What is the evidence that sound travels as a wasceaitsx x jgx772wk +ya,4-ukp43iv/ s4c k, ve?

What is the evidence that sound is a form of ejx 34jx/hk*k -.nx hiynergy?

Children sometimes play with a homemamrsj* qfl :a99de “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 clearly how the sound wave jfa*9:9 slrqm travels from one cup to the other.

When a sound wave passes from air into water, do you expect the 9() hqc3dr3fri t*y eefrequency or wavel) 3efhc(3iy9edtq*rr ength to change?

What evidence can you giveabhe29fs .ro:c 1wfq 2 that the speed of sound in air does not depend significantl9 2h cwfef21brso:q.ay on frequency?

The voice of a person who has inhaled helium sof9,2dzvp1 h;ctyzrp3pg/ n4z unds very high-pitched. Why?

How will the air temperature in a room affect the pit x)fw i aabjb/ wb pvsbc6m,3;py(.y(,ch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sountt;u/):( ebzhtx:aux9s.ao i ds in various frequency ranges. (An exampl 9.txstoie/;b :uzth uxa:()ae is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together td5sg.e3 r2qfz03rr u as you move up th 5zfr03 gtsredq32ru.e fingerboard toward the bridge?

A noisy truck approaches you from d-9d zfbtm4l bp01/jq /szmt,behind a building. Initially you hear it but cannot see it. When it emerges anl b ,//fztpz 4m-tmd19s0bdjqd 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 “interfermpt7o/e8xdas r 8k( ,gga9xz4 ence in space,” whereas beats can be said to kaz 4r8pem, /x g7gx9dsoa(t8be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would t*t ra8i bgt,9y-kf4 nmhe points D and C (where destructive and constructive interference occur) move farther apart or closer tog t,9mgfa-it br4 y*nk8ether?

Traditional methods of protecting tt- ti96:isz(-qu,4rh nz hzcc wkl4j0he hearing of 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 more noisew jq6 cutich-z,:z4l9(0ri k4tnh -sz reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–3o5hbd).b q; fd1. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explainb5d) ho.b;fd q.
(12-31)
(12-18)

Is there a Doppler shift if the source andq3od3 avcn98n ld6 * bcctw--d observer move in the same direction, ct--occd3 bna6 8 9ld3qn wv*dwith the same velocity? Explain.

If a wind is blowing,4ls-q 4nt tc,imu 6kpya.if5 0z0 +jgu will this alter the frequency of the sound heard by a person .4 m-si pi0 qkj6n yu5g04fcaz,tt u+lat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.hr4egic7imf c (/w 3+m A monitor is blowing a whistle in front of the child /4w+cfrmh7gi3 (me ic on the ground. At which position, 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 echo of her shiirsg6)br65 yout reflecrgis5 )y b6ri6ted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wnt+1 1hek 2 p /t.m *g5ea*qyq+dhkwxzaterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the o/ q tp hz.h1yk*dxk+1mn*gqta2e 5w+ecean 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 20 px 6(xi/br d6qie6d)o $^{\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 tuna on a foggy,ejk:1ogsxn 5 day. Without warning, an engi5nx1o,se:j kg ne 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. Ther/b p0 df6wv3x splash it makes when striking the water below is heard 3.5/b6rxp wfd03v s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike th us 3wwye;0 iup wz13)ew39gpee concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othez3 ug1uppw9w33e 0iswe;ywe )r 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 mmhc uyoimy)vg 9y,7 /f u7-8rrade over one mile of distance by the “5-second rule” yu79m c-g h)myif uo/r7 r8y,vfor estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ax.t2:u sc;h eht the 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 whose intensitym84s/jbm;7 r pkcc-ji is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of,hhe2rc 1l2b l 95 dB when fired simultaneously at a certain lle h1, b2r2hcplace, 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 ,kill2wz,5t1 wk3mgh 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: Adlmktl, ,1z2h3 wkgw5id intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 h-ipwz0d22u r .h g, tqx4-jmak2 xw3fdB, whereas for a CD player it is 95 dB. What is the ratio of intensities of tuz-hmw3jr a2p .g2,h2wk0 txi4qfd- x he signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sountt*8ub *fj1zuz ova1 9d from a person speaking in normal conversation. Use Table 12–2.1z* 9tuub*aovzt 1j8f Assume the sound spreads roughly uniformly over 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 strik,8soaa y5 mn,res an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whilevd.b/f, u do uptu(l+* the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turnf.t+p ovd( l/uud b,u* 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 f2x/le7vrns +,r/k sn 130 dB when placed 2.8 m in front of a loudspeaker on the stalnnv,2 krfse7 +sr//xge.
(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 typic zl k55kh(nn,tq c.c*)h+tggq ally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9qh,l cg )t 5* .zqknnc(hkt+5g.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bb3 ;r7+f/ akk*xirbe6,drsp jy what factor will the intensita/+k63f ;b7xr ,p djebr*s irky increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudjst45v9:cejg9lc9 ka es, but one has twice the frequency of the other. What is the ratio o 9agkc :949tvjcjes5l f their intensities?   

  What would be the sound*-jg5bvmk5bh level (in dB) of a sound wave in air that corresponds to a displacement amphjb-*vk gm 5b5litude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seep:*c-u)5,lhfz gdg ne c5u,npj ;/wvgm as loud as a 100-Hz tone that has a 50-dB sgp;5fne,u,gv5 gw -/:p ) hdn*cjzcu lound level? (See Fig. 12–6.)    dB

What are the lowest and wn;4e1( 8 qf8lgxpef qhighest frequencies that an ear can detect when the sound level is 30 dB? (See Fig.eqf1(n8 gw4pxq;efl8 12–6.)

  Your auditory system can accommo.x.gh) s jhowxj-*mv w)9b6dx; ee:v hdate a huge range of sound levels. What is the ratio of highest to lowest vw - m6x 9h:hxe*x vd;.hjobsg))e. jwintensity 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 Hzpeivde+p+,n 9. The length of theei 9+ vnedpp,+ vibrating portion is 32 cm, and 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 funda97 ecq rbgao- e8(ijt(mental and first three audible overtones if the 7e-qij e98(rog(b cat pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an e 6hr7/*fp zvwvmpty soda bottl/zp vrwv *6h7fe 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 with open-tube pipes sb:(wev:3d r ul6 ou9bjpanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the dubr 6u l(bvo:j3w:9elengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 54 b*xtzz bjb3*20 Hz as its third harmonic. What will be its fundamental frequency i zz*3bx*jb2t bf it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p2n gby-uca:b2szw *z9lay E above middle C (33za 2sbg c:-ybz u2n*w90 Hz).
(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 kh-,zz-4soj j that emits middle C (262 Hz) when the tempz- 4 -,jsojkzherature 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 cl/r2ymh6 h,3ygk sq3$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute cevw3gq zbr8b(1 8c8iin Example 12–10 should the hole be that must be unco ezvqrw8i(1c883b cgbvered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, anxohhd56;l ec dr ;ix2q.7s-yk3f lt r;d 616 Hz, but not at any other frequencies in between. (a) Show why this is an open ;hf y ;lx.5 -skril 23or;6ddc h7txqeor 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 ecan tpr8 /.s3znds. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What zrpsc .a8t3n/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 ; pehf8s76zavsd3 o ;d$^{\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 wig;-pyw *eh4bf nekc ,3thin the audible range for a 2.14-m-long organ pi bwg *;fnyphec 4k,3e-pe 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 open t eod0hnlw+*d f qw36t6o the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. Whatof +6ld36wtw 0h*qedn is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings,6 c)-s,cgj( +yua g,:vc gny q3k0zoxi one of which is soun i g(gy)-ucns:jx,0+c oyagqc6vz 3k,ding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andtrsgrj;k(7g8ux1vnq2 )rby6u x7bc37e /ur l $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operaap2b:z;a bt6xtes at an unknown frequency. If neither whi:2p x ba6bz;tastle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a5p/ i k q2m xph6-kd-;:kiuys8n3n qei 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explainmu;:sq6e ik iin/y5kn-q8 3xdph- 2pk your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tens6l; lish9. w:vzfq:0n8hurb uion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–1f9n;:b 6uw:rv z. 0lhusi hl8q3.]    Hz

  How many beats will be heard if tw) dlqh;y 7o)lxo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C axlh)qd y)7;lo nd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441jfm .o5(ne3 o57nfgh w-f:(zxfxes /n9 e vvt6 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded to 3(ge ( mnf e56vovsw.7xz - o5f/jth:f9nefnxgether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person s0l*vgngb;y0lv5ge p zjm68g9tands 3.00 m from one speaker and 3.50 m from the other *;gy0en jvglbg6 0vg ml5z9p8.
(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, buthqz1y ) :adkr) 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 kaz1)y) rdq:hthe 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 w. (1w.eunzuwo ;37 x-frk uvttavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume w u n;kvto7tx(.w r. -3fze1uuT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when ath3l5 n+f/:mmmz ss6 vn rest. What frequency do you detect if you move with a spevmnzsm5 f sm/l+:hn36 ed 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 fire eng8sb 2p9agdc/tine whose siren emits at 1550 Hz moves at a speed of 32 m/s cgtdb9 a/8 s2p
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in ytajl+ai-o ;9b.u7ll frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving towardlbu+ail -7a;o9yl t.j 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 the samea03* 94bbyq i8yggh4- bvs cnb single 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 th0bb-n*y sb v3b89 ihyg ac4qg4e frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends 69 j bmqlme22qout ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound fjm9qlq b2 me26requency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a koet9f5,q6hr kw. l6 ospeed of 5 m/s As it flies, the bat emits an ultrasonic wl hkq6ofokr 56te,.9 sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the origin, nn ;-t-krwrrx2uj2ial Doppler experiments, a tuba was played on a moving flat train car at a frw 2r rtj-n,;r-k2 iuxnequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usesi )bif. hmbsu; -s+;p 33ynssq ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if bli n f3yi.+;)-sbps3 uqsbs;hm ood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves oflgct-o k2:q0 ia dq0b 0*jnze7 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 velo jns1l7yn 31)3*xa 0tyt gaopecity is 12 m/s from the north, what frequency will observers hear gj*oyy1e3 nan07xp3stt l 1a)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(hq-pu fu,zn8 if its 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 (a) What is dii2m k *5he-xthe angle the shock wave makes with the directk2eh*xmi5 -diion of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a pl 2(-gnope d8yf5jb g*ranet where the speed of sound is only about 2fp*gj ory5 gbn-8 ed(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 str5 : znw +ry*u0lrdk- mu:c g1d*zxiai(ikes the ocean. Determine the shock wave anglelz +a* *rdg :rwud-xy51u:zm i(nkc0i it 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 o1 )wpy.yjrrh3/9r*pnll j,j$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grounw l1v7in 6 vh)+pftdgyxlc +7:d flying faster than the speed of sound. By the time you hear the sonic boom, wtc)v6ny+:l 7+ 7 xpvlhfi1dgthe plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dodmn p8*qe70lm wnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work i md8q pe07mnl*s 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are 87hu+5xh lg zruum;qw4iz -xo6a/ q6f there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispn hc7mo( 0kf/xlav8y (lay called a sewer pipe symphony. It consists of many plastic pi7mlx(vkof/c ny0 8ha( pes 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 2lj8 wlo/y /oimakes a sound close to the threshold of human hearing (o8wyl2/j il/ o0 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 sound arqmt tidkc(fhm :zj6ynx* id++8 +e +4qe heard simuhk+min: q++tctx6+yfdej4d8(i* qz mltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What i,),lcdd ct ,crs the acoustic power output (tcld ,, dccr,)W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powex5q7dh10il dec b 9(ffr output drops by 15f h1e0f bil9d q7dcx(0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over theic- f+ bt3yfhm9e +es5d-yh6j qr ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by atm+-+ 5 b jyfsdc3h hqeye69-fn unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g3t x5y:o yy8icain, $\beta$ 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 violinz0ahuu n 7h8-q is 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 betwt5 tqg dd(-, e7dg7isneen fixed points with a fundamental frequency of 440 Hz and a mass per segt,d 7in dt7 d(qg5-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 intau 7o3a5m1fd wo 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 h1adauofwm 7 53eard 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 2.1ex:a)ty mgv0/ypp j- 80 g is near a tube that is open at one end and also 75 cm long. How much tension should bxgamt:yp /0v8ej -p)ye 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 observedlpocw) ey)rz0*rru2a;6 l 7c s to resonate 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 tone in the 500–1000-Hz range coming from two sources.v6 m 6)z vcw*jr)sy5po The sound is5zv) r jy )pcomv6ws*6 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 whqyy0sc -y8jb (8lj ) dneh3if/0utt6j istles. One train is stationary. The conductor on the stationary train yu d0 t0)iqj-yy/ 88tjcfh (es b36jlnhears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H.o:q4.da+vpdhsu i g0z. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant veu 0ds+dv hogp:4i.qa .locity)?    m/s

  At a race track, you can estimate the speed of cars just by list4z*i9 vxjcw7rlknm;p 3e7-oq ening to the difference in pitch of the engine noise between approachi q r-wi4lpokx 37jn7cem;*9zvng 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 frequency of 11 Hhg+ p7fjl9:4nik+:) qumtge rz. The shorter one is 2.40 m long. How long is the othe+4peki +rt mhg9fg:: ujnq7l )r?    m

Two loudspeakers are at opposite ends of a railroad car as c bl )9w:kk3kgo1y png-b8tri 9x2 fe*it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency he3*-2gw9brc xkngkl :y8otbki)9p1f e ard 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 0x5a. ,etx df/j.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel /,txdxafe 5j.with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6160rfxd7/oqo a pe83a wpy j sl0ww3j3.5 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 reflects off the mxada0w j3/3qs7l 8w3 0pjpoe1 rwf 6yooth?    kHz

  A bat emits a series of hig5ubv7x /t-.u(mdamzpy8u6i xbl 2zc :h frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abo .5 mxu6x 2- uc8zlb:yib(/pdztu7 mavut 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once fc x*f35utxu--ead s l+)r0 kuused to 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 that only one of the overtones is resonating. The most popua+rlu305 s-t cx* dxfu)f-keu lar 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 compromised by the pre+my)5tp42(8xa j2f y txvb nqxsence 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 the fundamental frequencies for the sta82+nmt)xx2fqa b(yx4p jvy 5tnding waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratip gl*jh ed:3zi2,s8 leon, called “singing rods,” involves a long, slender aluminum rod held in the 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-lo jel2i*,z8 pl h:e3dsgng rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequenwh3c(r *)rzw ncy of about 1000 Hw*zh 3c)nr(wr z 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. 2ce-abg0p(5 n,nfwze An observer on the ground hears the sonic boom 1.5 minf05 2a (,zncn-gpbeew after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbb3ci/.j r di t)+-qxg( s)fhd:1bvsbjoat 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