What is the evidence that sound travels as a wavv(;qw-px 7rts.1iszi e?

What is the evidence that sound is a form o76kz;x7 b2 tug(n cre u-np+yof energy?

Children sometimes play with a +1oa5wdp*xdyf4o3k *nl(vj g homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child spex*odjgd5 (vf y31l+ w ona*pk4aks 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 fret.p/ v e/nwis+quency or wavelengt/ tpenv s/+iw.h to change?

What evidence can you give that h/ott0otluvk )/z.ktz z( tvr058o)nthe speed of sound in air does not depend significantly on frequencyr(t lo t5z8t n)t0.) k0o/hvt/zozvk u?

The voice of a person who has inhaled helium sound k1 (iojk qr3j1c;rhwd 71ke7ns very high-pitched. Why?

How will the air temperature in a room affect the pi g3x3tyfbg0y::gr(f dtch of organ pipes?

Explain how a tube might bef.4+yximhc l1n 9e;ar agv10k used as a filter to reduce the amplitude of sounds in various frequency ranges. (A iryhg190 a.n;lxcfm 4 e+kv1an example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog*)qk-w lq6snx3j j 7qrether as you move up the fingerboard toward the bri7xk)jsnw6q- *ql 3r jqdge?

A noisy truck approaches you from behind a building. Iniji9nh/a5e/xlm q) p hmc(9b q0 v1wd/ptially you hear it but canno/ hhecm)/w9a1l qdv05p ip/ nxjqb (9mt see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be(i ps32sbni393;da ewi n2 mni said to be due to “interference in space,” whereas beats can be said to be du ibimsin3an3n dsp3ei9 (;2w 2e to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowerto.*.c u,kpfn ed, would the points D and C .,nkuftc*p o .(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people t-yi18wsafg . who work in areas with very high noise levels hafy .-isawg 1t8ve 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 reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave 4x yxevb(+;z6st b2wq 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) o(zy4+2;q xv es6 wbxtbr (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same dire19 yvviu5 cxl 4,:e2ewu3bvr iction, with the suci3eyxi,2bwu: 15 vvle v4 r9ame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard :eg1) ,i :9,tsr cykxen ,rpkt+ a5qfpby a person at rest with respect to the source? Is the wavelengt9 in gc5)kykp +r,st:,ftp 1er,e:q axh or velocity changed?

Figure 12–32 shows various positions of a child in moeew,1s.whm sc u/5:xl*bg wq2tion on a swing. A monitor is blowing a whistle in front of the child on the g2 h5:1e w scuwbexw*lgs.,/qmround. 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 ple0-ypns.far+b*z, il2 7xy of her shout re-,i7ayx b+pyrl *zln es0 .p2fflected 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 justm/ au ss;ska1vyo(;sjr ws/1 8bt:k-u 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 significantl;:kusas-r a; ss/jv (y8b/kusto1m1wy with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength zpcb nia3rk+. qz4w2/s 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 school of tuna on a foggy davenwt-qn81l37 xob c97ar a;ay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (axoetq n7 wn8c7a1;bv-laar9 3) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes fax t;1jz ;+3sm xo,o.qdiv8(kyvh7uwhen striking the water below is heard f +, qdax8m;oi zvx.h;v o3k1y7 s(tuj3.5 s later. How high is the cliff?    m

  A person, with his ear to the grou 9r)id8vp0f5 0nuu g ke 80seb3y9cvdund, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s aparud c erg8n v9i5sud30v) p908fybuke0t. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distbbwkl66y ) j6ybm52lqb4 h2/ittzj1, ico+mu ance by the “5-second rule” for estimating the distance from a lightning strike if the temperatur6c 1 b6tuy+/klbb5b zj2hit ym2i,)o jlmq64we is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soqv5a1o e,a0m22)z fiec4tow kund at 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 luz17uak t4/ wwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultam92rd rb5edc2/n- z1 vf qktzm0yy*j5neously at a certain place, what will be the sound level if only one is explkc/q02yjb*rtmd5z - n1e5yd29vrzf m oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jd y3m1u 9j7sh) yz6zobet engines is experiencing a sound level bordering on pain, 120 dB. What sound lz)6m os1u9y3hbzyjd 7evel 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 sig pwont8l2i :0z)sgka 4nal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of ip0st:zk8owi2l nga 4)ntensities 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 nxye. q+1qg5lzormal conversation. y.q1x 5lq+ ezgUse Table 12–2. 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 strikesu0n3a f3/r::(fp8)kcpxtkrxr7pw aqs1 y l* s 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, while the mord :+hw6n3e,j6vtr bk/ z2 arvoe modest amplifier B is rated at 40 W. (a) E2nehrd6v3/6,wk : rtbj +za ovstimate 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 pva*n*a7w 0s1de dug7da.(em when placed 2.8 m in front of a loudsddgw au. sa7a *(edn7 1em0p*vpeaker on 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 2.0 dB. Wh7v0g .adq5ao wpi((ism/ o7udat is the ra7i w( m7(doqpvad/i a50s ugo.tio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will tfhjd f; xm:5u0hwo bs-r5-ck 5he intensity increase? Inrf;kmh 5d5josh 5xcuw:-b f-0crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal/mdavhng1z5.w52)cnxz;t xg) p 5 dl ts7di2x displacement amplitudes, but one has twice the frequency og/z5x awn dszxlt)iv 5dxptd .;m7 gc5122n)hf the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air;ii ge.y : )ewphj 1qit,k9)aq8 ;pybo that corresponds to a displacement amplitude of vibrating air moleculh)o9w p; bg a,e;ijey1yq i.k iq):tp8es of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to s fao:2i+mxb1qeem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig12aix +:bmfo q. 12–6.)    dB

What are the lowest and higfy3 7o gk(micp2o/2 qqhest frequencies that an ear can detect when the sound level is 30 2q opoim fg37/(q2ckydB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whgdwzk0 3;9v.woekkaw0r 9 (pmat is the ratio of highest to lowest ip ;zra0gk9.ve0 (km w dw9wko3ntensity 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 f)+epe -dd9rg+xb /exeundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the stree9+)rge bed pd- xx+/ing be placed?    N

  An organ pipe is 112 cm long. What j)ql/ wysc;1vqd-d0f:.ain x are the fundamental and first three audible o-i.1:wl ;jcq/fsq)yd v0dn x avertones 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* e-ms ck4b)uy across the top of an empty soda bottle that is 18 cm dee s4uyb)-c m*kep, 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 rangehr hy()+ii h3g of human hearing (20 Hz to 20 kHz), what would be the range of the lh rih(3ihy g)+engths 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. Whzt6lzi-qdexfa2r qy 2;-0l b*at will be its fundamental frequency if it is fingered at a length of only 60% of its orilt rq6-0iad-xz 2ezyb l*q f2;ginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p0z;lix ; uhn1:e 3irvalay E above middle Cra ii 3zehx;1;l:0vn u (330 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 emsujv3 (p ejdwp6 ;7l1ujx 9k1sits middle C (262 Hz) when the temperatuu9u; l kj3d(w61pxp evj1s sj7re 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 4xzhncn6k:e+0r j(q w;nd96lagdle 8 0 $^{\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 e b h66+91vfmxuoe+gp–10 should the hole be that must be uncovx ubpoh+6g+f9vme 6e 1ered 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, and 616 Hohpy5cx na uo8o rg +r92kqbn; 2-9e,iz, but not at any other9o 9rb oa x,-r85n2qok+p2ni; cgueyh frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long ig:pslrp(t42h2 gp h4 ms open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is4p:glh ptgm h2r 4sp(2
(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 ru:9gndd(qew4 (,pj 4 vjidt :*rpf 3f$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-lontpf6ffealu9tlj;l o 0 k:( e(6g organ pipe ak tueapl0el ot966jff: ((f l;t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approx9p(sp+ gxt- rmimately 2.5 cm long. 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 in the ear canal. What is the relationship of your rg mst-(+pxp9 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 2.0t )gz 1+gu,h2g.jfimqq vsv.+ s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequencyg,f+hv .1usi +ggt.j m)zv q2q is the other string? ±    Hz

  What is the beat frequency vy6pn g)20ld dhz5g r 8o-hn)mif middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another)nxot r5f8n 2q (brand X) operates at an unknown fret rf)2nn qx5o8quency. 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 wh/qw ,/g7oibuz-ka1 qkjd 5m6 een sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning foi w61ej5/qm-dg ,/q7 b akkuzork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Th)9:qrku b((ep8 3 s akk2dxkmx;(g hw y-.qsafe 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: Recall Eq. 11–139w:;ax( mgk(ss8kquk 2a pyxqbk f(he3r-) d..]    Hz

  How many beats will be heard if two identical flutes each tr 47s*5*r wdpehb z8)ipkmi 0bdy to play middle C (262 Hz), but one is at 5.0°C )iebk wm 78dp4zd* pr5*s0hbiand the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, *lx+cke/7*ec2wla)- cfue d z cds7(pand C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 )lc sx(7wk e7fa-z 2e udccl/*+ de*pcHz 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 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 3ukpjf,fdgzpf fsika ./7*. )speaker and 3.50 m k)*pkfd.,/zf u 7fpf3jgsa. ifrom 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 d9sbpr9cra9m2o4q2 k 132 Hz, but a piano tuner hears three beatsr 92p9kcqr4oab2s 9d m every 2.0 s when they are played together. (a) If one 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 +1egi mtk b.gpq f 8c(odh0*y*air. How many beats per second will be heard? (Assume T gb (hm g0eqfd*oti8pk+c.1 * y= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 db)yt4+hnwtj3w.k/ vHz when at rest. What frequency do you detect if you move with a .) ykh3tnw/vbt dj+ 4wspeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do y9o zlnf63;bnxou detect if a fire engine whose siren emits at 1550 Hz mo9 xo6b z;n3flnves 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 tow(pqv+ty9h/ 4 z:uatxt ard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sxv t/zu pthqa9t(+:4yame? 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 frequeu )qq dln*e/;d0t9 ild te7,uuncy horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emi,ddluuqdt)/u7* e9 0l tie;q nt? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5y dcf /o)l eh8.*jmdh70.0 kHz and receives them returned from an object moving di/jf h7omdl* dh)y.ce8 rectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the batp0smr b/1 pr /njqr:j-ctoc 86 emits an ultrasonic sound wave with frequency 30.0 kHz. Whatrtqscrr :j /j 1mc0pn68b-op/ frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on .: hfyn6 (2squqzz(d la moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in tn :y( qd6us( h.zf2qzlhe railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultraso;twpo mm 0her,ro 41l4d1l r7vund waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speedrdr7ph, ;4mew t01om l1 rl4ov of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of /oyu54(vh 3lp2snpxi55h eq;jqtu y-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 win6t uvqdb6h. ,3uvtw;yu,5ia t d velocity is 12 m utdbht; .5tv36, vwaqui y6u,/s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if it t/h9 1f cwdz abeq9w+,c1lp4ks 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 sp3wy/ visa* l7e m94 e7lpjtwc8eed of sound is 310 m/s (a) What is the angle the shock wave makes with the directjy79 mw* 4 l/icl s3vetpe78awion 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 wh3)b dlczuy; 9rere the speed of sound is only about 35 m/s9); zdubrly3c
(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} $