What is the evidence thavvh+fb-:lwylc kn().t sound travels as a wave?

What is the evidence that sound is a f x: oqh-wlt9)a6ck )sos3yf,lorm of energy?

Children sometimes play with a homemade “telephone” by attaching a sub c68f) b3qz.p tatm5tring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound c )tc zb5q6bfpm. t83uaan 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 expe (cwbi x2*flpk )0gs0vct the frequency or wavelength to chpb0gcfkw s20xil *)(vange?

What evidence can you give that the speed of sound in air does not depen f7d bi9 ,aptyq. /h)g5ga+hswd significantly on fbq /+fs.ga9h5g7h iad)tp, wyrequency?

The voice of a person who has wlq7 )c md8i.dinhaled helium sounds very high-pitched. Why?

How will the air temperatu9.:njle p z)1sm)hqeo*yy r6 cre in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun3v; win+)ejuu ds in various frequency ranges. (An example is a car muff;w e3jnu)uiv+ ler.)

Why are the frets on a guitar (Fig. 1 .i+r2e: m0 ouv/iw,uokaeiw02–30) spaced closer together as you move up the fingerboa :0w,w /.ke ierauoui 20ov+mird toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear iwmf kt:) f.h)b5udbf* t but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of td5fbk f ):m)uh*wb.ft he high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bek ko. fjc.f2hr.l3;b wac3 (gkats can be said to be due to “interference inhkrb kf32a(l .;3 c wfkgjc..o time.” Explain.

In Fig. 12–16, if the frequency of the speakers r+ 2pn 4/wppcqltkk4a8l4qj7were lowered, would the points D and C (tl7q/4 lkpnp4 cwq a4j8kp+2r where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas6 +fa1jpi e3ct61vut j with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which 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 rct3 6e+jjaf1pv1t ui6 eaching the ears?

Consider the two waves shown in Fig. 12–31. Each wavek t0*sdmcm5*g kepg )4 can be thought of as a superposition of two sound waves with slightly different frequencies, as ing edc50mtkks m)*g*4 p Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the souraa7e hrga5/,a4 4lgyzce and observer move in the same direction, with the sal7a h /gg z4,a5yra4aeme velocity? Explain.

If a wind is blowing, will thi(fbv t3r)q.4u:x mj( sg/p hfesbg7)js alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength ovqjxu.:f rebf/jgh(7s (p )m 4s)3tgbr velocity changed?

Figure 12–32 shows various positions of a child iebu3pivfd+1lo)ulk 5s: i 7l6n 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 the child hear the highest frequency for ti65kiollbu3 pu7fl+d )v1s: ehe sound of the whistle? Explain your reasoning.

  A hiker determines the length oa3x d06;+,g2uy l; nslardnf qf a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutinl +ndns;a gx u6ay3qf0 2;r,dlg. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He he epbyz/jariue( q8to yk17, 2,ars the echo of the sound reflected from the ocean floor directly below 2. ej, e1z(,ko pry aiq2ut/78by5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength .tml.lsjw2)oiz g p*vnyr0 bf7u*:j )s in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftuf) /aduyo; ev7/njy:ing just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on ua n/7) yuyf/ dj:ove;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 it makes when strikinc/+sts3z.m d t /jtl+eg the water below is heard 3.5 s later. How high is the c d3mtesjcl.+ stt+/ /zliff?    m

  A person, with his ear to the ground, sees a huge )/:ylhs 0rxwq 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 1.1 s apart. How far away did the impact occur? See Table/qyw:xhs)lr 0 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distd 3ypakegfm u1)u* j/8ance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 e/ y3p1muf*)dgja8 uk $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thef.ztm,mwt,1 ( pyxpy8 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 )abh1;ik nez o:f-x0l sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fit a)4gcilwr *:a 9syr0red simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s9icrg sa)a40 wty:*l r.]    dB

  A person standing a certain distance4 iy+egcnb-8hhs t4w5 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 experience if the captain shut down all but one engine? [Hint: Add intensities, not whcs+ngbte4 yi5 h- 48dB’s.]    dB

  A cassette player is said to haveel9 6uc 4;2 bjcyguq f+*crb2f a signal-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 noise for each device? 58 dB f brlfq6 uye29 bc2cc 4+;jgu*=    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spea x5rk13ll m5ohking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mout5rho35x m1 llkh. $\approx$    $ \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 eardru gy f-ow++cyoz0yl;y0m 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 xdjwugfs8)+6pw jg 1:250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker con1dj8uw gj+fp) 6x:g wsnected 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 regi )9 f2xg0wpdd-prm -iastered 130 dB when placed 2.8 m in front of a loudspeaker on 0x)pf -arg-92m pdwdithe 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(2t ptowvr2sg* + js 9k8kc5ud-c lc1z level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by tg 1ospjcrus2v w- dk+c k82l59cz*( tthis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) but zt ,6rc51 (v jhmd-qtw8uf2y what factor will the intensity increa1d,w - m68 rzutc (tvt2fj5uhqse? Increase by 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 thewt rzubq+u.*d52 nypuvbg) 2( frequency of the other. What is the ratio of theivg*zyqw2u(un5 p u)+2tr. bbdr intensities?   

  What would be the sound level (in dB) / jbksxd,bna+o/)e41e c uy)v of a sound wave in air that corresponds to a displacement amplitude of vibrating nx)4edcbb,/1+)av j/ skyu eo air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem .9c ,8mx;nv+ h/rbpcoav3rjyas loud as a 100-Hz tone that has a 50-dB sound level? (See Fip h9j8b ,m.xro c+yn/r a;3vvcg. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the s96a -2 hdpdhuzound level is 30 dB? -hh6dz2ua9 dp (See Fig. 12–6.)

  Your auditory system can accommodate 7czj4tr c2to/xol 3)na huge range of sound levels. What is the ratio of highest to lowest inten xlo2 )co3r zj7tc/4tnsity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengjm )dr7 ;glb.cwmh1 l5th of the vibrating portion is 32 cm, and it has a mas).m1;hl cw r5bgmjld7 s of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thet* yl :vb/,cwah,ut6g fundamental and first three audible overtones if the piv*:bu/tlc, ya htw 6,gpe 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 an e :oqmb xv/u eg+59:psvmpty soda bottle that is 18 cm deep, if you assumed it was a closed tuv9vqb+: o mse5 :pu/gxbe?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organydbe*;* tgxd8 with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range ot*dx;ge *dy8 bf 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. Wh4dzr+ 8rsg0 59znkc shat will be its fundamental fnshk4g 850s zzcd rr+9requency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7 zg;t, iy*3ids3 m long and is tuned to play E above middle C (330 Hzzy i itd;*,s3g).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that u5rv(ks uqi 4buf(; q)emits middle C (262 Hz) when the temperature is 21 ;qf i54vrb)ku(u(qus $^{\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 qlitm ft.*d)3)a-hn +qqk3s m at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hol4-nm)1e d hhzre be that mhm1der4 n -)zhust 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 reson1q saps52sua. f a*ij)ate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in 1saajsa)i 2 5*qpus. fbetween. (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 *x8 ugyq29jiz-mzur05j 8 pi vboth ends. It resonates at two successive hz-qip u5uzv ryi0* j8gmx982 jarmonics 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 w8vr/r 6 f0be5qum 8-nlp3 rdj$^{\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 2.14-m-long orgakykowri30x.m7tamhk 0/t9 .s7u,somn pipe at 200 mwh07/k.kuyx7osri tmtom.a9sk 3, $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thyen em+;v 8;fse outside and is closed at the other end by the eardrue+my es8;; vfnm. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two 4m.0ehshg i:nstrings, one of which is sounding 440 Hz. How far off in frei0 en4.hs :hgmquency is the other string? ±    Hz

  What is the beat frequency if middle melp-7f giy 32C (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) oper+ b1 yv(0bskjxb79p-bz4b g5,bx 7j4qbkmkz rates at 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 4k, - +s(p7zz 9b7b g1kk bbqxbbjymj04rbvx5are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 t .rkp1lcl+45cnwq h 7beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning foqp5k rl t +7wl1hcc4n.rk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sam*-rxoxmbg0vgid0+smxv 1;f(e frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency her i*bmd(xfvxogg v0 x-10m+;sard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pla mnh4mfve:) s8y middle C (262 Hz), but one is m8v ef4:nhs)mat 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 j4a)amxu4wc 6a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are j6wu4 xa4mca)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 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 3e2dvj0uf ;l jzc:-x:n(1glkd .00 m from one speaker and 3.50 m from the otherd2(klnfejl01-jx zdgu::v ; c.
(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 arevc xqk 68)csl2 supposed to be vibrating at 132 Hz, but a piano tuner hears three beatscvk 8q26 )sclx every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengttc 5ucx7ckz.l* 7r me-hs 2.64 m and 2.76 m in air. How many beats per s-ezu57k7cxlrtm* .c cecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren ti9m 4h :xthk.is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s htt49khx m.i :
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engin7 1 zrvepnfnn34 ju8f3e whose siren emits at 1550 Hz movef43pnnuv 8ze3 n71jrf s 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 90f-wxx,2j(z4: ,dplvjvo els vc9lqmoving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they closels0x4 v z,2plw9de- qxovj 9v,:lf(jc? $f'_{source\,movine}$    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. Whend *gp/e -ibd-n one is at rebe g-dn*-di/ pst and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them rek y:5 o e/pjrs;:s-dtx )t+oke9izl.cturned from an object moving j o .sk5r9x t:-oekis/: cy;t+zldpe)directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bas j1twn dsvjm3 az 4d)dr/ qhlf66ul4)t6r4 :nt emits an ultrasonic sound wave with frequen)s14r /4j fdu)l3w 6vhjnmsta6 tr dq:dnz64lcy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played q22gjded jufd6 )d92lon 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 tfe dd dq2g6j2)l9ujd 2he train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultraoq1g/rea1ah2 b0 2hu xsound waves to measure 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 Wh 11 aru qoa/g2ebx02hhat 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 usijf 0,dt*ah )og xi1k2 g6ew,vlwnwk;/ ng ultrasonic 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 5704a:is tf ;yjed 1-xa-u Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are:t--j4f1e ada;yi u sx 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 at 2s:u /awvycwyk5 30)lp0 $^{\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 w5 :cob dxe3lo9n *c0dthe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directioedbd*3 co:cnxo 0wl9 5n 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 souu5wbw0)ky1 onz) ,nn snd is only about 35 m/s sww )n0bn1)kuyz, no5
(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 8 di;gzsm:wp)(yt )uv+500 m/s strikes the ocean. Determine the shock wave angle it produwt )ypv+ iugdm:s; z)(ces
(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 7 inq2ev/ew1-m rgm2*. pfxlo $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly over .u;wh.rhx5.kfd7/01h h cyg-tasioshead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the k hfs1t..rxh5;ihys ./ahwg7ud c0 - oplane 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 sejvydm kd5m* /a zxdf5w/0cd1h 0a. (dunds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the mini/ada 5.vj/xfyzcdd1m00 km5hd* (wu dmum time between pulses (in fresh water)?    s

  Approximately how many octaves i+o8lb xcs9krk+g9y 8are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sjqss bqyg(dds624 a3 f( ;kt2iymphony. It consists of many plastic pipes of variousgd b2fsd3a k2 q (styj4(;s6iq 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 2kb5ugd.r- +isepp;p m from a person makes a sound close to the threshold of human hearing ;ip+pgek - srp2du5.b (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and+ ln;mu1v7*wl, haj yi an 87-dB sound are heard simultaneouslymuylhl,;nav + 1w*7ji ?    dB

  The sound level 12.0 m from a loudspeahe dwoa,y/g l+ujb44u3 0 z1ouj/9hhcker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, asduo,4c3 ubjae0+ h1wzu 9g/hl oj h4y/suming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W -ju ,j 5slwzv-output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the p j-5, -vzulswjower output in watts at 15 kHz?    dB

  Workers around jet aircra.c/ j:zoig i(xft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by g:cz/o .i xj(ian unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, thub0xw3(/lpr qk2pp 9ue 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 frequjby z m.;v3tx4y8to; yency 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 vi)6m8 a, pjt1,mi 0vdpcsds1 kcolin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unitckm)v1sd0pj mi6c1 sda 8t, ,p length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled witho8o 6; z cb6ib0ystyz: 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 water level is 0.125 m and ay:6i0yotb z8s ; oz6cbgain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tu/ks6kqk h) ce3j b2ur2be that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in thes ej)/3rckkk2uqb2 h6 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatv ,zk)nud a1ip+d ) biih-o.,ae 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 purek;kp 5 hzl(7av tone in the 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 fkk v(za57 pl;hrom one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conb orjr;n2. bn, d98pzzductor on the stationary train hears a 3.0-Hz beat fd r;br.n 2j9z8 z,opbnrequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl7wyq 5l8u:mtp:qbaie1lr k 9,e as it approaches you is 538 Hz. After it passes you, its frequency is mea7ekqa:llq15byrm:w98 tpi ,u sured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jusnmi nh;jvw 5 8kbdr2 p:/qjg36t 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 f:p ;dv/bjq8 hmj6igk w 2n5n3rull octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetul) 7tnp:q zdt ovghb53(ya :o3pf+5 mher, produce a beat frequency of 11 Hz. The shopo v:hy b5afn)+mo3pdtt7g(l3 z 5 q:urter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite e rg +cl:;q9apcnds of a railroad car as it moves 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 (c9 a;g:lrcp q+c) he hears the speakers after they have passed him, at C?

  If the velocity of bloodotl58fe 4u29jq(kyx kz ep0ghj(/ 1lh flow 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 wlugjq h8p1 ze0ekx 4y2j/k 9l fh((to5ith a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at sy5(bbtv /ta2reecl v d,+4*k lpeed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bal c 5 yb/(l*2+ vttarebekdv,4t after that wave reflects off the moth?    kHz

  A bat emits a series of hi 7inogm i,f-u:dd:de7 nj) bol0*o xe1gh frequency sound pulses as it approaches a moth. The pulses are approximately 70.,o 7fmexl u 0:ooid: e7)ijdnnd-g1*b0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one 8om:g9s te; nuye53w wAlpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone;9ownt s583 ywe:geum is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for ste7u9 5frwgd6 wjreo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure n56jdwu9 fw7rgodes. 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 rods,” involves a long l:8*ys*0 n lhf hlz6 nhzhllg5(h.zo(, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice nly:8nhg (5z .z6s*h*(ohlzllf hh 0l, 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 hearingq,d-rprp .(nh*spo5 j for the human ear at a frequency of about 1000 os(pd-phrp . rq*n j5,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 Mpf;uig9ffme ;4c(b o qg,4 kj6ach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What ;9gp4 b( 6c q4ff;fj,ieukogmis the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaz cxd1/d/bz+ gt 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