What is the evidence that sound travels w8 blb(jr1 e:nas a wave?

What is the evidence that 0 ssrkmhkbzb 1mj0-qj6 46a2d sound is a form of energy?

Children sometimes play with a homemade “teleph4z .mz v5npwipom8)t8 one” by attaching a string to the bottoms of two paper cups. When the sovznwz t m8.5)mpp8 4itring is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency ot4edxam. r- l-r wavelengl -4rx.mda te-th to change?

What evidence can you give that the spc kwd+y xq *,mqf17n,teed of sound in air does not depend significantly on frequenmxdc,1q+wn, tkqyf*7cy?

The voice of a person who has inhaled hel .lrd/pwm,i*o ium sounds very high-pitched. Why?

How will the air temperature in a robh-nw ;0stql)om affect the pitch of organ pipes?

Explain how a tube might be used as a 7*5pfp or ua- nuqd+c39/e utbfilter to reduce the amplitude of sounds in various frequency ranges. (An example u 3-bpea5toud*p9rcq7u+ nf/is a car muffler.)

Why are the frets on a guitarg mgi9vdizr. 3 t+goi;8 w4q:vib89km (Fig. 12–30) spaced closer together as you move up the fingerboard vzdt.iwm93+i9gvo;88 gir g i:qk 4bm toward the bridge?

A noisy truck approaches you fr6k t+d k(3pm:z9xui1r yv/pi zom behind a building. Initially you hear it but cannot see it. When it emerges mr tp/pv3+ k9z( u16i:zdi kxyand 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,” whereas beats+3ki+z n (tj mmv :19h/bicoes caih+o(nseb1c9 tmjkiz+ /3vm: n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the spe6d cbhdy4pxs-jadu)3 0i 8s /qakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apd6qy-ps sx 3c) 40hjid8b a/duart or closer together?

Traditional methods of protecting the hearing o*q ;ek3k/hs rof 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 noise reduce the sound levels re/;s keqo rk3*haching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be :cfe vfrmd+9jkj8j/ /n y :l;nthought 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? Explain. r;9:8nn+vejyf d:c j/ j m/lkf
(12-31)
(12-18)

Is there a Doppler shift if the so,7qwt bcw9vsnrv vl 1z -ral.,4:n k0gurce and observer move in the same direction, with the same v, q 4sn0,7v19agwlrtb zl:.nckv -wvrelocity? Explain.

If a wind is blowing, will this alter the frequency of the soun g2 zfrza1:zu:d heard by a personfr zg1za: :z2u at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in ml/iq1f r *dh:cotion 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 the whistle? Expld1rf ih*/l c:qain your reasoning.

  A hiker determines thexa0pn c--.c ww length of a lake by listening for the echo of her shout reflectawwx-p0.c- cned 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 waterlij.wrw3r 2;fk9ujp ai 61u0x gzne. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound up. r2z0xwf;k 91 3ajirug6jw in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng xcarx: ra*a25ths 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 drifting just above a schoo gh8d7f d*b eozo6m7x)l of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How o7gxeh fm 768d* )odzbmuch 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 y.g3uo(epr8un+ n6xyy9ypc 8 3opo +x splash it makes when striking the water below is heard 3.5 s later. How high is the cliff?+8uuyn .9p3py8yr( oe y3c pgoxonx+6    m

  A person, with his ear to the ground, sees a huge stone strik3- n zg0y*+o-32unshvd;fmppyv 9ucd e the concrete pavement. A moment later two sounds are heard from the impactg u*u2 v39- nco; 3dhppvydf -+sy0mzn: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one qqli07/p a.ob mile of distance by the “5-second rule” for estimating la .7q/oqpi0bthe 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 at the pain leveltewc+cdf;63 .y spx-f 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 8crzbl 3l4klx.)kh +l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers ed+: 9f wprhjt12j8n q,+wsz 5udsq: dproduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the +j:w,e:5dzd2 dhqj1utpr8w+9qsfs n sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from anmp vzhkyb)qn1a.. *,2y :iops airplane with four equally noisy jet engines is experiency1,2)kmz:*phb sqny.i .av po ing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-t j1 ogfiq)qww9(f6*frg z9b,c o-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is tg(j )6 1f,rwzbqiqg o*9wc f9fhe 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 speaking in normal conve w88t k8en6:xyze b*lbrsation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mol tnk86w: by8*bx8ee zuth. $\approx$    $ \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 ams*de x.y a74uimgb 4*oxwy)4rea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B fzxt)w7ow j*3is rated at 40 W. (a) Estimatzfwt)ox j73 w*e the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plmkyf,2y6b ; mzaced 2.8 m in front of a loudspeaker fy 2yk b,mm;6zon 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 typicalwgb)qb,p;z s(ly detect a difference in sound level of 2.0 dB. What is the ratio of the s;bzpg )q(,bw amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a s4b w9vnr0d:/n mhfm e)ound wave is tripled, (a) by what factor will the intensity increase? Increase :hbmn 09/dnwmvr ef)4by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twi.5+n 0en.nkhq;hx ioyhok /9wce the frequency of the other. What is wioy nk 0h;o9n5..hx/+hnq ke the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wm*wvz6, wai vmon jx8l;h-l(-ave in air that corresponds to a displacement amplvowli m*x h ,l;6--v8aznjw (mitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what1 *if*kj2bd1)mr nw;4 xaw nuk sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. i)21w*jmkf*nn4rdxk b;1w ua12–6.)    dB

What are the lowest and highest frequencies 7+d2tys411 kqsqi 5okvn8bi othat an ear can detect when the sound level is 3it7kyq obq12sn4 s od8vi15+k 0 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hn m-xy4r18qdd uge range of sound levels. What is the ratio of highest to lowest inten-4xdnmy r 1q8dsity 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 leng6lct(ww 2 a1p1yqf:bnth of the vibp2(ftcqb:wway6nl 11 rating 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 fundamental and first three audiblh joyj15tk(3; ie yj2ee overtone ik3e2ohej y(y;5tj1js 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 would you expect from blowing across the top of an ear47 thdhkf )zd0 s-6vmpty soda bottle that is 18 cm deep, if you assumed it was h-6hs4v0tkfa7z rd d)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 wi k0hsk*ckdt(- th open-tube pipes spanning the range of hum0h c*tk kk-d(san hearing (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 a frequency of 540 Hz as its third harmonic. Whq 3id v2k4z,sgat will be its fundamental frequency if it is fingered at a 3qvd 4g2,iz sklength of only 60% of its original length?   Hz

  An unfingered guitar string is gpzle)q, ,idw z5 ,e9tk ptrca1vd6 o d,lj6700.73 m long and is tuned to play E above middle C (t oqdlpez 7 jip6)95d,d,cre6v tkl w a,01g,z330 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 that emitss wr(f39lx+ta1w b v* h8l-bi,ptd63 pfb 9jkx middle C (262 Hz) when the temperbtbh 33 19+fl(awb6*wx9pxk 8vld,ij-rt fp sature 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 ape:wm2 vpe)9( j+lyt0rxp os8t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece sy2eduzx3yb9 l e-44zof the flute in Example 12–10 should the hole be that must be uncovered to play Due -4yy zsxd493z2bl e 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 616 Hz, but not at a(np 9ham.,ly76wztt uny other frequencies in between. (a) Show why this is an open or(7lam,y pu9zt th.wn6 a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.8g05cl8il o6 oqoh (ep80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz anoclhql o p5i86oe08 (gd 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 s8 bf.wq1iyx 2j 1k.lm$^{\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 gs:7 w:q9xmev4, dtz paudible range for a 2.14-m-long organ pipe xz etvs:,:q7wdp g4m9at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm 70ell4 olf8rklong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequo0 frl7k8el 4lencies (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 bei:n;x rc25 .-krzl xcwat every 2.0 s when trying to adjust two strings, one of which is sounding 4 l5cicr x.:-; zkwxnr240 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)9ypc oi-c+o2e b4jx6j and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) opau w q1,ht.ab;erates at a1.thwb ua ,q;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 simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wih *v3xny;6ngxth a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yon6gh y3v *n;xxur reasoning.    Hz

  Two violin strings are t jk p(pgnh+7 +eoel7m7uned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Ree 7m7 ghn pj+p+o7lk(ecall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C (a 0xgi4 /iuvd+262 Hz), but one isa+g/d04 uivxi at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a freque9q5wz;g,/v qc4mr u:h phui2r(jkdr *ncy 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 possizg q (*ucjkd5mrh: prq;vw/, 9 24riuhble frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. Ay0+ iw she**,pahn7b6 v26gwtp 5aniw person stands 3.00 m from one speaker and 3.50 mg2i bwphv*ptn6+y aahww5e n607* s ,i 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, r( wg.v4-ozxnbut a piano tuner hears three beats every 2.0 s when they are played together. (a) If one4-( xvrzg won. is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in aig j2py8si0s6 o.vme8 qr. How many beats per second vg6280pi 8.s ymsoqej will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s rd.sxz22t*g ,mwc e8o siren is 1550 Hz when at rest. What frequency do you detect if you movcs.mrtde wg2zx,o *28e with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if l)-2f7t4s 9flniwhk na fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s ffkws9 l) -li2n4nh7t
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving tow)-qo:wxfjo x 3ard you at 15 m/s versu ox)3oj-xqf:w s you moving toward 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 wjqfq6z 5vs ;x1a:jy+ vith the same single frequency horn. When one is at rest an+q x :z 1fsvya;q5v6jjd 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 yxx/wozu0 dbe*( 6i8lqg8)dd and receives them returned from an object moving directly away from it at 25 m/s What is the receud6e)l xi8x8z0 boyg/ dq( *dwived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall a2sx2a a7jx7qct a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz727xj2 qc xsaa. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on y1//fvtezhbtw-i; .iy-5 syza moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the statioeih1 -/ ytfy/y t.b is;-wz5vzn at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bb0zdwo )mza5 4tl50 oilood-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 freomaoi5d t )blz045z 0wquency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency i4c:mdn6migkb+ 6l j bm 89j iz* mzhea)27l0d$2.25 \times10^{ 6}$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 ohc 3fyq)/6c6pi)ajze ;wb7 qqf frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at res)cjc7 he6 ypq)6 bz;q3wf/iaqt,
(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 x,xb7l;eo/j wits 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 28uj oo5cj 7.ycv)+pmgdw k0.g.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the digc jo) koupd.5ygv7.mj 08c +wrection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where thfr- ora hi lprjy1/.b6,yb33he speed of sound is only about 3r3 r-joa y/ rb13,6fhy ipbhl.5 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 st6zf8nfl +;ax tzun vs2/hln65ijew;2rikes the ocean. Determine the shock wave angle it pronf sv tn/nx2265lzze;;h+j8 uwa f il6duces
(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 heh n)l,z54 ji$/theta$ 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 grouy7yhvkqu.iu5 + t 4,esnd flying faster thyy7+4u vsthe5k u.iq,an 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. 12–34. 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 downward fmso8yy hz 30j;rom the bottom of the boat, and then detects echoes. If the maximum depth for w8j m;shz 0yyo3hich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humayczx(zp6p;vp (y ol.6- 8a nian audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mat1x dwsu/l2 x*ny plastic pipes of various lexx1t2wlds /* ungths, 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 ma.t6 z7c t y*przr6qw5kkes a sound close to the threshold of humaprcktq .wt66rz z57*yn hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level wher 32 pbx u4nlw (khcik(.5p5ern an 82-dB sound and an 87-dB sound are heard simultaneouw un(r5pkpr.2ekci(53b 4hxlsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whab2h7 xht+qf/tt is the acoustic powe 2fh/tqb xth7+r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 15z/u 8+ zd* 6irjpi*hvc .:okuf0 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output z+k8jvc6z/ u*d.r :of *hipui in watts at 15 kHz?    dB

  Workers around jet aircraft ty9++:5u*ezif;wnb w q ghu*tb ppically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet air*zi5n9+ +w ubg:phwfuq te*;bplane engine?    W

  In audio and communicationstdq- 2e,pq4 tih.; *(1h2 odbq vyvixg 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 tuned to a)hy vytr8q zg,k, hy8a kic+0+ 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 violini59sui.uhhv / is 32 cm long between fixed points with a fundamental frequ .s9iuuih/ h5vency 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 wit0- vn/sdhaw. ykv x1o,h water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above thyvwn-h ,1d/sx .0 kavoe water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that)drs7w72r/s ss : pdjl is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmo 7 7sdrl/):2djswprss nic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l fpz.ej++otyp;8b k3voop ($\frac{1}{2}\lambda$) 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 twbw3 bemkxz.nr h+an,gfd ,p-6x2-h v3o sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound dm-2k. pf3, e-xbb 6h3,w zgn+rxhav nlevel 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 condu, 8fa 2sa 62wrchyy+kqctor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tra+cys2fa2krah ,6 yqw8in?   m/s

  The frequency of a stea y/)ol)yqct. pm train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hcp y)) qo/.yltow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to mgk7 0dmn/sl0wz/+ze the difference in pitch of the engine noise between approaching anw z/+m0l dszmk/0g7e nd 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 bea7d )cw)a x pwsi2arn(5t frequency of 11 Hz. The shorter one is 2.40 xscw)a)(2wa 5ripnd7 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a ra26 jhv9 y (-l 9nk0ndk.czj, u:jmefiqilroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound fre0v9k: fe c(jldj-9q u,nzk2jm i.h6nyquencies 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 ioe 9lld*3 d og,j)pg9is normally about 0.32 m/s what beat frequen9* ped9gli l)j3, ogodcy 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 s8d mxencz-bzq9 y9i61peed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off1ix 8b-qd9enmczy9 z6 the moth?    kHz

  A bat emits a series of high i84 :n7h cekeqxu j85nfrequency 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 bne:8e j5k7n8 quih cx4y 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 Alpiz3zu i0m:i nj3p7tqejq 3er7 ;ne 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 thatee;mzj qi:t7z3 37ip nj u3r0q only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by p(4wcccsl/w 1the presence of standing waves, which can cause acoustic “dead spotlc /w1 wc(cp4ss” 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 wj 4 yqlsqd4m 32e,,*, kt(swpme(9/fq odkhma long, slender aluminum rod held inwe,ohwm d9qp,f 4esskq tk*,ml 32q/((4y jdm 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-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequenlrm yd ca c/;g7:7aed:cy of about 1000 Hc r a:gc:7/ydae; l7mdz 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 2is55 zk*4tt+v cuyf- w9i kdx1.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. kdx 559i-ck ywu*4sittvz1+f What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat7 /zzv7iwks .j 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