What is the evidence that sound travels as a wave?sgl9 lr o;3im8

What is the evidence that sound is a form of.g *3l gmtvbt8 energy?

Children sometimes play with a homemade “telephone” by attaching a string to bbaev*-.ctp 6-xa h3 t0 +fp:3apwgbq5q6g ekthe 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 cup pax* pb g .:-ab3f03teqca v-t gwehp k56b6q+to the other.

When a sound wave passes from air into water, do you expect the frequency pd(3(fhu3gl.vuz /wqb f af-5or wavelength ./ h35fqluz3f(wvbfap (u -d gto change?

What evidence can you give that the speed of sound in air dp fyb2o j *4pgz)vc4d*0nym/ voes not depend significantly on frequencyv2p y4zjfbdy/ 4gp0*n)mc v*o?

The voice of a person who has inhaled helium r8nguvv14ids+8 ii,j0 aud, +imp1l xsounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of org)t+ mzjhsr6m/an pipes?

Explain how a tube might be used a2 u d9z5/3orr-a8fn7h ccb)erq dm:iss a filter to reduce the amplitude of sounds in varia-hdrfm)ce/8q2dui :7 5z r b93 crsonous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30 ,quradlhq+ -7) spaced closer together as you move up the f+h a duq7,l-qringerboard toward the bridge?

A noisy truck approaches you from behfe6db ci/n+v9 ind 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 diffraction. 6eb/nc9+ dfiv]

Standing waves can be said to be due to “interference in space,” whereas (xg(g ci mi35lz l4(*; ytb1am 2bolwjbeats can be saidig;3tlob y5 z2cimlj 1 (b4m(w(l*a xg to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spe4wb6f-z ib(uv r* gbavr c.,b*8u6bwmakers were lowered, would the points D and C (where destru-v6(.ubgmwu8wbb*c4r 6 *bzi ,fvbar ctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ar:.no5 u:dsy vveas 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 deo::uvdv5y . nsvice is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can beq;+kpok(w6co8linhtz) q-q , 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 apart? qtlhiw qk86p;(q, z ck n+oo)-Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directiosdzpn 3di*d -x, (g fn: fctznv2t4pq*,, vui3n, with the same velocitic,xsfn(p pzd d :-n,vv *qzn u,i43d*t3gft2 y? Explain.

If a wind is blowing, will this alter the frequency oft kr9zo0x/0iq the sound heard by a person at rest with respect to the source? Is the wavelength or vel90 z i/toxqrk0ocity changed?

Figure 12–32 shows various positions of a e 4zi vsx*aq 0c-r08eqchild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will thv *4 ee-0qra8 qcszi0xe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the e v oz:4pjzf9ie.3 w3buc.grz3cho of her shout r 3u:zw bj.ez cvg4f or93i3p.zeflected 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 hj5 9zdskf :e yjy3- y7i+6hfwxis 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? Assumejkysx6ffy37iw y9+5- jz:dh e 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 am 3:b4t7dcsl w7hf,oft1l4w)t w.psmir at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school o0z 7u)m)q8 dre3tegmxgf0lz 0f tuna on a foggy day. Without warning, an engine backfire occurs ond etu)le0x7 0zrz m)30gqg 8mf 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 splash itl71q o y:svg2f makes when striking the water below is heard 3.5 s later. How high is the cliff?7:of2q vgly 1s    m

  A person, with his ear to the ground, sees a huge stonb f0jjl3-*bt9,nwr d* ad+jsce strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12*w rd-,db0 9jsban +cl3tj*fj–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distake8rw-v6r,g k nce by the “5-second rule” for estimating the distance from a lightning strike 8g6k- revkw,r if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of l +i)*zcyuuv* 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 sea6knumi uu4 c6tq4 *h(ei*w cq5 f44gound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers producufme-ghz qr.ndl8jno :3o3 8+e a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is ed noun hgl 38zf3m e8q.r+-jo:xploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distancdrzp*:diq* uoh* ne 81e from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would1he iuddp r*nq:8o**z 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 signalq) xh)6gu:4(pdu xf epy,i+dv-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background ,pxg+dhuu) xf( y:ipv4eq 6 d)noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounecosf+di52e )0sysbf8nm1 /t d from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over 8yse)t/1f+s dcbe oin0m2f s5a 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 whosh/7z9mptpy8d)y86x l dxv4 gx ram::qe 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 rate6h zlnbb6a -u*5*c afwd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wou z6*an5*uablh-w b6f cld 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 in front g6z+vsaq 6bgp9qen ;a/w)m d1of a loudspeaker on the stas+qw6a/9z ;mnep)v d g16g qbage.
(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 s pwl (qwh3w.o/ound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: .wow l/wqhp3(See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled .oi* xwc8s+so+ol/sje g2hg ., (a) by what factor will the intensity increase? Increase bg s+x*ogjwshsl o/oc.e.i8+2 y a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the j zn0)e57.d(- dkh qdrfov yo;frequency of the other. What is the ratio of their in;yr) f7 (- h0do5njz kvq.ddoetensities?   

  What would be the sound level (in dB) of a soundk3nd -eqsz:;a wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? kqdzs3n; - a:e   dB

  A 6000-Hz tone must have what o nemduu:1:476suxw vsound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12o e4v u61usu :m7d:nwx–6.)    dB

What are the lowest and highest freque+3-k, tu.bk8z 8 anewmcz l14ptol .xhncies that an ear can detect when the sound level isw,kha tx n. k8l-z+4bpmeot1 .c3l8uz 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound le4 2eflq7 67vd9lxe*oy - xwcigvels. What is the ratio of highest to lowest intensity a -7eqxxvel4clw2 76gidf y 9*ot
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violinp9ea4:zw ngr( dhs55t qsc1s3 has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Unde4 dr53sptg 1hqnc5 (a swezs:9r what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundament4(rd(:qsdf17j + xeti)xek rd 4o5gttal and first three audible overtones if tsr(dx(qd dek7 )+t irx4t4g1e:tf 5jo he pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of a vk+;incmj90e 4ojye,3 vq/ gin empty soda bottle that is 18 cm deep, if you assumed j emj9cok q+;4/3ingivy,ve0it 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 spacd hyx6hg/ ccm36 9eo4nning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lc39og y4c/x6d emhc h6engths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hmzo+. z (/ljcgv-b9wkas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of b+gv . -zkjm9/(cwzloonly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tun,3czh3ole,t 8ai pt s td9)qr9ed to play E above middle C (330 Hz).q,rht3,aztc 9e3dp9)8o ltis
(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 thatah* mo6ciafwt74* gj5:se4 pq2h6 sex emits middle C (262 Hz) when the temperature*exm6pt a44g6jc7 s:q *o afh5 whsie2 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 20an ko*x-mi7 o) $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpg )yb+vukd)0r mf cdowr-r:-qj o*2*i iece of the flute in Example 12–10 should the hole be that must be uncove*-yg 2 w*f m+ orj)idrckqo-rb0)d:uvred to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, u z9kyr5e k,tvx*(i4 xand 616 Hz, but not at ant *,kex (uzirk5x9y4 vy other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tws px* 9odjdhnb t1c+ ) ustwg.4-7gu0io successive harmonics of frequenciodchg7u1)tbwp sx-409*ts .+gj di unes 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 q 75wccsjr.s)jx u+ /j$^{\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 wi ,ifk.dq2.n 2kkq eitbav2v*:thin the audible range for a 2.14-m-long organ f*a2 22 tqdkv q knibe.k,iv.:pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It x prnyt,6g4udfd5 6g;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.u 6;pnd td5gr,gf6yx4 What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stringu(yhfs 4c /vw+nwuda* 9q uy,3s, one of which is sounding 440 Hz. How far off in frequency is the otheu v,*yhcwwy3sa q9uudf/ (n+4r string? ±    Hz

  What is the beat frequency if middle -xy7n4ki*m)(sjc bdvC (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 at n lypd.qy1jee5i z//uso3,nw3ssb -b3x :y 1 ea :,dbzy//bs1xe uyp3yl5qj.1 n-o3isws3n e e n 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 simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz t7yp/bq8n lu ;vuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yu l78/pnv;bqy our reasoning.    Hz

  Two violin strings are tuned to the same f2k: 7ieh1:heq5ca/hul9bm sm requency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the 7152hlheb 9c imk u:eha mq:s/two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try qd8rkpyip 7x:o(imwts 58g2. to play middle C (262 Hz), but one is at 5.0°C and the other apsmg2ikq i(px8:t7dyo 8.wr 5t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequ o ght31/ gz3ie1qj:anency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are3tz :1i3gng q1o/h aej 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 pers:w6lsyz gp6* uon stands 3.00 m from one speaker and 3.50 m from the ots *lz w:uy6p6gher.
(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 atz:w7nngl(ve3 t 0f cv4w;m7 .*jexpwiuq+ 6lv 132 Hz, but a piano tuner hears three beats every 2.0 s when they are playedzw0wliqm:p.c ;3j7f +n (xev v* wn4gev76utl 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 k z/s n5mi t4+yp.sshp1qm x0q:+ze-m in air. How many beats per second will be heard? (As/+s0+-knzsmmxpm pqzy5q4h: 1e t.issume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eng0s,ns l c1l;a(4wza 0p.vvlsxj j5 o/mine’s siren is 1550 Hz when at rest. What frequency do you( 1n0j,vswamall/zl .v05jcs p4osx; 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 ;j9vm ,irjs2wa fire engine whose siren emits a2iwm9v;j sr,j t 1550 Hz moves 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 s6 jp:18 j s/m6it dnvw *wk6xg87bpflwource is moving toward you at 15 m/s versus you 6 t1nxvgw fjsjp8 p/im*8 667dkw:bl wmoving 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 equo,rr3*nam*d nipped with the same single frequency horn. When one is at rest and the other is moving toward the fir n3mr,**do anrst 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;t qc7, gi1zdpv+u7ot 50.0 kHz and receives them returned from an object moving directly aqtv 1uti,z7c g;p 7+doway 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 As9p;nai ,+4vizc bft4xdho8i :p mr +2k it flies, the bat emits an ultrason, hki ivmt8 n;ard+42ci:o bzx+p4p9fic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tu3tta n yoj rw+dmtz6n w.;o9.:ba 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 t6m+.t rww :ytoazjo.dnn ;93 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow ta:* vp7o tmv:speeds. Suppose the ttpma:vo :*7vdevice 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 at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultras/xpzv5lqe,f j u)3hn 1onic 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 g8aoz5xu;vo dl0/ +lzdy.ab3 the wind velocity is 12 m/s from the north, what frequency will observers hear w0.ob8xodl+d;a l z5 /3a gvuyzho are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed:dxba hi5du+lv712 om 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 oh +1:tv zzkj*gf sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mot +:g 1htjkz*zvion?    $^{\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 sounn /yz55hvv+p+opsxv ,4shg5r d is only aznxrsvp p h,h+ vv/5y+o5s 4g5bout 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 i8ye9 gl s5nr.8500 m/s strikes the ocean. Determine the shock wave angle ity 59iges r8.nl 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 q ct .i8j(p:pd$/theta$ 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 exactly 1.5 c6j m(feb5xmsfz/s - bc; ;u0ekm above the ground flying faster than the speedsme fb/6bs;x-z0jce um5( f;c 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 downward frof7k , kj-7irxxpjwm7; m the bottom of the boat, and thef;jw,xp 7-7ikjkr 7 mxn 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 the huma1gsrk jb31ev)n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display cal5 ab.9iewr1dwx 9wgl l3hs23k led a sewer pipe symphony. It consists of many pl53rx hsew 2ll9 . 9w31gkdabwiastic 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 persd ):+zi cyq e-ts9h1nqon makes a sound close to the threshold of human hearing (0 dB). What will 9)zce sn 1:yqhqd+t-i be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-lt6l ,wbu5 +qcdB sound are heard simultaneul5 6cbwq, +tlously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10yo/ /ouok60ez5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally iy u0/oookez/6n all directions?    W

  A stereo amplifier is rated at 150 W o mdz6b83l2xu futput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the pom63f28xzdu lbwer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theirww2 zlz vt/(rcqw/+ b- ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m f/ w/wv2 t(+-br zzlqwcrom a jet airplane engine?    W

  In audio and communications systrs0 vo 2z9:;;fari trfems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fr*(c /ti5lffaaequency 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 betwe/lt1lfma 5t2c en fixed points with a fundamental frequen f51/ca 2mllttcy 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 vibrqoooiw +6bgqt *r1i* ,ation above a vertical open tube filled with water (Fig. 12–or*qi ogob1qt6*+i ,w35). 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 isgb /rew67qod- near a tube that is open at one end anoegrw 6qb/-7d d also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as o /(svr cd rn8txev02us-dx5*a ne 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 thm,yh lq t:++fuunhgd ix/+9z0e 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what t:h zfyt9+i+ qdm ,uxu0ghln+ /he 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. O. t yj:,zb9, eha/9av.eox*hm1yk pagne 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 mo beyaj ghkpm, eaxt9.v*z9 yoh/.a:1 ,ving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it) -s ++- vhox1a:ncvni;l,b+a rqiwtt passes you, its frequency is measured as 486 Hz.) t-+ hn+al+- q1s,tbarcv;o:xniv iw How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you ca/)i b+jfdz j0gmd*- exn estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the soun j0x*dfdb )gmi-+e jz/d 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.p+i :st+bhfe1s/ 4m-k+rvqxi The shorter one is 2.40 m r+/tkv-e bmq1 hpif +4:si sx+long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mov 6f gbv4zi+8/t7mv ekt3nekd3es 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 position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears tv4egvbt /8f+e3z i7m kd6tn3khe 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 r :mm3sr.qfc2beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flowrm2m:fr cs 3q. 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 mdv ) 8rctho.f9/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 v)ot . rhf8d9ckHz. 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 soun3 zp1nmgnun9*d pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from onmn1zpu 9ng3*ne chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa(z xnh455xxx cs once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss,h55xn x (cz4xx long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for steyt34kdz91:ngtm ux a7reo listening can be compromised by the presence of standing waves, which can cause acoustic “dead syuz:t3gt 9 xm14na7k dpots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rgkzqtwg3 +p)/ods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stkzpwqg t3g+) /roked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequen6clyx* gv:/q smq cn72cy of about 1000 Hz 2x :yl q6mgqs/vn7cc* 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 Mppjpz.o j*s(b 7 +a3mdach 2.0. An observer on the ground hears the sonic boom 1.5 mi73 .o*pspp(jm+dajz bn after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iapc,h kt/,rt ir)vl 0-a+s ):8t8ml5xselkqes 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