What is the evidence that sound trav4 jfi30 gom)n56a cfucels as a wave?

What is the evidence that sound is a b5e/z qpak (5cy3,on0its8 /varz-wd form of energy?

Children sometimes play with a homemade “telephone” by attaching a strin htw 2*t6w)ocg3ztez ; 2hayysb( 3og-g to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cue( t26-2 two z;bhhyzggoy* wacts3)3p to the other.

When a sound wave passes from air inb 3i3wz.hue 3e5u eoljz5c2y: to water, do you expect the frequency or wavelength to chanzhe .iocjbu 52y:e3w3lu z3e5ge?

What evidence can you give that the speed of sound in air does not depend)-noc 6ao0 tfqvy ) 79ep3ntul significantly on frq 0cn3 -t6aovpfo)el n97y) tuequency?

The voice of a person who has inhaled helium sounds s ,5w ose33 h7glb g+c-1xjbrzvery high-pitched. Why?

How will the air temperkw1hys u 1vft858 hkz4ature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds iwfyc8,9 u z- d5k7maibgc2rh)n various frequency ranges. (An examp )r9k mgb7hfaz-5 ui8,2w yccdle is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togr b80wmq b16klgug5eo ,.cio+ether as you move up the fingerboard towa5l muw0rob+b.,6i18oe k gqc grd the bridge?

A noisy truck approaches you from 5)l+,qhszw4 a, jsd fbbehind a building. Initially you hear it but cannot see it. When it emelsa,q4jz+ ,sfh )5bdwrges 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 diffraction.]

Standing waves can be said to be due to “interference in space,” wherehmcexjp6a 28y7j;7h tas beats can be said to be due to “interferencmy6te8ph hj2j;x a77 ce in time.” Explain.

In Fig. 12–16, if the frequexm(ug)6wq nfag5)8hv qu4 wck2 dn;f+ncy of the speakers were lowered, would the points D and C (where destructive4kf dhgq;2)mwx u(g8 f 5+cwv)un6n qa and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wfurj5 ww it-t1zoq ;mp 5z1+uq ,hj9,tith 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 detects the noise, inverts it electronically, then feeds it to ttw+u91ji -rtf uhw,,z ojt;zm1 qq55phe 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. 12 095 k,fwau 5yxqsqygov: vthth *927s–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 fra*0hq5 t ysx 2vug9,yoq75fhkvwt9:sequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thedqipbpld s31ef8)m- 9+ve h.gc-q(h u same direction, with the same vcdsv g91(pqepq.i- e +-blh)3 u 8hfmdelocity? Explain.

If a wind is blowing, will this alter the fhv0el 4hj,dk.6m z,bzrequency of the sound heard by a person at rest with respect to the source? Is the wavelength orhz06z e,,vlh.m k4bd j velocity changed?

Figure 12–32 shows various positions oarr om+py 4z:g7,f s7jf a child in motion on a swing. A monitor is blowing a whistle in front of th7j7+mf goa4y s,r:zpre 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 the length of a lake by listeu5yh 4p;72fr9 6qfl*tnhl 6 jidpayd.ning 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. Estimate the length of the lake.;fjtau 45*l 2fny7p .phy66l qdhir d9 $\approx$    $ \times10^{ 2}$m

  A sailor strikes the si u(x2a nqc1/qode of his ship 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? Assume2n(uqc o/a q1x 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 at 20fwin15f 7 ./usa:hq c5nu 5sute+7ssu $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of ( u2yb8e goqhq3v:9kwtuna on a foggy day. Without warning, an engine backfire og 8kbqu3(qh 2:evw9o yccurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splastf4l,uk nws 5od:b; :lh it makes when striking the water below is hea:5l4wf;s nbtuk,o ld: rd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees2l bnxku;1op1tcl2- y a huge stone 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 tp l; o x2l2nky1c-1bu1.1 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 “5-se psme:bt 9e9oiow,inrww 99d7c c17;dcond rule ;brct ndo,91d i ewowm9c:797psw ie9” for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain leveq , pv 9,jecg6*+wdjkyl 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 intensity is ql* ztf2ps+l omy:+v5$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousqn j90* dk7sruly at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.] 0urn *9qkj7sd   dB

  A person standing a certain diycpe b0+ v,l9(agll ,mstance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person mlc,b 9laelv(p,+g 0 yexperience 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-nodo7iq ne36i zr/y :i7mise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sy 77i6zi n ieo3/dm:rqignal 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 igncgw)(/ r iyw x/c00sn normal conversatioy()i/0sc0gr g w/wcxn n. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose a0s v/1 ),1:fjenakmwg( ozryph+mxc q+;sxn/ rea 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 modr3h1g7-wto8 w 1 nkvtzest amplifier B is rated at 40 W. (a) Estimate the sound lev vhg17tn wzwo18t3k -rel in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m+34t0xfjvgv9mf k8 mr)ur m u )e;nrl1 in front of a loudspeaker ur+ j)g)vfre8 mlrmt0u4fnm19xv3k; 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 le6hxqer +epp6 d6g*r6ondf1/ -x f tj3svel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sepq16s hr e+f/ pxefd-r6gj 63tdx* on6ction 11–9.]$\approx$   

  If the amplitude of a sound wave 7ihff.2k y jav3v0mvm*7h *wkis tripled, (a) by what factor will the intensity increase? Increase f2i7j*hkh0 w3mvfva*mkv7y .by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes 9ey7lzz:.svfr ,cs,g, but one has twice the frequency of the other. What is the rzf7g,ly .s,z9rs:ecv atio of their intensities?   

  What would be the sound level (in dB) of a sound wave in ai1yw,+ dfpu01(c utuv.1 t q w2hgmxs.zr that corresponds to +mwqc1xp 0f yvzuh1s td w.1(uu2g., ta displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sj xms, kc e., i8ysqvaqx;-/v+ound level to seem as loud as a 100-Hz tone that has ,sjxk8vs q;,.x +/-meyvicqa a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and h7:d7 jo u4khsqighest frequencies that an ear can detect when the sound 7ohqsj:udk 74level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hug x,z4nqokxr2)7i cbu kxp(g*- e range of sound levels. What is the ratio of hixg, o7n2brx)kkp zc- *4xui( qghest 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 frequencue;4i2kb:9lnbx s v2kc9s o0py of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string v k2:sx2 kolbnpci0 bus; e499be placed?    N

  An organ pipe is 112 cm long. Wg*t ytum ()ag*mzh3+b / l6kgsma3)avhat are the fundamental and first three audible overtone 3mt))* a6bakhug mg(3*/ gsy tvlz+mas if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency woulnos4x4x ck,:hd you expect from blowing across the top of an empty sokhn:4 os4cxx,da bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range 8s3lp6t3j rn: 9qezv 3aguo k:a.4kphof human hearing (20 Hz tovp::grls9 6kzkhpj34 eqt.3onaau3 8 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What will4a aw+ jiuxk1qes4(05br p6na be its fundamental frequency if it is fingered at a length of only 60% of its orig(a i4w6 0kna+uqjx4p ras e15binal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mz1+uetx fq ob 3 i, 25vdi+s,yfc0bj,diddle C (330 Hz). b5,3q2bfc0 ,od sii+ , jdtey1uzfvx+
(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 ope m8*kdxu bzc+lsvzu, za w u1.+j/)4ran organ pipe that emits middle C (262 Hz) when the temperature is swvjk./ u auuzdbx cz,+4l)+z 8amr1*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 2wumb / bx4/ o:cs9p,gq0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moutyob*y 7b6 vc4:ej7 (c0vchhr kv3psy*hpiece of the flute in Example 12–10 should the hole be that must be uncovered tov3hrck7 cp:v4 s*jveh6c(y7 yb ybo0* 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 reb1sh;bd2pnxeom,c1 v/x +er 6sonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show w/ +nc12p ;ed b6sbv,eox1xhmrhy 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 resona4z/ b k( h jk/7uke(cr:aofx9otes at two successive harmonicf:xro e7/o4bja kh z(9ckk/(us 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 j,ahplmh/4 *ywo8 3ue $^{\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 2.1o wwvbk/j pv52ar3:k .4-m-long organ pipe at 20 /aw p v k.bw5k3:ovrj2$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It kw) ,sysjf+8 --j1) p fpmadhzis 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 relationship of your answer to the information in the graph of Fig.p))yw smz-+dsja pf8hf1j ,-k 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to mdi-mr/ksa,tkr -- z3 adjust two strings, one of which is sounding 440 Hz. How far off in -mamt- k-3d,r/kzsr i frequency is the other string? ±    Hz

  What is the beat frequency if middlenm xzhi *vx)70l;:ewcxl gx3. C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates a/zuh,*5a bw: ulgz8j. ic enbiy 2e3y+t an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played siy*e8.n3zzjuicb,/+y52 l: giuwe b ha multaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a kx-n/e zx;ga9uc 23q+3 aub:dd r3lzrnd 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain y u+lakru32a ndb ;cxz -xe:q3d/g r39zour reasoning.    Hz

  Two violin strings arwr7 f/wya zi5vc*+ 2zne tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%v z + z2/7fri*wcnw5ay. What will 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 flutes*kjdguzlx0f zzb: 6x4skpt:; jn:5-k each try to play middle C (26xt -j :kj4 ;kndzszx*fg5pu0l:k:bz6 2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has /sws 1d w hfeh/vxjh7bxs:4.jf(zyy5at - f 2+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 fw/jz4t517 :+yw bed(v- s fxj /hhfsf2ahyxs.requency 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 from one spqs0 zo,yrrod -w2k1 c -j8(fsleaker and 3.50 m from r,slowj0- drq1 c fz2ok-s(y8the 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 vibrating at 132 Hz, but a piano tuner hew-dvzo(- ue 84jdo; lwars three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency-8-uw ved(;do4o zwl j 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)( ty ukx5t6 wqk5ei6n m and 2.76 m in air. How many beats per second will be heard? (Assumenk65q(te tyi5xuk w)6 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 atco6h+b;q)isnlg jw8 93 k gdc/ rest. What frequency do you detect if you move with a speed of 30 jcc 8dgwbs ;ig 9l)o/nhk6q+3m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng39y b6 lg3 g:f)ty4cd2wu)qb wge,jwjine whose siren emits at 1550 Hz move)jjed)w:3c 3gbqt ,wub fyw2yg 4lg 69s at a speed 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 toidcj8hq :oa4-.)s7z rcnt7 bf ward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? A4c tro8b a n s-hz.df)qji7c7:re 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 i,g-d 70 ,jzztx7pm cqjs at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5t7z,cj-,mp0g7z jdq x.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 2zllatx 3og5/kHz and receives them returned from an object moving directly away from it at 25 m/s What is the rece2o5x/gz3ll atived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flie,0vov6hlqko6q 4jzgh - w ni*)s, the bat emits an ultrasonic sound wave with frequency 30.0j gn*l 6voiw )z ,ho-k04hvq6q kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experi8ic - gn/-(ga8rq sz9s mil58;byxb pkments, a 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 railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s (98nqs ci mx gkpb8lzbai r 5-y;-s/8g?   Hz

  A Doppler flow meter uses ultrasound waves to measur8el5 b yygiw1*e blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries gy1we *y8l5biat 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves oft wz;,ypgpm pw),sn5; 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 emi9pihhm1g9hh 0uz n13vts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will zh0nh 1vmpuih 1g99h 3observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if itb9.fpu4-nacss 1 ruc40 bbmr2s 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 (x;, ; i;2gxek vl ,au,txihjpwhere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpl ,xpe,xlhg; ;uii,v(; k2xaj tane’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 ar 61gy,bp 2uxk7rzlr ri4*a:im.w:ea planet where the speed of sound is only aum:,xpewgr: rzral7i61 by*2i4.ra k bout 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the j nfy tq8.1md+f 4,eofb i5cf/shock wave angle it pro.f/c j mtiq d fnby5f8e41+f,oduces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 50dbmsxvv-mv j 4i6ijaj , 8m)$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exach ayrss 9h ppb)7/6n-ntly 1.5 km above the ground flying faster tha7hps/6yn9- n)a rpsh bn the speed of sound. By the time you hear 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 that sends 20,000-Hz sound pulses doweat cm+;()xa :tuqt k:nward 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 fresh water)?e+ k: m ;q:u)ctxt(ata    s

  Approximately how many octaves are ther+ ynnbw wf+- tn2,:ldze in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe o; 1cgqvwu6(g symphony. It consists of many plastic pipes of various lengths, which are open on both endo (ggvu; 16cwqs.
(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 persoyw0s bk7 m+n:qt4k9rrn makes a sound close to the threshold of human hearing (0 dB). What will be thkrb:r4m97k st qnwy0+ e sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8la31y; eiv)g1 e.8ff nqyy oc.2-dB sound and an 87-dB sound are hear)3.1vl. 1ig;qeaf8f eyoyn cy d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105t3 i0qc 3gxmefry,z:fb1: o ,c dB. What is the acoustic power output (W) of the speaker, assuming it radiates equaffo yi:0czr tb,q, 3:x3m1ceglly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power oi u fdl71 057k:upzobeutput drops by 10 dB at 15 kHz. What is the power output in watts at 15 75d07 1u :lp foukbeizkHz?    dB

  Workers around jet aircraft typically wear whqtpg5b9 eq-ryv:84protective devices over their ears. Assume that the w: -bq8vp4hyq5rt9g e 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 engine?    W

  In audio and communi;)sfn gj q j/:6o4jxxx)*oehecations 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 violinrtvm i8j;0.(roth 5 gj4pps: z is tuned 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 with a fundamentalbms g7s0,ysr :hp ua.4 fre4uygs.h,r7sm pa0:bsquency 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 filledu)4ui/ub r7dixu i )h1 with water (Fig.xu4u7 i)u rh/1 ibu)di 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 neeeycl12osbv:vewi.e;5oh, t ul4tnu+ - j. x+ar a tube that is open at one end and also 75 cm long. How much eeyhlc+;eo-:52.b .1 wusit uevoj4t+v xn,l 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 obserq *z;btwabxvk99 )ve(ved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in th; pn.tmpux/) +oh3kqzz(i8oj e 500–1000-Hz range coming 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 finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frh;p3q8 . unzozk(xpj +mi/t)oequency of the sound?   Hz

  Two trains emit 424-Hz whistles. 6:jalp 7iq. kzOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving traipk qj .i:az6l7n?   m/s

  The frequency of a steam train a3 spu(4i nu f+bzsn7(whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz.(7uz pinu3 (sa+4s fbn How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate tb.yl kbr sv88* z u1skbi:d06bhe speed of cars just by listening to the difference in pitch of the engine noise between approaching and recb*u v.slby18rskzb k0i8: b6d eding 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 gl0 hb o j2dr)pul(:2y gkj:f,Hz. The shorte lb(lro j2d,j:0)p2 y: kuggfhr one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite yprq+;g14t+r; +mrgor ) akziends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37.ga yk)rop+;gmrit4rz; 1 +qr + If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beyn x m8elh, m0n3fm:gm ch:98pedc q7(at frequency would you expect im8h93pmy(8 ld7n0xc,em ecmg::n qh ff 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 while the moth is flying toward9fozv9b2v9w p the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequen 9fo2wbv9vp z9cy 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 /1s/dw9g1l+b uq yxyc acntu-uj:8c 0 it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far aw 8ubylx+c 9u1 /sj:/cna 0cuwytq- dg1ay 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. 12–38) was once used to send signals from one Alpine vi,95cphgll*f rllage 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*p5c9hgl, flr , 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 tho :cxqt 8l:;o88hit,yqjz0d oe 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 wzj xto ,;08 qci:dqo:hylo88t ide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender3 ak4uwy c6p qj)0aj)u 8jxmp2 aluminum rod held 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 jpup3c2m) j0ua ywk)j x8aq64. 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 t k53 lgv mh6hb4a+(ixshreshold of hearing for the human ear at a frequency of about 100a x+5lk6b(3im hg hvs40 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 hodd/k8f-ro c 9ears the sonic boom 1.5 min after the plane passes directly overhead. What is theo -fd8 oc/9kdr plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo40+c wg5y9,ug u lrtenat 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