What is the evidence n( -iz.b6q tdpthat sound travels as a wave?

What is the evidence that sound is a form of ea:bc4y,zt 9g0+joe i hnergy?

Children sometimes play with a homemade “te*x 8w n1 by,/dy+aj+ks-zxn zelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clea bzxxn-+kz1yaj+n/,8sey d* w rly how the sound wave travels from one cup to the other.

When a sound wave passes from air , rzb;yd/ryc 7into water, do you expect the frequency or wavelength to chcyr/ zryd ;b,7ange?

What evidence can you give that the speed of sound in air does n3*i wwifem16kkrp l.hxrw80xf t: 9v(/8 bodrot depend significantly on frequency?0r6wk d o8l:rhtxvf8w kmr.(1p3bf9e/* i wxi

The voice of a person who has inhaled helium sounds very high-pitc2 rnt1/qxin+msion(o6 ) 7urihed. Why?

How will the air temper(0v;w +* fsbz6;qqzutf xud k:ature in a room affect the pitch of organ pipes?

Explain how a tube might be used cc)9pigl*5m das a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffl*c)l c5mipgd9 er.)

Why are the frets on a guitar (Fig. 12–30) spaced clo4f8ul rok. )q1dppgy7ser together as you move up the fingerboard toward the b fkldp8ug. 7 q4ry)op1ridge?

A noisy truck approaches you from behind a building. Initially you he 6 b,5sh;fkxxsaw xm+3ar 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 11–1xfxk3sa s6m,h 5; w+xb5 on diffraction.]

Standing waves can be said to hf nh7fs/sy21 be due to “interference in space,” whereas beats can be said to bsn/71fhs2fy he due to “interference in time.” Explain.

In Fig. 12–16, if the frtqg wp crmdqj0/c; o(49yzsli;t(/p: equency of the speakers were lowered, would the points D and C (where destructive and constructive i04pl/pgs (di/wtyt cjr: om9( z;qc;qnterference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who./ohflh.mffp lp/x d 1ofcv-jx8 1+ z*h7no,z 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 headpho7j fm1znlxff.cpo + -o fv p8hlhxh,1z./*d/ones 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 o / n8zakrhf0.6f2leyq2yd- nrf 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 fyn2-yk6r 2n0dfl e 8qhz./racomponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction, vev;p ku6o9. lx-0 pjqwith the same velocity? Explxo-0l u69 v qejpkp;v.ain.

If a wind is blowing, will this alter the frequency of the sound z27 .a8zo9:nhdwz8ziv khq*x2 l zl4rheard by a person at rest with respect to the source? Is the wavelendila wx zq9lo*2. z7z2hv k:zr8nzh48gth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitorrp,o ; o+rvyc7strhpb: ;*8dypfe,)v is blowing a whistle in front of the child on th *os)py;bp:h;, cd,r+e7ptfrvy8o vr e 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 lengtj,:t i +b xmy;tne+/94 ma2*lclbmvo qh of a lake by listening for the echo of her shout reflected by a cliff at the far end of the laknm x/tlyoci9jm,;:eb *l2a m+v4+ q bte. 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 3l g6 lm x28bnk4bo(qyjust 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 (T2lybq4lmn o6kg8 x (3bable 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at f gbeba.24668yar knq oshbg9 )quk n/3eit5-20 $^{\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 da:2: 1uq9e k,ve0jh 4lugwchxw y. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is he xhl 0u4, we:ce2uj:h19wqvkg ard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash i2vyfzi;d ry-py5 :kf+t makes when striking the water below is heard 3.5 s later. How hv+kf-y2: iy rydz5p; figh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strijjii6ww6y/g:pa-3dr ke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the6jgy :r dij36wi/-awp 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 / 8op5tmbyb a,mile of distance by the “5-second rule” for estimating the distance from a lightning strike if ob 8bt/a,5 pymthe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dBc( f8xxjc :vmqn745g xmgw 9z/?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of aq-yd*; h+hmj qn;v8fn sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produe4d vvuu4 p72wce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intense puwvvu2d447 ities, not dB’s.]    dB

  A person standing a certao5.fkop, zlu /x-hl 9gin distance from an airplane with four equally noisy jet engines is experiencing a sound levelx5,l 9-kphozf/g olu. 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-to-noise ratio of 58 dB, whereaoy.isq u 1j)r(s for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 u.yr(ij)s qo1 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a peofda8; c x: z2v7gcn2qrson speaking in normal conversation. Use Table 1vzfn; c2:o87 q2a cgdx2–2. 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 strikes an eardrum whose areagryuv:t-97 ch h n/skmf3-qm+ 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 mor+ v7xe s,w;-rl3j ertge modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from ae,elsxvjrr+ 3- ;gt7w 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 rij6z0vf y2jh:5al di08j tzs09ph7ww egistered 130 dB when placed 2.8 m in front of a loudspeake6p 0 j0:izav lw90wsj td8hj y572hifzr 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. W,)ue b- ryu-iu) yz;hahat is the ratio of the amplitudes of two so;-ue,zb-ra y)yui u)hunds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wawb 6dyyk3ht 97ve is tripled, (a) by what factor will the intensity increase? Increase by a facthyy3w d7b9t6 kor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplin0o7gr u+moj :tudes, but one has twice the frequency of the other. What is the ratio ru+ o0j:mgo7 nof their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corf2p 3w:*cu(*n wuv/iyovfrg nd4ql4 *responds to a displacement amplitude of vibratin4cn*:*uy v3( pw gi2u lwvf *4drf/noqg air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whb m ;qv8x,xjn+3g y1ugat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Figyxgugbjmnx1, 3 qv+8;. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thac* yz5kd*5m ge sound5c*g yd5z*k ma level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rt-ywz 3yw n1b+ange of sound levels. What is the ratio of highnwy- y twz3b1+est 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 0 0*)hnwwu dxvfundamental frequency of 440 Hz. The length of the vibrating portion w*w0xhvu0d n) 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. Whfbeh mku/ /-5ydfi-6kat are the fundamental and first three audible okbe6ydm i-ffk- /5hu/ vertones 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 wozl:j ;a mz. cr9/htjvets 1*5xuld you expect from blowing across the top of an empty soda bottle that is 18 cm deep,mxrst * :9 hjae/ jzcvl.t51z; 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 range txmi :ap b13fig -)b1rjhod .,of human hearing (20 Hz to 20 kHz), what-g tbhdm)j,1af 31.r: bx oipi would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string/54piy edm5sr has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its ore5sym5 idpr 4/iginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p) wjb.s *q;k t8m2cchulay E above middle C (330 Hz) .q c8ht*uc2bkwj;ms ).
(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 emits middle C (262 Hz4fnkby r0 gp;)) when the temperature isnp ;y4fk gr0b) 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 2i43a 2a75m7oa. q1w3oknh2 y *hdly s dt-uyte0 $^{\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 hr mtxh t8qp142od w,2xp--pp12–10 should the hole be that must be uncovered to play D above middle C at d8h -ptpqx-oxmr,ppt 1 h2w24294 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 2weni pp,+m.(e64 Hz, 440 Hz, and 616 Hz, but not at any other frequ nmee w(p,.+piencies 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 both ends. It rea8 hfhh)1 tu y/8nqcqp05b3 xksonates at two successive harmonics of frequencies 275 Hz and 330 u8853f 1q qhnch b)h/xkyat p0Hz. 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 1pzd q7)ifyci f;7er6$^{\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 audibsj 555up2zi b 6i/gxehle range for a 2.14-m-long organ pipe as 5xi652p j5 ehiugbz/t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to xftwy(izgkg ql;/(kr, ,m-/s 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 answer to the information in the graph of Fig. 12–tm/kfz,wlsq( - xgkryi(/ ;,g6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying tctp /tth7y.o *o adjust two strings, one of which is sounding 440 Hz. How far off inh t7t p/oyt*c. frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz289kg50 sbvan,z ssn6devx v2) 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) opera.,v d47q:/*5 jja glbn*tp7dglpzqgstes at an unknown frequency. If neither whistle can be heard by humans when played separatelypptl 4 7.g:qbjl,a5gz /q dsg* *djnv7, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3500e.wr0e m f6kz-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string?.kw 6frzee0 m0 Explain your reasoning.    Hz

  Two violin strings are tp6:q)m qd(buquned to the same frequency, 294 Hz. The tension in one string is then dedqmbqp(: )6 qucreased 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 tw7je +kt oi fwx/rf8e4+o identical flutes each try to play middle C (262 Hz), butt4fo /ie +k87 rfxw+ej one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a4s1jc5vyj h wj i. )r*up:v2qqnd C. Fork B 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 frequencyj siu2pj*:1vrqc 4y q).h vjw5 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 apa+(faagvq, sk 5:5tqz drt. A person stands 3.00 m from one speaker and 3.50 m from the other. zaa,+ kfg5:tdq (sqv 5
(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 vibratinjh x7 uu1x ajjaf1i;47g at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequencyu; 1 ji1 jhxjauxa4f77 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 mac48q6swq0xrqlqwc2; ny beats per second will be q;x0c4cqws l2 q wq6r8heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’po93kwgaua(0r 32pczwn u, :gs siren is 1550 Hz when at rest. What frequenga90uo3 (agrzk3 pw2:wn p,u ccy do you detect if 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 a fire engine /ag:r 7tvnu*x whose siren emits at 1550 Hz moves ax unv*g7t/r: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 towaaftjfc 3:s4*k rd you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sca3:ks* tj4f fame? 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 s tu),ie0 d(xfin6.d ukame single frequency horn. When one is at rest and the other is moving toward thei.tk n (d0u6f xuied), 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 ultrqt cli*2/c f .p,grhc)nr-td5asonic 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 soundd 2,cn g5/ith. -)p rlrccqt*f frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As itk+i9 *e1w h9 q0walkbv h;(wyk flies, the bat emits an ultrasonic aq9+k ;h 1h0(wk9 wiwvyk *elbsound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original D( h nklz i/bp 0m33x(fuy.byl8oppler 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 bm( 3 (3fyub./xny08l khpblizeat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses nkoex1s(r , sd2*vish*pmj1/ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tis*ms 1ep,xnk h(o sr/* dvi2s1jsue 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 usinglmvg7kg:8* bh3v: s en 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. When the wind velocity is d5v;-q 4 wzssf12 m/s from the north, what frequency will obsersf4ds -zwq5v ;vers 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 onv0d)nbu4e ndn1 kb6+ n 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 M2 nf) q)u;3tnukffh v qc+ao)/ach 2.3 where the speed of sound is 310 m/s (a) What is the angaf2)qn+o fc ut/v fq k;3n)h)ule the shock wave makes with the direction 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 atmow*.s u r*9jhgysphere of a planet where the speed of sound is only ab hj*w.u9rgs *yout 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. D lmc078+gb/g xcq9uh fetermine the shock wave angle it producesgq8lh /9c0b7c ufgxm+
(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 ,v hwe gd.s 0fq+d(a(t j7g6vs$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ove 21.o81xc r kiap+uulurhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a u2 o1x+l cpi rua18.ukhorizontal 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 ;,qy9lnj h8tcg g(pt;sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work i tj t9cq;8;,ng(lhpyg s 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range? gu:)uql/n+2zxrvx7 f gr**qk $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cons d/mm :c f e;bbu5ofso.-05ojqists of many plastic pipes of various lengths, which are open on both qbf.-5 ; m5 bum sdcooo:0jef/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 the;s)j/t*b z ma jvnh s2ef +4d1bekd/f9 threshold of human /teb 24f m +bv;jas/s9hkf)nd*1d zjehearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when al* fwmx5ch8 *qn 82-dB sound and an 87-dB sound are heard simultaneously? fcwm8**h5 qlx    dB

  The sound level 12.0 m from a l urxz2-6yf0z (2gi dxboudspeaker, placed in the open, is 105 dB. What is the acoustic power output (x2b2f0x( -dgz6izruy W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dr+lf4mgvxh (. dops by 10 dB at 15 kHz. dv.h4+l(xg fmWhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircrax- +-vc/jvlig q:mc8:z t9h)g hwbxa6 ft 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 radiusx )vz6/:hg9jb- :8aq mvt wlcgi-chx+ of 2.0 cm. What would 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 g,s*dl6q xwcy* ain, $\beta$ 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 frequencyd 6p7s 59r tapy. v,grtwu9pk9 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 violxy 6- ce)rjs4pin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass4 r-j xy6s)pec 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 above9p-bvtdets+ 94 dof,u 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 levd+4b - pvte9tf,uso d9el 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 mass6 u ckqo5*)kns 2.10 g is near a tube that 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 harmonic in the tunusk )6ocq* 5kbe?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate aszfblib0 mrk4xx)twx / +4if+ mhjn -*0 one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourrrej,56* p4qq nw ep+9jmw td5ces. The sound is loudest at pointp+n5je 9j*q wdprmq64r,w5t es equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on th(jh lgf09ck -zjm :o7ce stationary train hears a 3.0-Hz beat frequency when the other train approah0j c9gc7 mk:-(zfjloches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it app.lcxf,l(l3.u bx w rw8roaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (a8w(x..lx ,c 3luwrfb lssume constant velocity)?    m/s

  At a race track, you can estimate the speei;+ +j zj,sctrn, oxm1d of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car dror,j j+is,mt;o1+nx c zps by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, gy xv;.qj 4su,sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other;ujsq4.gv x ,y?    m

Two loudspeakers are at opposite ends of a railroad car g;4evo k -qt9das 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 ovq; g-e9dt ok4bserver 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 7) ):.jifz c+m n*ot8xcu t 1zg1zxwvsthe aorta 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 blood cells? Assume that thmcw fsz *8c1tto 1gx n)zz)x7 +vj:iu.e waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at spee0vxmcxg r5p ;6d 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emc pvxr65x ;g0mits 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 pum( cw/u)2pj1* ;jusf vsea ql5lses 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 emafp(2j vqm1/ecl; 5 j*)uwsus itted?    m

The “alpenhorn” (Fig. 12–38) was once used to ut5c.k -xtos, cd .ej07,uwii send signals from one Alpine village to another. Since lower frequency st,juc ueiid -,s7c.kw0 5o.x tounds 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 bdd bk r4+/dru kx( 6s9cqsl0f.y 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. Calculate the fundamental frequencies for the standing waves in this rob9/rkfrxk4.c qudd0d (6l s s+om.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendegr(z y7ifyvpr ),f 9q+r aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod ,yy(qrig)f9fp7vz +r 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 snufti ;3mr+9*;bz lba frequency of aboutzur;+fs; ibb n9 *3tml 1000 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 Mack 9 u)0wy ashn(0cbf6hh 2.0. An observer on the ground hears the sonic boom 1.5 m 0ynw6sh( u0ckf9)bahin after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa)z s 2-ynn8.4 5(rqbp;3j tazt-jfnfi w5tktmt 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