What is the evidence that sound travels as a4h+stn4 y5lukt86po ;ijyc ;z :spiw2 wave?

What is the evidence that sound is a form of;mogmr*/5+wy z;k cch energy?

Children sometimes play with a homemade “telephone- j ;2,ezjz*rfizrv*y” by attaching a string to the bottoms of two paper cups. When the string is stretched a *2ryzz,jej;f z*-v irnd a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect th 0vomuqlmf5;/ e frequency or wavelength to changu;o 50ml mvqf/e?

What evidence can you give9 .ws rfeq)gm:fj5r4o that the speed of sound in air does not depend signif:s. rfjwm9)fq 45gero icantly on frequency?

The voice of a person who has inhaled helium so,e7(+ychg v zrunds very high-pitched. Why?

How will the air temperature in a room affect the pitch of g 7inh -.zi 4: cz/ cxd;px+sj2:ulnvrorgan pipes?

Explain how a tube might be 48 ye4+wpz+durp jq 3l1v mt4zused as a filter to reduce the amplitude of sounds in vz pq v4 ey+lz 18j4wur+t34mdparious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer to )c4v ymmgt75mjshx +5gether as you move up the fm m v+sh4jgcmx )75y5tingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear itqgvk. s 4d70yc ztbsq-w+;6n g 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 11–15 on diffracz7qdwk nt y c s-0qs;.b6+4ggvtion.]

Standing waves can be said to be due to “interference in space,” whereax tffe5x. 3o8as beats can be said to be due to “interference in xaexo8 f3f5t.time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would xx 2jv 8n2rq*vthe points D and C (where destructivev28n xjq*vx r2 and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas wpva/fey/xq xkh g46*kex9h,6 x)gb :hith 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 thxx9h ak,kgxvf/h)y/bgee 6x q4p h* 6:e 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 cntmht+u ntkv(.- 5e/ qan 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) or (b), are the two component frequencies tht5 vk.qnn /-mt(e u+farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mof0ye0 s y(a*gtve in the same direction, with the same velo0fseyy ( t*a0gcity? Explain.

If a wind is blowing, will this jmlfs57 iw-:wq()jf8ctljg0 alter the frequency of the sound heard by a person at rest with respect to the souw 8 tllqw(mij)fjcgs5:f- 70 jrce? Is the wavelength or velocity changed?

Figure 12–32 shows varioux70 qna eql-y*g)m pu:p67zfi s positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for tq7uf 0yq n ap:7*ze)glxm6p-i he sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listepkh c:9fvi)jk3ec .v+- ru t)yning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimac)-tcveh)jvr +uy.k i:9 pf3kte the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juvd5+)wpuqr u*pud5 ; zst 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 u )urz5pdqv*5w+;pud at this point? Assume the speed 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 gu7 b:j8:olqp 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 day. Wiehlo xk7q- *x6(y e.lr8cz3xzthouzllkx 6* 8h-eeycx7 x3o(qzr .t warning, 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 splai)/ oz0w-euaqoo 2:spsh it makes when striking the water below is heard 3.5 s later. How high is the cliff? pq0s2 :zwe-ouo )/oia   m

  A person, with his ear to the grl.; ketz6 d n-(vthh/qy yqo.:ound, 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 otk.t-o v. zqehy(/ldy;n:6th qher 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 rzxd:j(. ux.pdzenf9. ;n2la “5-second rule” for estimating the distance from a. 92dexun(:z;a lz pfd.xn.jr lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a bqe5ju; 6sy* ked gpe2r s3j inkx)t2pt1f0,+sound 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 whose intensb y+) ou,nc2ru3x(iquity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produz jdr)t 8cwq.)58r stg2g7k slce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only jrqtrzt c 8 sl)d85kg2sw7)g. one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a )h )tbdc ;eiv:(ul/c++ rb tlicertain distance from an airplane with four equally noisy jet engines is experiencing a sound levebt:lb/ic+l c) h d ;ertvui+)(l 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 ratioly kl5.j -ls9y(g ,jzm of 58 dB, whereas for a CD player it is 95 dB. Whatjm l sk l.,5jlg9y-y(z is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ) c1h7+jtl+brw1.aiitp6j m t.0 pbrloutput of sound from a person speaking in normal conversation. Use Tr1b7ah1+tj. b0+itmpjlpr6 i c). ltwable 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 strikes an eardxjs (y1(cf .khakf7* orum 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 amplifig2-9dye; g. xby9+hy uwec 0fber B is rated at 40 W. (a) Estimate the sound level dy.2+gxhwc9 u 0bybg e- ;fe9yin 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 wq:e/os41;s x( u cbqb5;dcxq bhen placed 2.8 m in front of a loudspeaker on the stage. bc;qxdu bs:5(c qosx/b4q;1e
(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 1s w8dk xbd)+b2h yjw6dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9wb1xddb sw8+ h )6kjy2.]$\approx$   

  If the amplitude of a sound wakd d2u5oe ;(p w5wopihql-;m8ve is tripled, (a) by what factor will the intensity increase? Increase by a factorqh-o (i5kud2p 5;m; lwowed8p of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqh5rrcn .2 tp1z8j iev+ual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intz28h jvpn5c ti r1.re+ensities?   

  What would be the soun w-u7 ce e3b+qr5 *(mkq8iygvcd level (in dB) of a sound wave in air that corresponds to a dibe+ i(w5q ymu 38kc7g*cvqe-rsplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must haveg6i(s2 t2b:vpvnei d-wud-za10g p)b3e h+wp what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? gwi+ wg eh)a16-su: 2-p (n2bddip03vev bzt p(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when txue v otekl8 +c(s7y,:he sound lev:ukx o(,ecslyv+ 8e7 tel is 30 dB? (See Fig. 12–6.)

  Your auditory system can a.g+ m 6djz5xvxccommodate a huge range of sound levels. What is the ratio of.v m+xxd g6jz5 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 43l8:rehb 8o mj40 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must tm3ho8r 8jbl e:he string be placed?    N

  An organ pipe is 112 cm long.r3atyteo7e k0zu7q+ rd hmi: .p( 0ud* What are the fundamental and first three audible overtoneauko+rie e.0ry3 0:hmtd * 7z up(qdt7s 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 fromlpxf +gx+jx8/ blowing across the top of an empty soda bottle tj /x+ l+xpx8gfhat 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 s4wenwkcf4v h * 2d)vme9 afev,v(x k7;panning the range of human hearing (20 Hz c9 n ;aewh7k (*d2vf44 vwevvmef,x)kto 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thi 4btxewt-8d *hrji/ e:rd harmonic. What will b-ett i:bdej4/rx *h8w e 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 aboit)ms0 :c: cmzojx+* ; v:jgg;eapn 7wve middle C (330 Hz mo;0egvpzxc j;c w:g i)+:ant s*7:jm).
(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 oeg2j3k-oq bc 4rgan pipe that emits middle C (262 Hz) when the temperatur2 43gcoqj-bek e 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, 6 fd4ibv (u5foi( hto6co(bb 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute.4s m3yhd.r xrvcm.40 ;w ytzf in Example 12–10 should the hole be that must be uncovered to play D above middle C at h0 .ryym cw4.st4vfmx3z.r ;d294 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 +t4w9f v,im* 1yp 5j5h sppy lsmtt9t(264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clovwljy*mm f4 p9tsth51p ytp+,5i (ts 9sed 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 2r51m(r no,gfa aq cgrh6s0xb4u1q2 gboth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wh1a qxbofrg2qu 2,ghgmr 1 ra(50n6 4scat 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 csw +jjht :/civkg;e.;fp((k$^{\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 rans;; ybsi (p3hege for a 2.14-m-long organ pipe at b; ;he3sy isp(20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximacbf6igqs2,su:kiapu )-+z5 w tely 2.5 cm long. It is open to the outside and is closed at the ot,uib):2+pu6f ck -agszwiq s5 her 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying t-7y; 4hzj ty z)z2zvtuo adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othz7tvz; -j2zyh y)z4uter string? ±    Hz

  What is the beat frequency if middle C hdqrx t*,,t8 h(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 kH(9 f8dikj be6 y ,e6mbsf 7o/f.;jropmq, xpo4z, while another (brand X) operates at an unknown frequency. If neither whist/ pkm(dmq,fs4 e ,py;r7f.e6bf8xoi9oo 6jjb le can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and gaj.vnr- x. ggx cu*5,9 beats/s when sounded with a 355-Hz tuning forjvn*g,uxr g. a5cxg.- k. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned l g eblcb47)2h-7d ikrto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recar el bkl ib7g)24-dch7ll Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play m) , i p2yefgo+ua0r:bkiddle C (262 Hz), but one is at 5.0°C and the opf2 k0iyr ao)+e,:bug ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; u;mnceb(1na 2qac 6+b when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togeth(n1;abcu eb6 n2q mca+er, 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. wp4i5 vkgw55(na 6wr) ,etmgl00 m from one speaker and 3.50 m f l,4i v(trwm5)w5g5gp kena w6rom 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 Hze(dt dq: /br1,*yxu-rz pu/ ka, but a piano tuner hears three beats every 2.0 s when theyqkxue 1,rr/(*dyu-dz p:bta / 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 wavelengthrx+jos0k fl8:sm +9phs 2.64 m and 2.76 m in air. How many beats per second will be heardf9 j+lsso:0xr 8+hpmk? (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 whexd3 h zb2n./id+vdy -)l abgi.n at rest. What frequency gi.x /daldzbi+- .h2 vb dy)n3do 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 wh: 1.vg2x+sdhpf2hp utn* a jh9p3) ezvose siren emits at 1550 Hz moves atvzfpgxv h2+hjehp anp9 ).st:1u*d2 3 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 sourceth5d0 w:tewd kpw8 t;n-ri, a9 is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exacthtn;w8ra,dip k5t 9-:dw0t ewly 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 frequency horn. When one is lkmia460ufpkn*3b8h nv1 yt- 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 ho3l k4-8b h kiyav6ptn0*mfu1nrns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives tz j4+ ex6n8ktv4cc,5e/l eok)c mwkr4hem returned from an object moving directly away from it at 25 m/s What is the recce6 nje w, vm8/)lcr4keto x+k 4k54zceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flie*sn5 )vyah3 g jgaw (2.2bcct ty*tek3s, the bat emits an ultrasont532 *gegt anha 3tcsvb(c2.wkjy)* yic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original xi:b)moqm(f8obwb u1 0b-v/ol8f cp2Doppler 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 / bl8w-fvfox0( 8b bb coup)mi2o:m1 qstation. 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 ultrasound waves t1evc jjtsnd()pe9 9+o-pf )uy o measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue isj1ju o+p- f9t(dpec)sy9)env 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 frequm0:q:bd sh1 whency $2.25 \times10^{ 6}$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 H zyxi+.-v20w4e le. vlmfxt t6z. When the wind velocity is 12 m/siy4-t w+m.2 ve6e0 .lt zvlxfx 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 lany(*.ll7v 3 rc uvty:,)ofanfh;mm e4r d 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 t 4cj a:im*lvl*k7d up 4h9ns)at Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock w 94n74t)a pdvi*h:m ulcjsk*lave 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 atmosphere of a planet where the speez b3 mwrdytm,+) bn+c*d of sound is only about 35 bb )w tydm+n* cm+z3r,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. Determin27nv) rc 9hyqqc ozo:c,:6b jne the shock wave angle it producecon r6yzq oj:7v 9bhc2)q: nc,s
(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 tia8ot*vt 7 wm.01r zx$/theta$ 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 kqx alc7tzr9ee je 28e6a;+njrl+iw6) m above the ground flying faster thanjl rt+q 2eze9je+x7 a6;ar icen8)w6 l the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fri-nn h9oa h61gom the bha9g 1ih 6-onnottom of the 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 manylmq0zn+ f( sk+cw,*v+b;icw c octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewyx (fxcw u3+p hrk/df-m (m*/ser pipe symphony. It consists of many plastic pipes of varix-(u/fmhx c3w+s/ p(*r dmykfous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closy2ygkllh aqq(ko8) 5kowubf 27:u 4f:e to the threshold of human hearing (0 dB). What will be the sound ol u:g 45ykh( q7buf2l)y8w:o f2kqaklevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soubxwd/2.n ec,cd- xo:b nd are heard sibc,wc/x b 2n.ed-:doxmultaneously?    dB

  The sound level 12.0 m from a l4ppy a p:f(dqc-*rg/coudspeaker, placed in the open, is 105 dB. What is the acoustif-cp y p4gqd/crp:*a(c power output (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 outpu.9ibc 7kjp u) qao6:rz/jxk2kt drops by 10 dB at /kbzi. ):pxc oj jr6au7kkq2915 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraf1gqxpww:c z 18i:qjk1z ;k/ijbe;i;vl7v l0j t typically wear protective devices over their ears. Assume that the sound level of a jet 0 ;;q zcw1z/jiipq7l:8wk bl;j1:g v1ijex kvairplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the ie1j( yst(th vrz vo6 l+ax43kb83xl(gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freq2lae 2lyvu)kh7v 0qg*0*ce a ruency 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 points with a fundameh y3j *so-ebl4ntal frequeleojhb-s* 34 yncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wio:*zgc; q;g xater (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 thezcxqgi ;:*;g o distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is y4 wettla93 p 6rm a 2qw/rf(o28qtc+eopen at one end and also 75 cm long. How much tension should be in the string if it is to/2cwepyo 4a69r 8mfaqt e 3l2(tqt+wr produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was ai xs17mcpe;3 observed to resonate 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 tone inxn/azr 8r8+fl57vq sg the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistantqx7/r8 fl gz5+nvs a8r 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 c8v d* a..eq 3z6jtyeiponductor on the stationary train hears a 3.0-Hz beat frequency when the other train 3te. j*vi8.6q adyezp approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train gnt+1q qlw 24m)oz 6miap(zqpm:h /h/whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. w t 4qi) /qhz/+p:qz2ml p6g1monm(ah How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just 5+a(qg6b(ufo 4wfty pby listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the soofpwb 5uyf(4ta6( gq+und of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a x;fj )o4q.j4 aj+tccebeat frequency of 11 Hz. The sho) oex4j+j t ;jq4fc.carter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends3l(p0yfgjeww+-+ pwvftf -g . 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,.-f(pfe-t gp +vjwywfw 03+gl (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bl2 g z6hmkl y9ww.k1:ywvt*;xeat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waml.xk: 2z l w69*hgw;wytkv1 yves 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 whil8n*kn9 ko rr+ v19o;r a4rtyule the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave rt8nv;9ronr yluk o* a1k4rr+9eflects off the moth?    kHz

  A bat emits a series of high frequency soun3c0ooyk1,n2/ 8hrv r zyatu, xd 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 emitte, 38aou/ 0ty rk,hn2x1zcvry od?    m

The “alpenhorn” (Fig. 12–38) was once used tob j(xp 0eok*vxw5gb9: send 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 inbw(jvo b5 xpk 9*0eg:x 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 l 12iefjiw6gh4istening 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. Calculate the fundamental frequencies for the standing waves in this room. h2gji46fie w1
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invz yum8:xb/sxl+ b)mp+olves a long, slender 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 can be made to “sing,” or em) /u m+s8 :pyl+xmxbzbit 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 e8;*wyveb7 zrcar at a frequency of about 8*eb y7zwrcv ;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 Mach 2.0. An observer on the ground hears the soni m5q: ydh3gdv/c boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu/mq5y 3gdh:v dde?    $ \times10^{4 }$ m

  The wake of a speedboat 1rvt .to9bd/p 8:i ndhjsy4v 2is 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