What is the evidence that soxp-u oc0t03nx d ,3hnv.di2fu und travels as a wave?

What is the evidence that sound is a form of ener58 l5bzj5uyfu+;k2vc bhm5q3 n4g ms ggy?

Children sometimes play with a homemade “telephone” by attachingwhoy85 /i/ mzs a string to the bottoms ofso8 //yzwh5im 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 to the other.

When a sound wave passes from air into water, do you expz./. thv74h.nguuactect the frequency or wavelength /4g. tuh.7vzc. natuh to change?

What evidence can you give that the speed of sound in,buw7yvz 3h01lc;y5e q)f uag pg() ec air does not depend significantly on fre7u)pa)e,c zf0g gybv 35euqch 1y;lw(quency?

The voice of a persocfnh+prvu 8:v(b1wi 2n who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes, *dbk4gi+iesnwh*h8+4jq b s?

Explain how a tube might be used as a filter to reduce theay. tl .pqpo k 8c9,72lj5tpdh amplitude of sounds in various frequency ranges. (An example is a car m.. 7c2l9hyka j,t8 ptd5plqopuffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move upun v8-oag 0)kp the fingerboard toward the bridgen0p-ogku)8 av ?

A noisy truck approaches you fqj, y oj(c(8hqrom behind 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 diffra(hoqq jj y8(c,ction.]

Standing waves can be said to be due to “interference in space,” whereas bea5pxfh 38ljdjk1- 9g mmts can be said to be due to “interference in time.” Exp -93fj8m 15pl mkjgdxhlain.

In Fig. 12–16, if th2t m:lp,,glike frequency of the speakers were lowered, would the points D and C (where destructive tmig ,,l:pl2kand constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ofnk(mqq. 0z :ih people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not 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 mk mqq0nhi: z(.ore noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a4rjeiyn ev6d q*14/jo;o h+ik 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? Explain. yjdrqe4n*k/ vj1i 4i+oe 6;ho
(12-31)
(12-18)

Is there a Doppler shift if t6aijmka/e o2, 2*nt nkejvc4z* +ifzqx48qi3 he source and observer move in the same direction, with the same velocity? Expf/t8x2+4a ejk *,kja4* z 2ivonqiqie c63 nmzlain.

If a wind is blowing, will this alter the frequency of the s6m,n mslcls 86ound heard by a person at rest with respect to the source? Is the wavelength or velocity ch8s ncm6 s6lml,anged?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor r wg yfrjk-n6xp:7/347efazvis blowing a whistle in front of the child on the ground. At which -zrp7g 7ayf v6erw3kn /4fx: jposition, 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 listening for the 3 4(7f 1em llcfko)hre8 ct7jmecho 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.37 c8 ecl7fmfhj)or4 lmtke1( $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the eh ,fh,qu f mf3:aqk)npf l90kt)6vm/ xcho of the sound f0fk / 3qkv,)m lfn h,9p)uaxfqm:6htreflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ay7 z/de+a ctpa/-/xsair 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 of tuna2 )rtznqz9 *rk 2pjn:v on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km anpt92 r*)2zzqv jnkr:way (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 splas4;+ hedhrt 1agedeqtuq9b66t ; r-4cjh it makes when striking the water below is heard 3.5 s later. How high is the cliff? 4det; ubqe6rrjh ;a1et +4t9hdc- 6qg    m

  A person, with his ear to the ground,mml4j9ll+- ae r3s6hai5n a5w*rc g) n sees a huge stone strike the concrete pavement. A moment later3n4 +5 enl9al-gah *ilmw r6rcmj)sa5 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-se9my eea aj;8/ncond rule” for estimating the distance from a lightning strike i8 j/m9eeaany;f the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thkq;.z wi:tsm) e 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 sou b6xy; 2s47rhrvqxznvf 7m(u/nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers praizz5+.vqp*yd l+ffvv .c83xt 0ni 7k oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [H a3izi++pyfv7 f5c z..v0tqd8xk nl*vint: Add intensities, not dB’s.]    dB

  A person standing a certainmf0y6x)yt , oa distance 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, n,oy) ta mfx0y6ot dB’s.]    dB

  A cassette player is said to have a signal-to-nozam.l orome8z8f m9 :+ise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the sig.eoaz 98l8rom:mmz f +nal 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 innqdgp q 9(26jx;hrrt : normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over (q6 djp2x:;9rrgnhqt 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 whon+nocll-og .)se area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifi)(ti 1*3n,ti pqveovsqbtq2(7ze of7 er B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a po,)f2(tpi 7oetqv7e13zbvi ( s*qn oqt int 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 registes(2h 76u*lj tupgtk:ored 130 dB when placed 2.8 m in front of a loudspeaker on the slt:(2uhosk u7ptg6j *tage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What idla .- we; s4umka k8rt6ijr9;s the ratio of the amplitudes of two sounds whose levels differ by this amount? [H;tsw aj 4dk6k-rr8 melai u.;9int: See Section 11–9.]$\approx$   

  If the amplitude of a sou,y0u hutt 1dyjb/af3 )nd wave is tripled, (a) by what factor will the intensity increase? In3,f)y/uutby a d0jh1tcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hvj2( ma83lh yaas twice the frequenclv j(3ha y82amy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a v dpdd4l7 on59sound wave in air that corresponds to a displacement amplitude of vibrating air 9dodlp dv4n57 molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what r.fxkqcmb( c( /pjq29 sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–/ frj.bp cm9k(q (xcq26.)    dB

What are the lowest and highest frequencies that an ear calgj (bt4 12ofjn detect when the sound level is 30 fjt bl421jog( dB? (See Fig. 12–6.)

  Your auditory system can acctazk .j9wvt*+v1x yr3a6 yok(ommodate a huge range of sound levels. What is the ratio of highest to lowest intens3o6ryvw1j kxza*9a+vt(. tkyity 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 f4cx-aflrmmp *hg5l0 *undamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, af 40c*lgra x-mpm*l5hnd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first th/k 6gbf0banu/, s7rpl d15junree audible ovek/gan0p6us/l 57 b r,nfj u1dbrtones 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 frequencyonl, aiwe d551i( fbrea.u 2/f would you expect from blowing across the top of an emobe 2/,ual51r wid e.5f infa(pty soda 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 wca8;pa6wa9moqd0, f mith open-tube pipes spanning the range of human hearing (20 Hz tomcd6w0moa apaq9 ;, 8f 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 harmo4-a 6tec1)tqswmi)+ mzw vrk+nic. What will be its fundamental frequency if w+ 41 tmat6vzr)qsc +ew-)mikit is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is -z(/sl -ap +h0wr/pluat t+uutuned to play E above middle C (330 Hz/t(/-apt+ lu +rla 0suhwpu -z).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middl 0;8rsh elm76.ctns bne C (262 Hz) when ;c 7st .hnb0 n86rlsmethe temperature 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 20/*l.ue )xneviae m -:o $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of :wxbunnix8+dh k*h64 v45xstthe flute in Example 12–10 should the hole be that must be uncovered to pl+8 ht4xsk4db 6hu*v nnxi5w:xay 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, and fu3*ph: frd;k616 Hz, but not at an3fudkr;h p*:fy 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 4 rtt,43 oyd(s ,rtgg2avr1z*- fbeubresonates at two successive h3v tb4g rr4otua,r z teyb2,g1f(-s*darmonics 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 lgx/3-bmwj s+ $^{\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 f9cebwq.p3n779 x mcf hz;f3meor a 2.14-m-long organ pipe at 20 x.e q93efb zw 7fp;nc7m3hmc9 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5xskap+i9fq,8mb- hs3 k (o1z l cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) oflosmh93z-ab +pkxs1,kf 8i(q 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 /e,koj1 ju )avtwo strings, one of which is sounding 440e,v uj1k )jao/ Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if mu0lo 7lv m71j/z u0f2 gvdu*tciddle 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, wa,;,:+x3 bfiw am ugouhile another (brand X) operates 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 are played simult;o,f,aum w+ xbgaui3:aneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 -p*cx sxsc1:cm;z ;o.vdw lo6beats c;o1s;6cxd mw*c lv:z -pox.s/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tens7 (2ksnr1t omfion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two stkm712n ( tforsrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play mi ez/73-j a efq-doixmlbu30 .pddle C (262 Hz), but one is at 5.0°C and the other atb.7z3dxuij -p3/am0 qfee o l- 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has kk-pr.a iya7x wl7(c0 a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possibleawp cy7 lk0ir. k-a7(x 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 pe 6nshil9ur(.b8zy ts+rson stands 3.00 m from one speaker and 3.50 m 6b .l+ns8s uz9rh(y itfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrlrdr) zka,rzi85e1 wioi3n.5 ating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (kw, n)8a iriliz3 5z51eordr .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 2.64cdg6t ytvfs*d*(3e.l:5 i oag m and 2.76 m in air. How many beats per second will be heardg*c 5tsddg*yfe 6a(t:l 3. vio? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firb-dxb/ w ia+quk*w.z2rkgt85 h b+ or3e engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a-oxq8ib k. gwr 5r+*b 3b+h/w zda2tuk 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 a f9evmt7ej r /gsqzwr zj3y4*2/ +;p kvqire engine whose siren emits at 1550 Hz moves at a speed of 32 m/sv*e7t p9z;j r//q+gzjve 4kwq rsm23 y
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward you ;ve6o,g1n smyat 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exs6; ,myg o1venactly 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 equi 5l-kom bu41qvpped with the same single frequency horn. When one is at rest and the blku qmo51-v4other 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 7*i7 esgnr91dlhn1 fwz, e )zgat 50.0 kHz and receives them returned from an object moving dg1* n g7n)ewzsf 7lir91,ehzd irectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ultrcr(yfhv1n+ n 5asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in n n+(y1vfcr h5the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubtbmht9 onhn5 fcb51 2h0-z k6 ,zpqc5ra 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 frequen,n obm9 pztr6-05zh1t5fqh5 c2cnhkbcy was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses 0lw3ack+ .gg aultrasound waves to measure blood-flow speeds. Suppose the d. ggwc3kl0a+aevice 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 ultrasonic w17sfp,(u0jhu 6sooq/q -wikp uvl 14raves 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 frequ n(ng/yz5agwx9i6o)t ency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rewg/g)yn zot6x9 n5(a ist,
(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 itsla/ bie j7yk.q ) u34ynyd*o9l 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 g (cwc(xp*5x82 zc*m xtihuv: 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of 25c(gxhpu**v(cwim8 zc: xx t 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 51n u. tqp(tadspeed of sound is.5(qpntu1ta d only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine taooto1+xf;w7 g k: gxk8z/y 0she shock wave angle it prod zogo;7:otxkx+sf0/k 8gayw1 uces
(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 uns1. a v(a5;kuim2ls$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and senh5p 9b2-aam we a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled waa bhm59-n2p 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 sou1c4x.yq yp+ha w kn++hnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which itpyxq1 n4hka +.cyw++h 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 human 8;kdrhq du4 2xaudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consoe t5b/41j e/z awwl.bists of many plastic5 zwo/lw.ab4/eejbt 1 pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person maket4)mfd/jz)tppc,+bj- h c.v o m w/(kcs a sound close to the threshold of human hearing (0 dB). Whatj ,j//c).zvbmptk hf4c (m+ c-p)odwt will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8vu+q yr67y) he2-dB sound and an 87-dB sound are heard simultaneousqy)hy+u v 7re6ly?    dB

  The sound level 12.0 m from a loudspeaker, placed 7k s,egcypoly 6ht.4yyu2+c7ji2( - wio;kt ein the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all d k, wt+2lgue.yp7-o6cjkio; 4 7e(hitycsyy2irections?    W

  A stereo amplifier is rated at 150 W output at1 .rrya+1jr n p-nn d+wql37gl 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watt. nj3ryl+ r 1rpnql+-nw7g a1ds at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over ths.r1di fsfzem6;ez)d+5p m r*eir 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.d 6smz+eise*f) . ;frdmr15p z0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,,no6g.jqoob7 ;n we:n 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 d2he3yrv9 m-6vuz ig4 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 loc).jmuufesrn n 4)74 x8f3ryu ng between fixed points with a fundamental frequency of 440 uu4mey83nfs)rxnjfr uc.47 )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 verticalgzs) f,x3b1ng.2zgyy qvje*; open tube filled with water (Fig. 12–35). The water level is allowed to dez 3gqvz; 1jg*,s)n yfbxgy2.rop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a4hkmbr3u ait:xuu 13c1( a3c4 ;mrv xa tube that is open at one end and also 75 cm long. How much tensurru4xxvaabt ; 3:a4ccmi1m( kh1u3 3ion should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fch;ik 4fr7e sl kvm.4:zt :z:bull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range cdv nyucvf u*og9*0 1;joming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency o9 j uv*dg1n ;yfvc*0uis, 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 whist sz*u tk;ef6u(3v fyyg+t()i kles. One 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+kt)gf(uyt i fzv(ey 6 uk*3;s moving train?   m/s

  The frequency of a steam traiff ;hr k vpd99byue h5(dv;0;pn whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (d 9dhy;;p90evf;k hf(br5vup assume constant velocity)?    m/s

  At a race track, you can est a)zmonfc5oak, g+3,timate the speed of cars just by listening to the difference in pitch of the )aoc+g,kz3nf m ,5ato engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freovd0 omq 0ddtfl5dhj9 (y -+(g.q6aqaquency of 11 Hz. The shorter olq09hg (6da(5-amyoq d+jvfqtdd0o .ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past pm,hfw76 s7uea stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 H77hmw,s ufp e6z, 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/h 08js/vlcpu) . bfh9ns what beat frequency would you expect if 5.50-MHz ultrasound waves wulpc)fh8n .9hvb sj0/ere 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 mo7y7v 8b q6zrxyth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave vy 7bry8zx67q of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sou 1z4b3x yn(zpmm/k7 (oeaj2 j14bqvf lnd 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 one chirp returns before the next chirp isb 1kf7m (44oalpv/mzq 1njjbz(xye 3 2 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to pfqt./katx n+ j2l5zu tcj++; send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way;p+q.+t fntlxt5cu/j2 j k+az that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromis0d43phx,gvophx-i o. ed by the 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 wide, and 2.8 m high. Calculate p4xpihx0v g-od3 ho.,the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationpu).q 0u a .rt v:,*puhudepo37emhx+, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the. x ho+r3 uev07uh)mu:app.qd*ue, pt 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 /2 z54/merst 3w ccrlhat a frequency of about 1000m trh4l 3zew5//r2ccs 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 theb :v m 2onm( m02gh;j1zmgxg -cat/iy3 ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whao2gm y ;ga/tj:3(1i2xvhz 0 -ngcmb mmt is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iszcx: a5h4qz .z 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