What is the evidence that sound travevq7ji2a3)y w)wru0p pwrg ie);g ed*(s5ow-b ls as a wave?

What is the evidence that sound is a form ofo/w 85:lq2bx1pxqjo c energy?

Children sometimes play with aw xv1,isrq3) s homemade “telephone” 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 clearl) 1v,sqiwrx 3sy how the sound wave travels from one cup to the other.

When a sound wave passes fro/ukio3r 7p3 bcm air into water, do you expect the frequency or wavelength to 3/ uio7k3 pbrcchange?

What evidence can you give that the speed of sound in air does not depen.8dlmnhs82s a d signifdl. 82hma n8ssicantly on frequency?

The voice of a person who has inhaled helium sounds very9ul;n v1v/wmb high-pitched. Why?

How will the air temperature in a 4..cnq0tin y9fj/xh t room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitudz9k7u hns18 tvfu:p )te of sounds in various frequ )z9hnku7 8t:tp1v usfency ranges. (An example is a car muffler.)

Why are the frets on a guitar pjp 4 pkny-;ru;lup,a)xo/l. (Fig. 12–30) spaced closer together as you move up y lrp.)u; pon-ap,j /; lkuxp4the fingerboard toward the bridge?

A noisy truck approaches you from behind a builij:r5dw -th3j ding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mo3ij- hdw5:tr jre of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “intunmqp ;6h,z :ferference in space,” whereas beats can be said to be due to “interferencep u qmzf6;h:n, in time.” Explain.

In Fig. 12–16, if the frequency f1 c hljust*)com.8 (bd,mn. bof the speakers were lowered, would the points D and C (where destructive and constructive interference occu jm.dh1 *)ncfo(mlb8t,s .cbur) move farther apart or closer together?

Traditional methods of protecting the hearing of peopy) q(,m.j akz90 lovofle 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 th,loovzqj (m9y .a0k) fe ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Figc azc4;dm(98juisxe-. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different fzeu d s9 c4-cm8jxi;(arequencies, 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 ax+qwaw+l jpm8k+ x7t.wp: h( if the source and observer move in the same direction, with the sap .ak jxtm (ha+wwp7q:8+wlx+ me velocity? Explain.

If a wind is blowing, will t *;dvwpvv+5 vypshwh+hs6 *z1his alter the frequency of the sound heard by a person at rest with respect to the source? Is thd vpsp hzwv*;s5+*v1hh 6w+vye wavelength or velocity changed?

Figure 12–32 shows various positions of a;u2 fvuslo7s d5 -nry7 child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the7uf7 2snv s-yl;r5odu whistle? Explain your reasoning.

  A hiker determines the lergye x izx3pg;+ zgrj/l3j3- 6ngth of a lake by listening for the echo of her shout reflel +33; z-yri6xjxr 3/egzgpjgcted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the /ujpusgescq2i .82)k side of his ship just below the waterline. He hears the echo of the sound reflected from the oceq22j/up c8u.ssieg k)an 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 waveleljuu0mxiw)jj26 8 g ;ngs4 h(bngths 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 driftiojz4n +hm 6/t*.uskh dng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befm*t. o zkhjs/+4 n6hudore 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 s7yyy.4 f2ir 0y frc7dcplash it makes when striking the water below is heard 3.5 s later. How r 2iyy7d c rc.4f0fyy7high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike+3iwz0; gyhi m 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 th+zih;m wi0 3gye impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance bycik /3-r-l gfmir3rt (/-p ntjx8r i.e the “5-second rule” for estimating the distance from a lightning strike if the temperature is.rrglnfix r3t-jtc/ri -i8p/k(-3e m (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lev3mm7r8hnl guw4 )ue.iel 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 levea 5/c2ldu9 bt0(y1myngd ul :sl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously1/;llgyw nf0v at a certain place, what will be the sound level if fwn/vy 1g0ll;only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanem .t h 1(.zp ad-v.tzszr;g)k,anjql+ with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would aa +zm (nl1.v; s-,k) .qjh.rtzzdpgtthis person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 6j)q /rb- .oxiqktrs+58 dB, whereas for a CD player it is 95 dB. What is the +x-r6qk.)jt iqbrso/ ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spec + 0cynw/q:aejh55c-0cd pw vaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly overc:cn5w wv c-ap/c0 qd 0e+hj5y a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ar3++jcjh5da6m9y.f/ b p hg .fxcjftq3 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 is rated at 250 W, while tvecsi/ 6 9xxy+he 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 connected in turn to eacxis/v9x ye6 +ch 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 2.89lmeig d(m329 ing 4qvcb/ r0a m in front of a loudspeaker o4gdn v3bmr 2q9ma(l/ie90 gi cn the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in slx dc2r1(rios5wukdr7q( ; r8 ound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectu l(wrrd 2rc85 r1idqs( 7kox;ion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intensi5m1nm;xi hj4wty 5nxh1wj m i4m;increase? 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 j2;y jj t58b:css rpm:has twice the frequency ofcy8 p :sjrj5;sjbt2:m the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponq ctcnp*3q;.uds to a displacement amplitudet q;qcnu.*cp3 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 ton 09anx;jxnyc )e that hyxc 9)n0a;xjnas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detectt09 ;or lgv0gv0ji 4ur when the sound level is 30 dB? (See Fi0rv l04 t0 gv;9urgiojg. 12–6.)

  Your auditory system can accommodate a xx)gm 1.3ibxm huge range of sound levels. What is the ratio of hi mx.bx3 1g)ixmghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental freque yc.ot b/m,e9yncy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mu9e/cmoyb, .ytst the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aud;o p/px gz5fd- dqu/0nible ovzn;fupxo p-g/5/d0dq ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency wouldo/ge3o: hu bj zg6 n0gn8d1:no you expect from blowing across the top of an empty soda bottle that is 18 cm dg bg: 1je3/ nzuo8: 60nonohdgeep, 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 ;wdod,j t; g+h-r j6ivwith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), wotwvi +hj-; dr; 6dj,ghat 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 harmon7 9o1zc*d6kbef,lrgi ic. What will be its fundamental frequency if il61be,rf7 g9d ckio* zt is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long ad4b jj(4 o zve+xznz76nd is tuned to play E above middle C (330 Hznz v46xj b(z+ez4do7 j).
(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 middle C (wov/bu cc/n.8i k91ew262 Hz) when the temperature is 21 e/bic/n1k.8c ov9uww $^{\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 n*g l m06k zkoff2,n5(kl-zla20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the6(fueq+/ m p.(yfykbbnw(9c t flute in Example 12–10 should the hole be that must be uncovered to play u(t9y(y + b/kffqc6mnbw. ep( 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 6m7i:7 n; e)r2-fgsuktfk)k sj16 Hz, but not at any other freq7su:if -j;kke)nrsftmgk )2 7 uencies 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 1.85,: ri y sdw72hdxk4y1n,e5p,hssh db0 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 1dkwns hye4sp dy ,2x5:, hsdih 5,b7rHz 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 c/*g-;m+im( w 5dcabvx)j 6cls: nkrs$^{\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 ty2j .efibi3:pm 6od /nhe audible range for a 2.14-m-long organ pidbmnp2e6i .3oy : f/ijpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is edw8u-7nqo nm2m3j 4w open to the outside and is closedqd4nmj e-82u nm7ow3w at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears o +5s bv01fonftne beat every 2.0 s when trying to adjust two strings, one of which ifot 5 fs01vb+ns sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle fcrop -nd:0 y5C (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, tgesdchh,ri7 k6 u7+w) yx66 ywhile another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played ser+,7shhkyd 66 w 6t7icg)uyexparately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded,(g5bz+v pbp nf7av8ncd 5-y m with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the g5dm7fyp ( 5-+ 8vazbc,nnpvb vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are e5k; 0f; knvyj:kmky2q:s.rn tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the ben:2k;krkyyj :. eqs;0 m5fkvnat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hexhlu3/ grl /7 /oeu(-geq0l geard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ot3g0g7uleeh/ gu/lxr /ol q-e( her at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.wi4xo /*h/p - wli9hvx Fork B has 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 possible frequen*i-i 9lw//hxhvwp 4oxcies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an vg-/9s2(d ql5sqf,. ssckokpd 3.50 m from the other. -flso9gqs5s2 ,kqd. kc v/p(s
(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 supq:h4,qzig ari1 og46uru1- jkposed to be vibrating at 132 Hz, 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 mgoirqu: 4ajqi1 ,g6uzr-h4 1 kust 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 opnf):yw3d dki mxk 7lfs8ss7h0u3 i5:f wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T5ds:km8n0yhps3)7fl3w xdu7 :f i ksi = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ceegwn +6n k8ukd)xb.7(e oisij 35 etr;rtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 j 7ki d.5ek8ub(erx3 +i n); wes6tnogm/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stillh2bye ,wcv7ud+fph7,na. z 6z . What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32uza6.e2,hbwn yd,c7hz+ f7pv m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fr;(/3z) cnjmb pnqjdd 5equency if a 2000-Hz source is moving toward you at 15 m/s versus you moving tow;c/n5p3 j)q b(zjmd dnard it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with w a4 kxlj;e:ni+2alm) the same single frequency horn. When one is at restkj; )2:wiem lnl4xa+a 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 receive (iyx *lve*6wt zf42nxs them returned from an object moving directly away from ey(6i*4tvnf2* l xxzwit 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, thodesg0iwl8::yl3(x /c 5khwbl g-8j he bat emits an ultrasonic sound wave with frequency 30.0 kHz. Wdw 0:3h8gyj:8i(whck /lbs-le5lx og hat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playl *.zqk8;7 ;sba ve kj59blufaed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard ifz.* jlkbv7uqka b; 5asfe;l 98 the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavesh np*59 k j:rrqbg95ct to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and t95*bkpnqrgr9c 5 :jhthe 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 ul wze8+4gr0jmh trasonic 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 wind veloc,rz:+ oyqw.gvity is 12 m/s wo q, rg:+y.vzfrom the north, what frequency will observers 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 its speed 97, a/gg fc ow58prww1t:fzxwa 21a shr b;t+lat 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 (a) p b8gwf,65sr) wi1u lqx52 uvmvqd 38xWhat is the angle the shock wave makes with the direction of the airplane’s motilb xv 2qr63w)8pivmg5x1u,5d w sq8u fon?    $^{\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 sb8r9o9o mka/z peed of sound is only about 35 m/s obzakr o/98m9
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave au)go i56qbi2 xngle it producesi5 gubx)ioq6 2
(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 sq q,e(.hn + ta9z0o pz )svlw7c ;ct:(;capqq$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan80.l;k9 hs fsc5h:zxz .uuybwe 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 5zs hy u:.9x .lhwfskb0z8c;u a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound puls)3 hzto*mide/35 agz jes 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 minimum time between pulses (in fre ei/5 3ajhzgz*d o)m3tsh water)?    s

  Approximately how many octaves*toy c 31psg+l are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display caoot0 jf,w7e i ut(:tu:lled a sewer pipe symphony. It consists of many plastic pipes of various lengthsw:jotto ,t7i(e: uu f0, 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 then8fq0t pyy uqy*kg) 9: threshold of human hearing (0 g 89y0f)y*n :ukqypqt dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB souf+k pshvi yo6p93(zr 5nd are heard simulty5 39k(zpsvfiop +r6h aneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What wxo eqw.k zcc :wi1yf n(*/np86ot 0m1is the acoustic power output (W) of the speaker, assuming it radiates equally in all directiopi1 n(c: 0ck6wf8.1qxmnywz/wetoo* ns?    W

  A stereo amplifier is rated ar c( 6)a0tidaeii. 7ibt 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts rb 0dc6(iii7) .aaetiat 15 kHz?    dB

  Workers around jet aircraft typically weaba)dsl s,)*zh r protective devices over their ears. Assum,)) z*dlassh be 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 communicatikm 55fzpyb/ e4ons 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 iso fmtc20 :uq;xcig6s 6 tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamenf6(7 zwib y/nb6z (gmommr, ufu.ew/:tal freqirfm .b:w b(u6f,n/z(6um/o 7wmz gyeuency 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 int us:q)zm/8uqtd g/w.ro vibration above a vertical open tube filled with 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 again at 0.395 /usm:zq8u rgw /t dq.)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 kgjuek,u 3 :4sthat is open at one end and also 75 cm long. How much tension should be in the string if it is to produce reson3 k:ekguu j4,sance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loo+ b3.81miol2(t01dycjas rr :olprv ep ($\frac{1}{2}\lambda$) 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 coming from two s,y n5pc(h4 wnuources. 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 lpn (5w,n chuy4evel 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 conductor5mzy3,qj;4ykb fd qg2(nt 8fr on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mo;5( 8 gqk3nmz,y ry2td4qfj bfving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Af,di z ;m8wfiv/ter it passes you, its frequency is measured as 486 /divm8fiw ;,z Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed vjn gb,r 82ba9of cars just by listening to the difference in pitch of the engine noise between approaching andv8b2nbrga9 j, 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 frequenczjh2rhj* 2y r3y of 11 Hz. The shorter one is 2.40 m long. Hoj2r jry3zhh*2w long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movesrc0c 6(:ieb4i (bsndl 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(6nc (0br4 lidcse: ib B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flo4 qrdxq0m :i( g.qe5af.ezxut(p 3 3uow 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? Axgqpz xef ma do:uq5.3e(qru4t.0 i (3ssume 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 6dwmiz7e e4ma z1l881+4 mycwi.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 bat after that wave reflce41lm w74ya8 8i d imz+w1ezmects off the moth?    kHz

  A bat emits a series of high frequency sound pulses.:-j2y djiph6e3b hzj as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. 2jyejp d3h b.j-6zh:i 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 Alpine vz ftydm5t4, j9l j5i*+qfd0sm illage 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) hor ymt9f45l+50,itjzfq d*jm sdn. 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 compromised by the presjh m3+5tl5vzxm7xul *9nytee m5d./c ence of standing waves, which ca3*n 5mhx cu+yde.t5l me/z97vmxj l5tn 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 “singin c pc,-43ksilkv p;r.cg rods,” involves a long, slender aluminum rod held in the vc;skp,4-3rkcl . pic hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 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 f1eu oz;g(bn)zlm u1m*y+z uq 2or the human ear at a frequency of about 1000mynboezuq 1)gu;*mu2 lz1z+( 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. y 3kjeq(pj 56bAn observer on the ground hears the sonic boom 1.5 min after the plane passes direcyk6(3j qej pb5tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ldn bfb x/oi.*is0x (xbi5 a1x8;ke;w $^{\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