “5-second rule” for estimating the distan8j a/rr8v4n czce 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 rvkt9w50s 4vfat 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 of a sound whose intensicyraa;:,a jw sxazg5n9yt((u: 7 ly)oty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously yyd39pht:.qo at a certain place, h yd :ypoq9.3twhat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fourr i36a0 et,y n/:-3dywj4i tco osy9ky equally noisy 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 eny9nei /o4rdo ycw 0:ytyj-ia3,t6sk3gine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for 5skg6-qo b )lar/w fn)jv75u ta CD player it is 95 dB. What is the ratio of inten)tavwj67oqls/kfr5n) 5-ub g sities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaq+o9h q6q/g nc5eot*q king in normal conversation. Use Table 12–2. Assume the sound spreads roughly uoq9t h no*5qq/ce+6 qgniformly 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 strikex)+0z36yet i)svi, ee xskxx /s an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest ampliqgft(zol2w r :m(69jyib*q: + v p.qmefier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point tq.ijew om:vf(q69+rz pgymq l2b( :* 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 placed 2.8 m in frontd+mo-gu91df). bdhqo of a .q9obmh- fgdd)u1+o dloudspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound levci3kr xzn+t 47el of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diff c+znr43ti7xk er by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound k0.x0ptdwa 24 mctld) 8 ;p atwfru;2bwave is tripled, (a) by what factor will the intensity increase?x)l r c.pdfaa4p tktm2; d028u; tw0bw Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal di2,sv2 hdivpb3splacement amplitudes, but one has twice the frequency of the othervsi 2p, 2bh3dv. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in/it; xutm *7ansim1r 6 air that corresponds to a displacement amplitude of vibrating airn6;mxu *t/a7smi 1rit molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have wqqdgt lu:uoh 7qk7+p9ug k: 3e)ea-f6hat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12qht lp3da 7q-u:6u+e9f kq ku7 ggeo):–6.)    dB

What are the lowest and highest frc .cfg-xuu0,oef(x. gequencies that an ear can detect when the sound level is 30 dB? gefx-.,uxccfgu(. 0o(See Fig. 12–6.)

  Your auditory system can acntrai 98n *bo.commodate a huge range of sound levels. What is the ratio of highest to lowebi8na 9 torn.*st 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. The le.c6 hg4ut lar jrgd898ngth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be g4dhc r ug 86r9ljt8.aplaced?    N

  An organ pipe is 112 cm long. What are the fundamental andr (wjus ,ua,f/: (luvx first three audible overtonesxla,:sujvu, wr (uf /( 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 frequencxr./b ef:wrq 0y would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you/ :x0brqr.ewf 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 pipes spanning the range of fh3)0 z2sm bcnhuman hearing (20 Hz to 20 kHz), what would bfbh)s z0n3c 2me the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmo,9nypv.uwq+0scu;t j nic. What will be its fundamental frequency if it is fingered at a ly +puv;,jtwc09q . nusength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned2 fdv gaa kd qdp-/8ev8:v:p ngj44an1 to play E above middle C qv 4 g:a vj18:naf/4kadpd ve2ng-8pd (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 an open organ pipe that emits middle C (262 Hz) uey*u2xhh-6s when the temperature -ehh2*uy us 6xis 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 20o:8st*r,kur ftu.y : q $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the vvc:pzyv83 x*hole be that mxvvy: z3* vp8cust 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 xiq 2od zdwsmi6/3e;/264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a i2ed6/so;iwzqxd3/m closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.)cgc,q 3ud6kv 80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is gq c,d3)u6cvk
(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 bss4u7 7ee2xbu nsx* +$^{\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 rangzw .tryzh 1 r1t7cfla6/yz:7 qe for a 2.14-m-long organ pipe a:6fy 7lw7/trzcz y.ath1q1zr t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lcii29q w s z6i2hf2cg*ong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationshfi i2 6qwcg2i*h csz29ip 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 toml*nfd97 c1bd adjust two strings, one of which is sounding 440 Hz. How far off in freq1*ld9nb7d cfm uency is the other string? ±    Hz

  What is the beat frequency if middle C (262 27jdo9wt *t9nh rcqk7 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 ap t567c4m/wyj3fax-i i+jlwct 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle ca5afyiw j+ 4/cjwtip-6xm c7l3n be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produc5 , 1avq 6new6sxkmk4xes 4 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 awe sv x6,5mn6k14qx kfrequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned ts23/b mb7),jgs :lvkkc5nmn ao the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What wilbs/skcm bnaj,:2l53m 7g knv)l be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical fljg/uvg7f1sq d. : igfeagv9 /;utes each try to play middle C (262 Hz), but on:/ffgu; 9s j/vqg7.eav gg1di e 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.au h72gp+ry0x :c*xi svpxave6 .on( 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 ov a*h70 .sx6+ r2ie.n vpaxoucypgx:(f 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.xwks iwu;c3js47 7 pth3t6 3hw A person stands 3.00 m from one speaker and 3.50 wjh6wh3kt sscipx7wtu;3473 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 am0f:8);txwf:gjqxktl oo : 5 be vibrating at 132 Hz, but a piano tuner hears three beats every ;8wtot kg5 fxx:f)0jl :oa: mq2.0 s 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 m in air. How many beais*af 0a6pk4 *an t)xsts per se0)*x6ka* na f4tsasipcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh,k1fzmc kh dd2* tv(6zen at rest. What frequetkf2v zh6md,1 (kzd*cncy 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 aw sfj..s co9k) fire engine whose siren emits at 1550 Hz moves at a speed of) .ssfwoj9kc. 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 c q:kb :nb.sj*you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same?*bs. :jkn: bcq 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 horn. When one o. c;qs8h)jgv 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 horns g.v;sq) jc oh8emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rethvz 3dbh27+saq e5yn5urz3 +2hnd bye75vsqah5ned 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 an ultf x2tmt)*ax-brasonic sound wave with frequency 30.0 x- mb*)ta f2xtkHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a gjo.ga/9f2ss 8- 3o(vlse0 wmnjc zv( tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwaya -vg zf 3/0 o o.(elv9s8js(nswjc2gm 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 speed8 i ,ft,fiis3ss. Suppose the device emits sound at 3.5 MHzi8 3si ,siff,t, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of vw c59p avi k/3jp t p;);zv1zmnnvow2:6vgk6frequency $2.25 \times10^{ 6}$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 570r2.7 lsr sjoip3ft )7d Hz. When the wind velocity is 12 m/s from the north, what frequency will obsdol27) 7f js.tpr3ris ervers 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 cl*; az9 ryp)sb*hxje 8g/l8fif its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound i k f01+lvhosay0no )f-s 310 m/s (a) What is the angle the shock wave makes w 0yloh+nv-k1 oaf)s0fith 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 j9ib3u5ax oyd 4p;8pbvp5 (eva planet where the speed of sound is vbp395eop id 54v;p yj(xabu8only about 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 850l9 . (dvq lk:8vgtjb6f0 m/s strikes the ocean. Determine the shock wave angle it prok(.bgvv t9lq f8 d6:jlduces
(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 / ukuzi,3hk/lh8/oj u fkvg:;$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andnq 2jhao76 hshyzdcb4fx8 ; 9- see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, j fd7cn h-axhys94ob h6 82zq;the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dom3pmt7 wj,f) ax b+;rownward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to3ofwmja+ ,xp mtb;7)r work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how ma756n3eb hvqu ony octaves 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 of manydfx23ld kpox4/- ,s;zs fo5up plastic pipes odp/xx f, f42 ld5s3o;opksu z-f various 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 tzy34j1o (vsd khe threshold of human hearing (0 dB). What will be the sound level of 1000 such mos3dso z14 (jykvquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dm0t t(3 -o9eqt.yr0zeln be8l8ee 3epB sound are heard se 03tet t.b o3 e(9e0elnpyr8-z8lme qimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 134j+tf k0ueqionz3f7twz * t 105 dB. What is the a4it303* kq ef+towf7tzjz1 nucoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W/cumn,18gtw xvug,g ebe)wfq 8-5 .o e output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 5o8.ufv,gg tqnbcew g,8/-1 u)ew xe mkHz?    dB

  Workers around jet aircraft typically wear protective ofq q;)o d0ny9devices 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 ofooyn)0q 9d; qf 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 systems, the wtk/z .c c2l:rgain, $\beta$ 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 8vnw 98g i7raoa 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 xaczu9z s r(q/trj b79,9s jp:gx4p i/long between fixed points with a fundamental frequency of 440 Hz and a mass per ungbsc9(ajtpqi :uz//xsr p9 9 z74rxj,it 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 intg lmjzcx3lt 8oa.0z6rekk410o vibration above a vertical open tube filled with water (Fig.4jt1eac3 g8lr 06.lkkomxz0z 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. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tffkt+mn*ul:/y c8 pg3ube 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 mcgu8lk* 3y/p+:fnmtfode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one a.3 9fpmi421evch)wqre( m/hsg kb h7full 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 comi myciws)mc lcc760:+mng from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and flc0+c)6i ycmmms7 c w:inds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor ons- p(uml.tg -b the stationary train hears a 3.0-Hz beat frequency when the othergl-b (sut. pm- train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Auxnn m d-7j;0:miqkk fui9,n-g k1c)nfter it passes you, its frequency is measurem n)jn-u: n7mc;ug0 -9fd i1q,ikknxk d as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spee j+,ey :ip sromh87mx:d of cars just by listening to the difference mo8x m heys7 ,:irpj:+in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz.v(2ja )6kqk fu The shorter one is 2.40 m long. How lo(j6f)aqu kvk2 ng is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movestts +q7tli +frg*usx62pp y40 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) h str 2 lxgtpp7it6+*yqsu0+ f4e 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 aortqk79ljn; o)q ya is normally about 0.32 m/s what beat frequency woq7;y) jqk o9lnuld you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whil; rz mtt3z2 uz cf+xi(*y4,dote the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wavzc tudf ot+(z 2tx*;i,mz3y4 re reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses 3gj+vz, zce2k as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp r,gzv +cjke23 zeturns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from onx i khwywkj+ai27x7 o7*hd.0 oe 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 m.ax+ 2i7d xioh y ko*0w7whjk7usical 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 sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presstqm p/6bftrxqe;g z.n:j(in d1 q0) -ence 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. Calculate thedepgq b-(.mr/ 6sf1z0t nqjtq:); n xi fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrah .ya.7u+ kfwjtion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, th fya+wuj.. kh7e 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 :lur:jl2 /;/geppet s threshold of hearing for the human ear at a frequency of abourgl us/ptpe;2:e / :jlt 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 ground hears the sonic b 9(n:rcepv 0wfoom 1.5 min after the plane passes directly overhead. What is the plane’s ap(nv9r0e: fw cltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 18npc.sx8kp 5co / a3fv5 $^{\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