What is the evidence that soundxm x/;kkt7on8 6z 1uos travels as a wave?

What is the evidence that sound is a form of energyz;ga*,7ydck )gdlj 5(kkq 1ko?

Children sometimes play with a homemade “telephone” by attaching a stringzio)1s* os4imt3 iyf / 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 so/imisy o3oi)f st*14zund wave travels from one cup to the other.

When a sound wave passes from air into water, do you ex c-w h -rk3v/xdtc91fgpect the frequency or wavelengtgc /cdvrx39 hw-f- k1th to change?

What evidence can you gcat/:z.fzpas fvu: eqbfd p65f2* u* 4ive that the speed of sound in air does not depend significantly5uff.q*cua*:6 fb:4ts /vpzf 2zadpe on frequency?

The voice of a person who has inhaled helium sounds vqn;3 b2zg c+ebery high-pitched. Why?

How will the air tempera :3u64aa7e hw 75cb3om .h4jzqy lgwopture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter4dc r1 (5b igvm4icdu9 to reduce the amplitude of sounds in various frequency rd cdi9 i(br vg5muc144anges. (An example is a car muffler.)

Why are the frets on a gui crr*sh5kf tp,t (*e6ytar (Fig. 12–30) spaced closer together as you move up the fingerboard toward th tcsr6p *ytre (*k5f,he bridge?

A noisy truck approaches you from behie zvp2fzvk- */1ibfj:a+ebz. nd a building. Initially you hear it but cannot 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 + az- 1jzek pv: *fbevib2/fz.11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” bqt;pua i(nw3b4mj3y,: f7gswhereas beats cu7q;wpf gi3s ( :nt,bjamb 4y3an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers ww hev rdu6k 6:e8jfz, qaq-* h)f,q*jgere lowered, would the points D and C (where destructive anzhw,j6j-v ahqdf,*:8kg*q f6ee)r qud constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas withft + r6(cwkjnf lnn.lek73s 4- very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wornf ctj3l-wr 6sk.k(n+4n7e f nl 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 can be thought of as 0jce8p m++xfy0d8amo ;28svz r9uggt a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or 0g9 8y;8+us xj28odfga+0 remcpztv m(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 sak4) sa; yq3l wa6ju)6rinxcbq86y p-ome direction, jb66 )o6 8xq4yyiplcs k;n u-a3w)raqwith the same velocity? Explain.

If a wind is blowing, will this alter the frequency ofq6h- qez.e4au9k0 w- gdpje k6f+r.ij the sound heard by a person at rest with respect to z.we h6kqj4e ga. q9+0 kuerjd6-if-pthe source? Is the wavelength or velocity changed?

Figure 12–32 shows variz(q ly* pn3;xgous positions of a child in motion on a swing. A monitor is blowing a whistle(lxy* n;z gqp3 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? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her snj.9kt j2bp ry 9.3kle uf b5pw6v9(gkhout reflected by a cliff at the far end of the lake. She hears the echo6nvgw95b (j urk l..b9e39pty2p kfj k 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just be/8 ij7w 84ktn ws2qkc4aur9ftmub9s0 low 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 4k8 m72aufjk/b99t0r tcww4u qn8sis 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 a6dqj 8(ks /e ;kowh5:xv hu.pair 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 s ifw(s 5d86je+r2wa+2 rmswq drifting just above a school of tuna on a foggy day. Without warning, an 86ri+ms5 2d(w qw saewf2+jsr 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 tolhxdua-z973 fp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the c3zahud9 fx-l7 liff?    m

  A person, with his ear to t hk4m (,vvjx qdzb +17lfyct3l j3)m+phe ground, sees a huge stone strike the concrete pavemmh+m3b dx (3yv4j,7jp)q1lctv+fklzent. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of disxq1j)et-xv8- (6b eutqxu* ujtance by the “5-second rule” for estimating the distance from a lightning strike if the temperature qt1u-xue*jbu(q xt jx )6v8e-is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dit)dc xdks md6z5.e0 bi;hi23 B?    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 d dsq k*8c+7cfis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whi etqz9qs7ykqk t+ ic: c/+3)ken fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Addytz/iq: q + cks)eq9ktcik+73 intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane b0jbi*qe cgxuk 9 gb9,w2w ./gwith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the 9i / 2w*.jgekx bg,gqu0cbwb9 captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saidd a*n 899i *y1jkstebp to 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 sig*b1 ptk99ansejdyi* 8nal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powocb f( 72ka,1a0vcy / qj2muqlovj8t 2er output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphecm8va jbq/ 0j ak7o22,oc2fy (ulvt 1qre 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/ssuou.lu+lyk) 3yl 9*+f qrn es 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 5 (m(gb3 rlajsbjrls 67 o2co0rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at ao5 l s3g(0 (omj67s jl2rbbrac 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 placed 2.8 m 2qrsv i;k;o)lin front of a loudspekoi2 )sl;; qvraker 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 d4j)uefdj2 y:betect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose4 f )yeujj2:db levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave )s *d hby;rs7m4u8tfvis tripled, (a) by what factor will the intensity increase? yhb)mu vrt8*d sf4;7sIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equalq,a.mo ml/6 uscg 9hf8 displacement amplitudes, but one has twice the frequency of the other. What is the ratio of6goa8.9 qlm ufhsc/,m their intensities?   

  What would be the sound level (in dB) of a s(; x wup)smf8p3mwcx7z2ia9 u38rif sound wave in air that corresponds to a displacement amplitude of vibrating air molecule8ru87 wms ;)fpwxaxf29ci z3 u3( mspis of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a .yv qhb1x5c ht69u9l w100-Hz tone that has a 50-dB sound level? (Selchvyh bx5u9961w q .te Fig. 12–6.)    dB

What are the lowest and highest frequencioez),ui+f gf 8bvmo ;/j6jm 4qes that an ear can detect when the sound leve8 4gjif m+e/o6mof );,vzqjub l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hugi-lf/t 4kx3bv e range of sound levels. What is the ratio kbvx i/4 3lf-tof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 44ehj+mxgr :7:xq5l.5a trwxo20 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g..wlrt jx:+x5eqh 7x5m aor:g2 Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental af+/ rbdxcq i+.nd first three audible overtoner+./ +difqxc bs 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 fo4j q,scx8j7n rom blowing across the top of an empty soda bot 4qj8x c7,sojntle 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 t0 oay3yj, x:jjku00r+ q re8kmhe range of human hearing (20 Hz to 20 kHz), what would be the ran0 y3, mky aje:r00q+8ujkorjxge 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 harg lrbm;i1/. eu: vwi.m1zos(smonic. What will iz1..eum wr;sg1/mb(vl osi: be its fundamental frequency 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 above middlbc.)8 d*ibzb 3 ntmao8 4hv,zze C (330tzhadb vnz ,.cbbio* 8 m843)z 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 pi-l65k 2b xtp g,gkn+szpe that emits middle C (262 Hz) when the temperature is 2+kg - sgn6bp52lkz x,t1 $^{\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 an n:p.uvym;;seq xt6d b.x -5nt 20 $^{\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 12–10 should the hole beg,wh/e8 dj:hj 6j*k lx that must be uncovered to play D abo* h6:xjl/w,degkj j8 hve 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, bzl z89 k 27fs;5hmu)a7ozcnjhut not at any other freq2m )7zc9 onl57hsakju; hf8 zzuencies 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 is open at botzox a; gh1cmpzi5c4 ;+h ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is5;c+chp4xg1zo; m za i
(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 p 6*n ozgknna u5+s67q$^{\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 witvf*rfg gv 4h;,p15zfpq 3t,ychin the audible range for a 2.14-m-long organ pipeg54 ,;v*tqcy1 fpf,z3 gh fprv at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lon/y wiayqoj +nn38ry07g. 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 trnwiaj7n 3q8y/ y0+yohe 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 evedc 7cvu4z+8ut ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othe+48ucc7d vzu tr string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andk +qcwr;is38 aq-g8 gz $C^＃$ (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 axactjt :fg* 5qvs7b/m*k0vm p2yl ) )kHz, while another (brand X) operates 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 si*q pamc 5k7v vfb*/mj2x:tg)yl s0ta)multaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded withm++hu ,6qk mkv a 350-Hz tuning fork and 9 beats/s when soun+6 m+kuv ,hmqkded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency,+s)w y0i/:hg7q umqs pdzl31i 294 Hz. The tension in one string is then decreased by 3q0i ywp :dg7i+1 slhsu)mq/ z2.0%. 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 identical flutesi :y7lr .hev5p7e-miz each try to play middle C (262 Hz:y7pi5ev7e mr- .lz ih), but one is 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 frequency of 441 Hz; whf pjc;yg *:u vio8*v2 ;nwzky4en A and B are sounded together, a beat frequency of 3 Hz is heard. Whfy2*;no4 8uj; :vyig wk p*vzcen 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 spe.9ml li5sq,m faker and 3.50 m from the other.5i lmf9 msql,.
(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 suppy*j4x(fen7,ubykf x: yt 9em8 osed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they ar* ue8ke,n7: f9y fjmybyxx4(te 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 pr6 (;lbk joadmb +r4wkd+c-;2.76 m in air. How many beats per secorcl(mdb + j; 6k-rbp4 +;owadknd will be heard? (Assume 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( 2* j3mdj;otg:qtpp.q dv6jz at rest. What frequency do you detect if6q( 32pm dg.zjtp; otq:jv*dj you move 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 8)zp bqbeq(9ja fire engine whose siren emits at 1550 Hz moves at a spp(b q9ej8z)b qeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000: wl8g : a,z i.47eibiuw6padg 07vgda-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are the7w7g6v.eb4iui:g8dw pa : agzlia0 d,y 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 frequency h4v+k-kva jz r;orn. 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 frvvk+kraz4;j- equency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and renaodj (cha:2.ceives them returned from oj.a:2(had nc an object moving directly 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 fl+2sarkit: l 23yfrn*e ies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does ttns*r :r e+ifkly2 23ahe bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplwiqr+l8w/ -jyer experiments, a tuba was played 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 fr -w/j8+liqyrwequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo05t i 5odgnf1wd-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 in large leg arteries it1w5 ndo5f0gat 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usinqoa b/:slkv* 9p-ce0/: 6pkn1ss vurqg ultrasonic 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. Whe7h9qdekp oicuxn5hoh:x )z hq y// :+)n the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at res:57ycxudq:o ihn)okq heph)9/x/ z+ ht,
(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 movinga.2yhwlo/ pl1 on land 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 oiobjn9:-dm0 bib *bf:f sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane b*9b:obfj0im dib-:n’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 atmospherujpxc k,-r13pe of a planet where the speed of sound is only abocxu-13k, p prjut 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 h5q4/m -.c zmsfr6vrj wave angle it producfv5jrm cq.h/ 6r m4zs-es
(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 6gfq2a,omul2w8 /mxq $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan5 f9qb y t5;ahako4 gr3m6kjr5e exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, theqh53 fkbjy;r agm k9tar64o55 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 dot:db7s; 9ab ctwnward from the bottom of t9b; t7a:sdtb che boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the huma+bqtrahv6 : w6n audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer1gp*j vk m .rpu/h39er pipe symphony. It consists of many plastic pipes of various lengths, which are open hr1 mvp9*.ujr/p gek 3on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the5ee7b:*djecd mbm9b / threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?mdeb7 /bdjcem* 59eb:    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are he(abjh58 nd-p)4jx n a) q/ncqpard simulxdqa)- n5nq4bpjn)8j h/ (pa ctaneously?    dB

  The sound level 12.0 m from a loudspeaker, plah0 y qien40a5tced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, asqn0 5e4hy tai0suming it radiates equally in all directions?    W

  A stereo amplifier is rated at r3z zg ,f;ev tk5qpi 3om+y*y*150 W output at 1000 Hz. The power output drops by 10 dB at 15 k+py*t*g3 ,iqyoz;mvfr5 k3ezHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet ad2 ba/an1;z)tv)gtglayb) /eircraft typically 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 wou) n1b g ) gay2/tt)lavad/b;zeld be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the w3)eit.vuq/y:r i 9ujgain, $\beta$ 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 ao y klr, (luwii3tqn*7-u)j5u 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 betwee-+r 9b cbgjj1gn fixed points with a fundamental frequency of 440 Hz and a mass per unig g-1jcrb+b9j t 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 vi5pizeevhi p;:h/d -5x bration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance h hv-p5/;e:dxi5ip ze 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 9/ty-pzw zkxg89(2hpkyh 7zpmass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in thewh /zx29-pyzzy8(th 7 g9pkkp 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 resonate as onemy6bk;74dix1 mh ndn, 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 toneay,yq(w1 oio7 in the 500–1000-Hz range coming from two 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 tqy7, aywo io(1hat 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 condu mv9kuh)( ndc7ctor on the stationary train hears a 3.0-Hz k)mhc79 v(dnubeat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam4 mgt0,h,n2 pisdffh2 train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (a,s2 f2 hfg4d,0nm hpitssume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to th0k x- b10bjoy b8yyi8ne difference in pitch of the engine noise between approaching and receding cars. Suppose ty y 81ibonby00-8 jkbxhe 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 togetherskqh/pvt(/t. gvjbg44 ;1rtqn +t j9m , produce a beat frequency of 11 Hz. The shorter one is 2.4qp.4q1s(hjt gm9g4 + tkr/jb/vt;tvn 0 m long. How long is the other?    m

Two loudspeakers are at opp ;se,aw5( wepcosite ends of a railroad car as 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 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?ec;,5p( a swwe

  If the velocity of blood flow in the aort5irgq3/8 ut qta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bloo u8 tq5g/rqt3id 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/s while the moth is flying toward the 8(s nmv fg)7qb6q-wjzbat at speed 5 m/s The b gvj6n)zsq 87( fm-wbqat 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 frequency sound pulses as i nw8k49nsr3v mt 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 vsw4 m9nkr8n3 be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sene(.t ka2murdsc. 6;cud 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 popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What istcdk. 2 ;u.aemc6r(su 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 list-,- xuv,aad uoy1xvxbf a:.j, ening can be compromised by the 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 m high. Calcula jxd1uvo:yxf .u-,aavxa- ,,bte the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called 8no *hr e *nha9)eye2c“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. Wi*2 oreh *nan c9ehy)8eth 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 6,inasw;s+wp*zp v e /hearing for the human ear at a frequency of about 16nwpp;ea+,isw *v/sz000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on thzfm c0px5 7cpyoby/7 9d/tp+ge ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu/9y dp50/g+ t7 cxfyzopc7mbp de?    $ \times10^{4 }$ m

  The wake of a speedbo1op+2* ,yqrkd5ox*b aaqht 9iat 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