What is the evidence that sound travels as a w:6falz- uoie cdwovb4.b- 74oave?

What is the evidence thep8zz wtkbi57es5q 0x y3;b z *rej10vat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to9rf /osy.n3vv9x4x0fcqm /8h 1juub m the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, fb 0.1u/93v4sy r fq89nj m/xcxmuvohthe 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 expec6m ifm 0r pj+q*bu,aqg9,a4gh t the frequency or wavelength to cp0mj,4uq b+, *i 6ghaq rm9afghange?

What evidence can you give thae j7s0ehzs/*x t the speed of sound in air does not depend significantly on frequency h*s/0ee x7szj?

The voice of a person who has inhaled helium sounds very high-pitcheda,h) 9 cb7sjtbx,bc,yjs d7v /. Why?

How will the air temperature in a room affect the pitch of organ pi*yp/c(jzo 14l, 8b kxw/dguvppes?

Explain how a tube might be used as a filter to reduce the amplitude of s ds:je a/rsqn*pe(,3 rk*u-ru, zyc/ zounds in various frequency ranges. (An enjsz, u-k rzeqs(c, r*ep/ayu3dr/:*xample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together asljrx920yzw3g9j8a0 nh5yjujis f13 g you move up the fingerboard towa9z0 gljy3r1x aj gjs5wu320hny8j 9 ifrd the bridge?

A noisy truck approaches you from behinavzv1. nhiis(r sq0/3 d a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on si q0nrzv1/(av 3hi. sdiffraction.]

Standing waves can be cbcf+9ks2x bz3yozx m.c 5; 0csaid to be due to “interference in space,” whereas beats can be said to be due to “ixmocx .b0;3kzy5c 9b z +ccfs2nterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerxqn1 rc;g.4n3+3 (,l pi2oyftci d klnleb39t ed, would the points D and C (where destructly2( qnd,l49c+3pgb ; e xoni3t3nkfilc1.rtive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hea uyl)+ ic f uv9,rk ffcd:6qep06aa5)uv65xolring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not bldoraffve6 y)6l q, pc0la6 kuu+:i x c95)5fvuock 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 show h86 z:rnab6ctn in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig.rc6 : 6ab8htzn 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 shift if s6to/ d7;qfjpthe source and observer move in the same direction, with the same vel/s6j ;pt7 foqdocity? Explain.

If a wind is blowing, will this alter the frequency of * joq0m*na;r48dct5h vc;onc the sound heard by a person at hmdn0;8 5antc4* vc;or *c qojrest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in moth)9(/ijyhxc m ion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A throu(mh yxic/9 h)jgh E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length ,vy )qdmjdxu5 hc9,y5vz*k+iof a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears thc 5)k5,,dj9h vyix dymuvz *+qe echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be0 uyc:q xo)*tb/fzq dityn (6,low the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1)6:) *cbtqyud fnz(tx ,io/ q0y and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atj-dm59i8 yjeqc7a x;y 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:m4 io/60d;iiwh qgu q of tuna on a foggy day. Without warning, an engine backfire occurs on an0q ihm6/4o:;igd qwi uother boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whu3/i f+mos 0scchr 1p)en striking the water below is heard 3.5 s later. How3 uc)1/+opsirs fhcm0 high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the ( k gppb*d7p.aconcrete pavement. A moment later two sounds are heard from the impact: .b gp pad(p7*kone travels 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 distance by the lj9*))n s wtr+m(q 1,wlzfnwl “5-second rule” for estimating the distance from a lightning strsww(9m )t w +rlf,)jlnq1 zln*ike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitaq5l6q:2l: nmnpr)k xy of a 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 of a sound whose intensizv (atq36j- ylxg ix:+ty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of /tx*nm ,fjj/4 pd+eg n95 dB when fired simultaneously at a certain place, what will be the sound leve+djpm* n/g,4 /exj nftl if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancqi(fmn qmc,f; bo0a 2:e from an airplane with four equally noisy jet engines is experiencing a sound lqf0c mf 2q(n,ibma; o:evel 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-nof pt9,fhl+ v ,:8wvr81ypblwzise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of w yf t vrl, 1,w9ppzfl:+8hv8bintensities 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 speaking in no9-b8*-lvctfapgc:rp o /ukv04mmzq 4 rmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cep - 4t a0qcrg-vofbl9:p8m*vmzuk4 c /ntered 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 strikesom)e1a- 0(gyb qml) io 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 ampzsagan8 yb ;9*cxks 44lifier 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 turn8yc9*b 4za ;gxska4 ns 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 plu fn3,7h jtzw(aced 2.8 m in front of a loudspeaker on tj,nu z7 w3fth(he 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 level o2) q2uhhwtv0an/jccs - n0zc3f 2.0 dB. What is the ratio o)/av -tnucnj0ch0zcs2q2h3w f the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi5 ;+, ab1mmde 0wlitrefm1 i+lty incfa +ti;be rl ,+ demm5l1mw10irease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa rw: faotkju *ho,mhk9+h9/4ge:a7 xb cement amplitudes, but one has twice the frequency of the other. What is the rat*u jox:ah,fhb+49:9 o kmth/ekg wa7rio of their intensities?   

  What would be the sound level (in dB) of a sound wave in 2axvbtup( nz e11j dt jna+bxc97+t6,air that corresponds to a displacement amplitude of jvtu n j(+2ztn t a6d+9b xxp1e71c,abvibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leiu8/g:ys/ qnn mzigrx ( +ux11vel to seem as loud as a 100-Hz tone that has a 50-dB sound leve1:+ 8 u/mqugi nrxiz1syn(/gx l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies uen2at/ bya kgw*s4 --that an ear can detect when the sound level 2-gaeuyw/-as4b *t n kis 30 dB? (See Fig. 12–6.)

  Your auditory system cae6ahh-b wl )zyft)9z6n accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity fbazl hty))6 9ehw6z-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 fre;5ve6zn d 4j6c-rhzgnquency of 440 Hz. The length of the vibrating portion is 32 cm, and it5z6g- z dnr;4vecj6hn has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and f2 m:uo5ni y4lc cqd9h*irst three audible overtones if thec9u*clqio 4ny5h m:d2 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 freque l1s1b,h. hmvancy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if ys1 m,ah v.hbl1ou 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 with8zxhgiqtb nc7:* x7y1 open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ 7hi*ng8bq tzxy 71x:cired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thxvw/q,7kfjca 3w dur3e6f8 u/ird harmonic. What will be its fundamental frequency if it is fingered au 3xu//ed7f wkcf 63r,qvwja8t a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73lnzc y)h0ss-sd8no4 )-l ;klk m long and is tuned to play E above middle C (330 Hz). )04okn snzyc dkllshs)8l-; -
(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 pi c8(1mx5tad;fq nzp5w pe that emits middle C (262 Hz) when the temperacqdw 15xa pt;zm(nf58ture 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 at 20v l8t)6e7k:) 1lbzf4mnrhmjw7 m 9 nol $^{\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–ek sb-3 k2ely0zxyk/)m9 jj.p10 should the hole be that lj.z2x kke-ypky sb/0e)3 m9jmust 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 7p3bql cdvd*6resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a)qpb d7dc3*l 6v 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 op,fe:mlwy00i- z t0ugmen at both ends. It resonates at two successive harmonics of frequencies m0,my ig: 0fzwlu0 te-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 r mb)c jq),mz 4)v7)gjjy z1sx$^{\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 rmmn t6t2bv .;jange for a 2.14-m-long organ pipe at 20 ;j mvmt6.tnb 2$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is o y .i+-wildwvpue; 6)gpen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship ofdi6 w ei-l up)v;.y+wg 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 b-:+-ftuk o hqs when trying to adjust two strings, one of which is sounding 440 Huo f-bhq-tk:+ z. How far off in frequency is the other string? ±    Hz

  What is the beat frequency j(, 7nzynfo(atp1jn m*h5;r.+s btg x if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whim y+jue40vct)5j; c1kkdkp d0le another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrik jjcv+k)e0cy dm5 k t041pu;dll whine of frequency 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 with55msdi,6y slo a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the il,6 sm dys5o5vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensj1f1b bs;xthd)iu t uw q.614mion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are platb14f)t .smbx j1iuq1dh ;u6w yed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to1 d+uns0dzg(u play middle C (262 Hz), but one is at 5.0°C an1(+0u nudz gsdd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; dw*am.pf :1jza6w 3vz when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded 3aw*zdzwv6j1: .mafptogether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m cwwnrytr :ap,abr vt 61)+q: sc6+pb+apart. A person stands 3.00 m from one speaker and 3.50 m from 16t: ,)pnpv rwt6+ q+b:bwaya rr+sccthe 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 bl xrwjv3mb- 5m1 y w63s,pnsy*e vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one iw v 6*3sjy,xm-3bnrs1m5wly ps 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 wavelengthszclsc v clej8h/e3kis aa9: .dl9)*v6 2.64 m and 2.76 m in air. How many beats per second will be heard? (Ac:ai ve a6.cc d 9l9 ess8vjl/3*zhlk)ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at 2xaq:z 3z*cq6r 1s cwureqx:zz1crq sw6c2 au* 3st. What frequency 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 duz ( pz(sn*2(l 5mnxcbo you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s (s ncu2*5zl( (nmzxbp
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yoxm73irory: q4u at 15 3qm ix47r y:rom/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with tlbhndf ig n (/nwyja-c7:7c9,he same single frequency horn. When one is at rest and the other is mo7i chnnjlfb dc/ a7 g-:,(wn9yving 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 emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz an4s,bgfv) rw n*xc7ec/d receives them returned from an object moving directly away from it at 25 m/s What is the receivedn,erb)/4fswc gv*cx 7 sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a b zw5zz wha h 9.4-ecn;xlsa;(wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thlzshh-;ae;9 nc 4w.z(x 5b awze bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played 24(r rxrkv gh56 gk9kx/vb 46jo2*vqooy/pwkon a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s*krpvbgow/ kq2o 26 4 jghx5/xkyrv4k(9vro 6 ?   Hz

  A Doppler flow meter uses ultrasound waves t+x )n4lc bo53cog/ubqo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed gc+bl3q 4nb x)5ocuo/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 ul-d7(9*uq mp7svgtwmn 3;qw )qyxqdg5 s95mubtrasonic 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 frequency 570 Hz. When the wind velocity is 12 si87zxcwo* iie :q1 36,xivnfm/s from the north, what frequency will observers hear who are locai317c: zins8q*vfoiw,xex6i ted, 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 s x-ew e l2, x8wsk4i1s3lyc3ykpeed 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 Mabz shwh en - 8pn8o0t8aka:56fksx;6rch 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makesb8tnh8; 6paa sozk8 - 06wsf:kehx 5rn with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of sounea q0f1)xme)fl km o53d is only about )emlafk35q)f 1exm0 o35 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 850gj g+b;q r7vb0 5sv+hk0 m/s strikes the ocean. Determine the shock wave angle i qbkr0s;+v gh7bvjg +5t 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 0km jmy22h c9z$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sm7,ekmy4cycd r6d,gm,)/3 fq +okifsee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveledcyf rsk)q+ke ,mym,d ,/67iogcf34md 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 s 7daq7 v0) g5zsw6mptzound pulses downward from the bovg z7qaz5 d)tw smp067ttom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in :u/1n s(hchvz the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy ei4,t-esn n;ecmht i5)06+hqcnd xy9mphony. It consists of manyh9n,mdqs-x 5c+tiny;e4 n hi t6ce)e0 plastic pipes of 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 z,b1w:qtfw, ethe threshold of human hearing (0 dB). What will be the sound level of 1000 sbw1 q,ztwf,:euch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound areu (ooalw*6yt8 heard8l (ywauot*6 o simultaneously?    dB

  The sound level 12.0 m from a loudspeaker,i x1rqtrpfcr;;-o2wb r,21ws-uuxy8 qi;c+ q placed in the open, is 105 dB. What is the acoustic x-,qifqy1r+;q2rr -1ptcub 2;s xurwo8c w ;i power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 y6gqbfu.j)ms15) dtn Hz. The power output drops by 10 dB at 15 mb).6t1yjf us5 qngd) kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears +ariak*+j)mm . 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 airpl)jm+ma +* irkaane engine?    W

  In audio and communicatioewf6 tv /;w:bqns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tu/jlu53yv1v4de mn a-f ned 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 viovg+avf:+-30+jts8gi pu m jo glin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and ai- mgjg ags +3+v 0t8op:uvj+f 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 verticaj1v7qgtlk : (dl 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 g (l :1tdqvkj7water 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 aj1nxz x l;qw0m2 g bln(2(qum1 tube that is open at one end and also n1 (g;1q0j2bn(z x2llx ummwq75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful5dyb z8wg4( b+nkvr /al 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 pur9oy.o lv+ d4ufd *y3mxe tone in the 500–1000-Hz range coming from two sources. The sound m vy4ox9.d*3yufl+od 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,ww 5oq:4pppw is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approacw ,:qpwp o5pw4hes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it a1yrgc: x 2dj oyjol5 c dlmt-wm;e352;pproaches you is 538 Hz. After it passes you, its frequency is measc5:crlj1me-2gy dm ljwd y2 x;o;t35oured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spee ahh63ocv57ex s(,,epb*fibvd 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 bc63( foh eevxh,as 7 5ib*vp,halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soun lj+i b1j.d34itv5d*n(jz x.;dcosnwh qjy 78ding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is tzdiij+j7 1 dnj(tlxo. ybn5 ; .cv*qj shdw843he other?    m

Two loudspeakers are at opposite ends of a railroad car as it 8f ii7umezv89lp61 enoma/.xmoves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the po8xa/ipenul1 v 78o i9 mf6.zmesition 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 fy0: rrekie7vl d12es4 low in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a se17lre2di0ke r:vs 4 ypeed 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 tohqtc*-da sy.lh1w yv)l.v 69wward the bat at speed 5y vl)qdy as lh.h* c91v-6tw.w m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as ikgen.ukq bh g xz3h3)uk 1,c60t approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the mkzeu3 ku6ghq1cn b.kx3g0),hoth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onci2fwhp3 dr7x0z *+ ya2ylte:oe 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 ofxf +p r2ylwe73ia02dyz to :h* 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 thenu/q(4 nu 6dkg presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a livingknq4g (u/d6u n room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”2 cv2xfazz .y ;7ku 3bgufdbo8hh) s.8 involves a long, slender aluminum rod hel;fa2b s.c2)bu3 f gz8yok78u .dxvh zhd in the hand near the rod’s midpoint. The 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 n*ut) rs1v qz7lv-d(eat a frequency of about 1000 Hz is unl z(dvvste7 - )*qr1$I_0$ = $1 \times10^{12 } W / m^2$ 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 Macz6x32yoc1 ayqwm9cv9h 2.0. An observer on the ground hears the sonic boom 1.5 min after th2y 6yc3ax 1o9mq w9zvce plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbozz29 8jpz z;w2nix0l2t;a fftat 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