What is the evidence that r/rd5mot p s8x.nk/9x)le4 wssound travels as a wave?

What is the evidence that sound is a form of energy?:ff/birs,6 e a

Children sometimes play with a homemade “telephone”z1iju :gcu u29 by attaching a string to the bo:uuj9 iuzg1c2 ttoms 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 travels from one cup to the other.

When a sound wave passes from air into water, do (2 t6j0 -et qztds/d3e w9tdh.amuy*t you expect the frequency or wavelength to9t2e wd6j-as/ey t.0mdtut(dzq t3h* change?

What evidence can you give that+a1ojgf , c :eu: 3.wah3ctzji the speed of sound in air does not depend significantly on frequ,co jh :t3.i+3cg: z1fjaeua wency?

The voice of a person who has inhu/f ld:a5 9n gfm xij8ku0*yxo5z r*j/aled helium sounds very high-pitched. Why?

How will the air temperatu;mrokl9 f458 sl-tqbzre in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplklh1h5xr *v ,yx/1 ti.4ne wdwitude of sounds in various freve5nd*1kh,.4 y1wx r/ ltw ixhquency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closy49g dt5+k+ 2tzdnsmyer together as you move up the fingerboard to 2 +dys5gmknz d4+9ttyward the bridge?

A noisy truck approaches you from behind a building. Inio0vhizj+j f *,;0cc 0pbfk9 autially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the0*pf 9b fzv;ukoi ,c+jcha0j0 high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in shwe *sp4k 0./6lu 9nrftetz- space,” whereas beats can be said to -s. wu *pk0n/eeh6rlt 4s9tzfbe due to “interference in time.” Explain.

In Fig. 12–16, if the frequen2;e6.e( r wwflhp)i blcy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther aparrewel6 l2hf w(.)i;bpt or closer together?

Traditional methods of protecting the hearing of +4af4d*gk 5fcnhytf+ 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, i kd44ny+ 5fhf+*gf actnverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each 0 a7iik 9gnxtv5nki 2;wave can be thought of as a superpositionx av5k7 ii9g20tk;nni 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.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsq2s fr3+uums8r+;a, upd4qu werver move in the same direction, with the same velocir+ qqsm3+du;w 4u28 up uafsr,ty? Explain.

If a wind is blowing, will this alter the frequency of the sound hef3)o 3 r0:dggpnoce( q1pqa:stet92r ard by a person at ref0 q s9or1nge3ecr:p tdpa)go3(q 2:tst with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in m hsdgriza 7.h: 8i6xcjal6b*5v))w ytotion on a swing. A monitor is blowing a whistle in front of the child on the ground. At whic 5wzgtil:r6)js)dav6hx yc8* 7i. bhah 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 shoux4mmm:d:j3mfx m wuxo/* i 5r(t reflected by a clif3mmr5om jm:x(uxxm /*:dfw4i f 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 moo( oociai. ()yv+0e69 q xbnof his ship just below the waterline. 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 in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depthc0 mxo (6y.9 aoo+v()bieino q.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air-csme(;6mw j o 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 drz3( *in dw8eli al0a. r6bwbn8ifting just above a school of tuna on a foggy day. Without warning,(r.i 3z *l8i6w bn8dw0nlbeaa an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes why;p37tziw0 qnen striking the wzpn wi7qy3; t0ater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone str c/z5b(ovaww1v xoe; t9ljw )u,b* u,dike the concrete pavement. A ( axco)5 9vu wbdbzw;,o,* u1jetw/lvmoment 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 the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “nlt78o jx-)le5-second rule” for estimating the distance from a lightni7 jen-l8o) xtlng 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 level of 1 w,57bk 4vnn.ree*i zz20 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 intensity c+y/uj2um6az is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wh57nc:f *fr-zf zh8fojen fired simultaneously at a certain place, what wi rzo -5fcn z7j*f8fh:fll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplbh, .qz; p(g*lb-f/ih/ jroi iane with four equally noisy jet engines is experiencing a so .g/r *lii qh,j/;bp(ofh zb-iund 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 tp8:d j8anod4j o have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise :j 8ojd4d ap8nfor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power out, nje p 7f(1pxhqw6zr7put of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniform p efz1r,xj7hn7q w(p6ly 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 strikes an8ih*k6,ogj2+ qygmb o 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, while the more modest amplifier B f ;ez0t0nj dw3is 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 eachj0fe; nt 0wd3z 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 2.8t6(sxp/wlg;c+v q;w 3) ohw,h rtwy :i m in front of a loudspeaker o:/, +hisw;wy o;wgtqc3(h 6t)vlx wprn 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 sound level of 2.08)w-teqo* lqd dB. What is the ratio of the amplitudes telw 8*)q- doqof two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tr*u3c(sz+ i)1wgu jlxw 7ucyy :ipled, (a) by what factor will the intensity increase? Increase y+7w3*jc )uxisz u gyl(uw:c 1by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, r r5g:vijq am9ytt,p626k m5u but one has twice the frequency of the other. What is the rap9rrv565 tmau tkg j,26mi q:ytio of their intensities?   

  What would be the sound level (in dB) of +lje f *yusi31a sound wave in air that corresponds to a displacement amplitude i u1+f* el3jsyof vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sei4ig6g eduvgd5nf)1*:(d kzx em as loud as a 100-Hz tone that has a 50-dB sou :ex(k)gdg6 n54zu*dg dvi i1fnd level? (See Fig. 12–6.)    dB

What are the lowest and highest freque k6f(sf)o5a dkncies that an ear can detect when the sound level is 5 ffd koaks(6)30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound l tjztsq.)-2 nnevels. What is the ratio of highest to lowest inten-.2tzqnj)stn sity 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 le*lc xd,7; jxf)x)px sdngth of the vibrating portion is 32dx , 7 );xpx*ldjsfx)c 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 lous- f*v9 *kxmzng. What are the fundamental and first three audible overtones i kmzv9*sf -x*uf 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 sh.f55 ;w8 dllsugk-f blowing across the top of an empty soda bottl w;5 ff. s8ukgdhl5-lse 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 spanning the ranl4zdmjfdyp /p9a* y e;kofq.8y45y a8ie t5(nge of human hearing (20 Hz to 20 kHz), what would be the range of the lengths9my dfq5kyoj/t4dy*i8p.l ; naf ae4e 8yp z(5 of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540zkq+7 k*vrm) pecq)*wq0:dz t Hz as its third harmonic. What will be its fundamental freq70r+ we tckvd ))zp zq*m*qk:quency if 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 play E abocftljkmq7 9 9-ev- 6dbve middle C (3qvm9let6 b d-9fj -ck730 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 oadr r3y* n;+ax xkv8o;pen organ pipe that emits middle C (262 Hz) when the te*o +na k r3r;;8dxvaxymperature 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 2-z,9 d nrpjk mq7d(lu50 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–1,+y ojsd 2ptyh; mn7d5uqi ;4i wyc/s00 should the hole be that mpim,/+; n7q20tysu 4y;jh io yds5dwcust be uncovered 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 caj*iybagi d;ue gkh61t,pr1+ )n resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pi1dp+y *gre6,h kagj )bi;iu t1pe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resona 2 exwjm3 kbaju-9)p,ates at two successive harmoa j,p mk)x2-ae9 uwj3bnics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 nrqdq+)t8,/2xl+ug bpv j2ey$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2,v c/vy3bq7ga-)d hjy.14-m-long organ pipe at 2y jg 3dyhvc-/ q),avb70 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm l4jzslb) 2 t2s2 p4auyndi5 5szong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves nslsz sib2p5224u ytd)45zaj in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to ai:r4j3vmdp3zm: va +edjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other ste3:iam 3vzdp 4:+ rmvjring? ±    Hz

  What is the beat frequency if middle C (262 Hz) igtm08g u:d .kaikok,8cp u4xb0 u y2k4m))wgand $C^＃$ (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) operaee c 8s2;9ko 0od/hgbvd/b.u gtes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultane 0/ uee8ck.;o hb29s db/gvdogously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 be .sg,,n 1 e8kewvblggaz m:9f5ats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-e m ,lgfn.1wbgk95g:,ze s8a vHz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings areepn;t0)8u e gtbpn)i( tuned to the same frequency, 294 Hz. The tension in one string is then decre n 0u);nptgeti(e 8)pbased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two fnx ys0(/07z sa hhc2qukf n**identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other ahn/h0n*7uzycsf(x0* s af k q2t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B ..u;rnitliwqv+j p ( .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 frequencies of A and C? What beat frequencies arjt(.i+l.wvp i. rnuq;e 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 andfb ynnk ).2.zh 3.50 m h).nkf2n.zby 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, ff,2/ +yopr.ks lmpcd83-ybl but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz,3yfp,8rf obk cl+d.-l/ mysp2 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 air. How many 4i19ftyp t wczr cwo 6x.q2u):beats per second will be heard? (Aqc.f:6ty r)1piz4 cx2uw 9wotssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when kcdt pw/ ) tvivkrbw1(++71)v lmbb:iat rest. What frequency do you detect if you move with a speed of 3 1wvbcmb kv1/dk( li pwtv+b: ri7+t))0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fmf 68/hwt gbc,requency do you detect if a fire engine whose sirechw m,/86g bftn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving to c(nlad /n0)vvh19izl ward you at 15 m/s versus you moving toward it at 15 (nh c/ni9d1)0avllzvm/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 same single frequndg f6;09df jjjr(mn; ency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest j60 frfnj (9gnmdd;j;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 0phqh 46p yva5out 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 ph6qyvha 04p5 frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a.wx;h,oo bwglu j0:p.pf 57y t wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hj,p.ol7w phbwof y.50 u gtx;:ear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pla x6tw 8n2lv5pjyed 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 if the train car appro52ljp x68vn twached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses 4bdf an/l j:i lo/u9c(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 blood is flowing inbll 9/f:4cjan oi/ ud( large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrjy2ub0 *r(m gwasonic 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 ai 7q:o9cga(r the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest,g97oa(q:i rac
(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 3tz0w6 x)7 kppbc 3fwnqs h,l6if 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) g ,;,kg r-dg6bdecz/+o- sbwp What is the angle the shock wave makes with the direction of the airplane’s motiogb-rd 6w,p/- gbgk+,oed sc z;n?    $^{\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 where2uh)o17-4dudj wysub the speed of sound is only abudsoy jw 4d-bu)17h u2out 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock kxnhhv tr:dm(*;wm3+sx r ..q wave anglerdhq .w:mns(.x kx*+rthm; v3 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 ogx ymcwr),z9a)x1vv2 xks6d.+u s 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 a9r*a.l2 hv)+.uz q hklajw(sqbove the ground flying faster than the speed of sou.r* v(hk wq+sllzjha)2 u9.aqnd. 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*ejgnjuy3 7 /i 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the mini 3ijy/n7*u egjmum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the h ba9nh +gy7pddu b(r*/uman audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manydpxtkh ,p*45sce 0 j 7)evkot- plastic pipes of various lengths, which are7etxtk4)pjkch op e- vds ,50* 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 personh-wrw2 9ffnkkcuc. qy( 3l;k2 makes a sound close to the threshold of human hearing (2 u-lk f khw2r.ck3nyw9fc( q;0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound levelxr4id3 hu a-i4 when an 82-dB sound and an 87-dB sound are hearauh-id4i x4r 3d simultaneously?    dB

  The sound level 12.0 m from a loux (6agy4+ tpa*u*qdfe dspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assum(x+t4af6dagep *y uq*ing it radiates equally in all directions?    W

  A stereo amplifier is ratekev wx+e+ je63 yhl;/ri9gv6w n* )xmed at 150 W output at 1000 Hz. The power output drops by 10 dB at +e mn vwwjxer9*yh;)xgevi l6+3e /6k 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicesk0t1aih * s ): zgna(kq;-gzur 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 fr z1( a g-nthgk ai:z;*surk0q)om a jet airplane engine?    W

  In audio and communications systems, i ;x)b;luq37a5eatc nd ry5)jthe 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 :l29 buh5n8m, 3cnxkq2ql ouwis 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 bbi )67 dyogu*points with a fundamental frequency of 440 Hz and a mass per unit length of )yg 76bduib *o$6.1 \times10^{-4 }$ 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 filq*;7w :4s l1.p szmj uijhv,wjled with water (Fig. 12–35). The water level is allowed to drop slowqhp;zi4j*svu:w w1m. s l,7 jjly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass ns zhjats s4b5 5+q 2tner+7z82.10 g is near a tube that is open at one end and also 75 cm losnq 8zt7j45zh5 2++sa bersnt ng. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resvx a08s m/kl drdm:1:donate 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 to92fwp7a0tdg l8z6 t8roq lo3cne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactta3tld cq7zf r89lwp 6028gooly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on igln,)n-n;a*vfnq l 7the stationary train hears a 3.0-Hz beat frequency whei)gn -7nv;,lnq*nalf n the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it+ bi 0g7z2k;vez 6 -lokmx9tsy approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume cbix+ -z6l2 v70m sgeko;y9tkzonstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the 0 l:sh dheuz3hl+15ti difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it +0idl1t5hse l:h uzh3going?    m/s

  Two open organ pipes, sounding together, produce a beat freque:k hrmz7d.u vg;1m5h z,b8i6 yxbi5na ncy of 11 Hz. The shorter one is 2.40 m long. How8:,rz ux5zbyi5hv m1 ; hbdga km67n.i long is the other?    m

Two loudspeakers are at opposite ends of n mlve72 hw9.r7*acbta railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sout9rv *.e m2h7awcnbl7 nd frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood kxf m0 :m*ajdk-/9rvaflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultra *k:v9m/ j0xkd-ramafsound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/c+jeohme4*6 ,60w t wel.bvips while the moth is flying toward the bat at speed 5 m/s Ti60vtm l+.ohw p eee c6*j4bw,he bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frlne61;po up3 hequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitt6 3;p1lhou epned?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from wn;xnxe qj4o9yv x;*zub*vv4a d48r)one Alpine village to another. Since lower frbd*4nzy4) e; xuwrxn*v94j a8vo;qv x equency 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) 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 thefnuu037 g. nqgmwmu8 2 yzz5o1 presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 mmw u0n1qfu3ynu.2 z gom5gz87 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 :yyd:ybzq/lx 5e/-aa m0k0nn( *ca8ssc2 hlj rods,” involves a long, slender aluminum rod held in the yq:x52/ma lnd0c8el/bj s n0 y:s*a (-kz ycahhand 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 :fa ym pjh32c() 0fmyvq2q(tghearing for the human ear at a frequency of about 1000 Htgj(2: 2 fv(phf3 q )ymycqa0mz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An obsd hfbyp,v)4 +gerver on the ground hears the sonic boom 1.5 min after the plane passes directly overheadb fg d,v)yp+4h. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbohubo s:2oz:7xat 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