What is the evidencesokp84 6e ofa7 l +iupk,c6tm9 that sound travels as a wave?

What is the evidence that sound is a frtc hn. izp:5ok)g/0iorm of energy?

Children sometimes play with a homemade “telep+pp; sbk .r8vi8dqeo 5w*p g l55aw0rewg*o*hhone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travelhw5r 5rw +.qop k0ppb8;wgds*o ** ei 85veagls from one cup to the other.

When a sound wave passes from air into water, do you2j;l5 jkv ft:bkv +0mmc/,aup expect the frequency or wavelen cjlvv0;mak pb/jfk5 :u, 2t+mgth to change?

What evidence can you give that the speed of sound in air does k e(e1 *3. *yer dzykaqo/arqblrn51z:k;.oknot depend signifi15boy ekky*l;za :.qr.qn3rkza d /ok*1(ree cantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whr+c1- :scbj7fw 8zsutxbtjjy4w4*: h y?

How will the air temperature in a ro(xual l o3yv*;om affect the pitch of organ pipes?

Explain how a tube might be used as a filter to *g*; yomf lcr2reduce the amplitude of sounds in various frequency ranges. (An erfgyl2;mc o **xample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as4vaeg83ev2 x e4kjqf;29 ibf w you move up the fingerboard toward2efj kqa4eg 93 e8bx42;vvwif the bridge?

A noisy truck approaches you from behind a building. Initially yoyfbp b+,lyj .ls p+5 ,2wqbv8ou hear it but cannot see it. Whe,+ywb, 2p5p b8y .+vlsflo jqbn 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.]

Standing waves can be said to be due to “interference in space,” whereasps4s kv0(uissp) kh34 beats can be said to be due4ppsih)(ss4v0us 3k k to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woul j0 p4hleo0z6bd the points D and C (where destructive and consjho 0zepb40 6ltructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wit6bj3a:vhh .wvu s z47ch very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphoness.w:437hauv hz6jc vb 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 reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of tqti n8.6*x 9-4j8umnuzjspo as a superposition 6qn sm- j98uznjtip4 * .ox8utof 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.
(12-31)
(12-18)

Is there a Doppler shift if the source and tg ,x, fi3n77*cmjae 1a8erijobserver move in the same direction, with the same velocity3jeicag, 7ni* rtm ja7,1 8xfe? Explain.

If a wind is blowing, will this alter the frequency of te*4:e*; i mxcivu:dw xhe sound heard by a person at rest with respect to the source? x4e i**x ::;imvcuewd Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child * bz 1xsdx+chej 7k+nac)c.h8in 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 freque. ccjh 7+ac+n* xeb1h )zxkd8sncy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fkum9f , fb3d-0sq3 nyoor the echo of her shout reflected by a cliffd b-mun39fqsy0k o3f , 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 his ship just below the waterbdkt):c m*5rbc8 b ruk*1x o.n8c;lik line. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How t 8.1kdmkbblcbcc):;o* u8kn r5xir* 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 air at to.c t6 h8tfq120 $^{\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 boa0qvvcdgfp, s9mij: (- t is drifting just above a school of tuna on a foggy day. Without wif0q (m-j: dcs 9gpv,varning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striking4k2fq+ kp9 q8 vxde1sj the water below is heard 3.5 s later. How hig9jqdkek8f+vp x2 s1q 4h is the cliff?    m

  A person, with his ear to the ground, sees a huge s*j;yk3rolmgz,de0 m + tone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the cokm 3y * rjdem0z;lgo+,ncrete, 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 *m -h4iz7rkx q:+ mouei8fas o*av 6m1“5-second rule” for estimating the distance from a lightning strike rm68fmi*k qxz1i+:muvha o-4oas e7* if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at t)a8rqs 2:auix he pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wb9 1qj -aa;pyphose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dc92 j,cjvn/ xwmwy ::xB when fired simultaneously at a certain placx29:wnjjc: v/ymw ,xce, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equmnam c 2:p(hf6 89tvjually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pers:pnft6 u9(ha2jvmc 8mon experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to7d68qp :(ty4a o xhrc:f3rjcj have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is thpqtcr3cxra : 6djj8:fy(4 oh7e ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power okvyhx m54u0l kot4mq818kao ;utput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth.a10vyx mmt4u4 oqohk5k8 l; k8 $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ar(tus4 hkn6a j*a3pf.v ea 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 yjm lyq n9x()1y:vac f-dz09fqc 6m1h is rated at 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 )q6yv9zqc(fln1:m -y0fh axm 1cyjd9 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( u vujdclnfh4)7c 3ra3.g.hm .8 m in front of a loudspeaker on the stagglvr()uhfmahj ucd4c33 .. 7ne.
(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. Whnafe,*,ehv * o4wew a0at is the ratio of the amplitudes of two sounds whose levels diewo a h4vw0af* ,,*eneffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by; ens5xa gee2;rm+v/h what factor will the intensity increase?/2xee s+;a grhvm 5ne; Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement am-lww m;gta:/ bhc(h.p5fel y(plitudes, but one has twice the frequency of ;:mlw-ap/.5ec ygfh ht (w(blthe other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in ug)nze1f4 ; b(kxzf;c air that corresponds to a displacement enz f (;fkxbc;u g4)z1amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz ntdu(6 c,y5 t;5ttvcctone that has a 50-dB sound level? (See Fig. 12–6d tcnu ,c56 ytt(5t;cv.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun1xvh4pwn.q,n3rh iof4ai/k .d level is 30 dB? o w.h4qn1 i4hk.ir n x/3pvf,a(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soung+u 5gc,c2m; :tyywke d levels. What is the ratio of highest to lowest intensit+k 2 cgywc:,g u;5mytey 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 lengt (+6t golflbx.h of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed.(fg+ltbl x6 o?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible ovbi46mnyop9 zl*70ry vertones i96rynmil z0v p4o*7 ybf the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across thv9bwc)p m e.y7o rrz)5zngx*-e top of an empty soda bottle that inwz7mrx*p r ))gv-zbo9y5 .ec s 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spa( (upjgxuvu1g+ sg;/jnning the range of human hearing u u pjugs(j1(/g g+;vx(20 Hz to 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 am ;b*w*7aj51ndj uddv frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of ivj*j mddn1b75uadw;* ts original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to pgi: jpzeg3x3*lay E above middle C (330 H3z:iexg *pgj 3z).
(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 em;aft hoce2 ai:blw-(c1y; 3hvits middle C (262 Hz) when the temperaturfcb e2 a- vyh(:3;oc1;witalh e 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 t*d,:+h8cadviy7zmi 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 E*nr)-:1nh po:4 ed2e9 yg klv8ukljfqxample 12–10 should the hole be that must be uncovered to p8n-1dge:k)k rvo ully2 q9pe*h4j nf: lay 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 resonatecc w0+8-ulpee(br 0kz at 264 Hz, 440 Hz, and 616 Hz, but not at any otherz(c pk+ru0ee 8 bwc-l0 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. f :qhr5 +tp6obip3yh8It resonates at two succ ritf6qyb:h5 ophp+8 3essive harmonics 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 (-z/ga4ecwpbnyvx r9 t b o*r0ng+0x1 $^{\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 1aq6 )re *gjogorgan pi gj *ore)q1ag6pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appq omr+w )/bpmagm.mw:xn t-8)roximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate twtnbw+m/o :-. qam mm)8rxp) ghe 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 t 3 e 2gjll1huffcc:c-5rying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is hl fg-c2eucj1 3f:c5l the other string? ±    Hz

  What is the beat frequency i;o bq gv ds ;mm7c:94rf9ysq:vf middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while ana fyp+3wb4(orw *ho8yother (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 simultan4 *obr y83w p+yfwoa(heously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded do+9*niac xb2rw5o.lwith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency oa wi9xoc on52.d+b*r lf the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequi dpcxy,2o7;uency, 294 Hz. The tension in one string is then decreased by 2.0%. What wu xd,cp72y ;oiill be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twoh bz-5hpp in47t8/x zx identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other ahib 4x8 7/p- xzz5ntpht 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44ea;. h .w bjgwbl,jjtp/(yvy ;ne7k7 :1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soj.jy;ykt,vb w:/ hawnl ;(7e. jgbep7unded 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 1.808( thwykm3kugbud ,; 0iej.4d m apart. A person stands 3.00 m from one speaker and 3.e8k3;hdmj 0,uubw(. y tk gi4d50 m from 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 vibrating at 132 Hz,nipo s*2 r. yj22rpss9 but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the s yj 92noi*2rsrpsp.2 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 in air. How many beats p(kpfem3;)v5 gv3p)cnzaf+i xe6;l hdck .ev:er second will be heari mek lv);3e;p hn(cd)3a v5f k:x.6+fcezg vpd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencybi tzs ;7p-;gu of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if youb p-z;s;gut7 i move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. W/*jigfsdey 6:he 4v/ h:aiaw1hat frequency do you detect if a fire engine whose siren emits j1f*/ aes:i/:wd6 ye4gv ahh iat 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 source is movin+c7b 0ibxf/xpg toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close?pxcfx+7b0/ b i $f'_{source\,movine}$    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 sin9eyy; .,6idjh 7g y .js)gioaegle frequency horn. When one is at rest 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 frequ .aise7.g)ioyyjg djye 6h,9;ency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives ne (esc.eab rd7 4 7dkz:op)7zthem returned from rz47s(7ke7.nd eo )cz:a bpd ean object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ahacmja7wl0 mkih k9) s 2g/60,7vucvi t a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecteg0 )/7ah7jcw ma,slvv 0h9ikm uk62cid wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentsjx.fazl;*c *o , a tuba was played on a moving flat train car at a frequency of 75 Hz, and a sez *;jafc*.ox lcond identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mek7j8xt-w7 0cx baj f:casure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the0tccxf b7w ax8jjk-:7 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 ultrasonikp2yb k2 sdpqt :xb87kvd p1(8c waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wiec4d;2 a rh.oxat 2 tp2l6xlgfsi )o)+nd velocity is 12 m/s from the north, what frequency will obtc.)2xe 2a )ldsof46t2+i o ;hgprxalservers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if i; aqbn0/m7n 0ukvldwj ))g;mp ts speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (ak kzjp 0 chkouru3fu1nq )(ct+en9,*:) What is the angle the shock wave mak)uq foc*e91p,(th0: 3n nkk ck+ruuzj es with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the tht4w u;ye.bc .s(mf0 duin atmosphere of a planet where the speed of sound is only ucw ue4;ts(y.md 0f.babout 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 stri9; bsb23ymuf6 ub4uwj kes the ocean. Determine the shock wave angle it yf94 u;6wmsjbub 3ub2 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 775vfjsf+j sbk0)d qm,z-vfz $/theta$ 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 exactlrf o fm, / m/z+pv 7t/ev-qfgld8qa:p(y 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 a horizontal distance of 2.0 km. See Fig. 12–3af (r-vp/g,7qflm+:/z tmpeof 8 dv/q4. 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 s9p; owne da9i:onar device that sends 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 ai dwo9;9epn:200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many edd7qao:/5b aoctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c yzq.ko/ulu3l.,a -caonsists of many plastic pipes of varia/yzc .kuuq,o l.a 3-lous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the throc )f z yj bewdvbipw0o1.h16h .h/tvry52;8zeshold of human.15fb.ivyre 6zbo h;cy/wo2w1hh8 vz)j 0pdt hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when4w9( p(rq1mp bnrwbf 6 an 82-dB sound and an 87-dB sound are heard simultaneouslbf 9r(6q1nw4 prb(wpmy?    dB

  The sound level 12.0 m from a loudspeaker, placed in 9:/z b/;aqr/(ogdxxhn r n3bnthe open, is 105 dB. What is the acoustic power output (W) of3/nbo(qd hbr;ar xngn/ :/9 zx the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at: *c*4d tgip +rpc zg.xi.x2hi 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wathd.x+i*xzg .ipg* p2cc :tr4its at 15 kHz?    dB

  Workers around jet aircraft tys 6eqw dp5td7ghl 3*s;pically wear protective devices over their ears. Assumew e d p5;d6qs7lsth*3g that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicateo bo lpot4 76q:6c1qkions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned16fwuyvytk 6 , 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 miqho(a lvu+l) :+s2n is 32 cm long between fixed points with a fundamental frequencyohnlv2 m+u :sl+a (qi) of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with watervtb 35lgqoehvfpxv0 h:hdu(76 5bo94 (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 fork5 gvh36o5 pbhu47bo vd fh (l90tx:vqe 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 a tube thn*:et tqml afvv9,;i- at is open at one end and also 75 cm long. How much tension should be in the string if it is-aqlv9 tnf*, v:tm; ie to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resowkpj1u .k;zlm9 0sc t.nate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tonek1m c( 4w7sazdg7( hu82lyw3iv6 fg ki in the 500–1000-Hz range coming from two sources. The fu vl8i7whi(asd34w myg7 (k1kc62 gzsound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductomsrjgsk5 /f5 y+h3*sjr on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What shksrfgy35js/+* mj 5is the speed of the moving train?   m/s

  The frequency of a steam train whistlcr, k et6ckk;xfn/xvj:: 8ejr5 h0 xc7e as it approaches you is 538 Hz. After it passes you, its frequency is meax kr0 c:8 /6tf; rx75 vh:cjkej,knxecsured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estqv0:y njlc.iz co/99 wimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a ylwo:0iv /c 9n.zcj 9qcertain 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 uje.,rskw5 7ivh2 v-u frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other k5u2- vrehiu .,svjw7?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastye9 tro-qe+.l:y,bwg a stationary observer at 10 m/s as shown wyb lt.e-e9gro,:yq +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 the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally aboutskw v: *te1hodaa8:( h 0.32 m/s what beat frequ(8h:*ats e d :ohakvw1ency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towardj1 rxid ;b7 9(t)o mvs0cwls 8v2lyt0o the bat at sp92rb8701x ;s (il socotv0 ) yvlmdwjteed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencm,.o 0hhp qlv2y sound 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 tml0.,vhhoq 2 phe 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 sign* wl)9 bc+ bzyimo dyo699sx+yals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about) byzoy x99 +mlo+diy*swb9 c6 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 v,ydwo+z v 8b;listening can be compromised by the presence of standing waves, which caw+v; 8zod, ybvn 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 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 longn p2feq 357 ooaab0:.z k9hmzxd w.yz), slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littl:qx yowoz3)0 fz.2mh.9ba zdap ekn57e 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 5p d7nng;k ikk49u2 qm/ni,)( vlvftnhearing for the human ear at a frequency of about 725) iptnnk/g4,dmuk(lvk9n i fqn;v 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boorl: h8h6r+fpam 1.5 min after the plane passes directly a+6:fhp rrl8hoverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbcfp)km1v:n1 co.4 roroat 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