What is the evidence that 4 cr c7b6,9sdrsyxg3k sound travels as a wave?

What is the evidence that sound is a form of enet zn3r6hro i*:rgy?

Children sometimes play with a homemade “telephone” by attachi6xq/b6gnbot * jb6wz+f ,/jiing 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). Explbwt6oz igjbixq/b/*6 6 jf,+nain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fre*cx-0/znzf.dyz k jqem *kp,.quency or wavelength to changek.fj cz,0dzny ez *.px/q*-mk?

What evidence can you give:xt:r mbcqoa(-: y2ze that the speed of sound in air does not depend significantly oemcy:rz:(x :tao- 2bq n frequency?

The voice of a perso-a kt3-qomjy:i :-sf sn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of or d416cz+jlc7- cp (mmb(nihxwgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soun kc43 hc t)gptyt; -v;/rq8delds in various frequency ranges. (An example i c ;;pyvegq8lk4t- dttcrh3)/s a car muffler.)

Why are the frets on a guitar (Fig. 12–3n l/ty ugj h(01h( 76z*cgfxgd0) spaced closer together as you move up the finger6cghxdyg/l(fh7t 10ngu (*zjboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hee5r4mzjr 0baw 1.b2r bar 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. [. bj1r z mr25b04berawHint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inter 8q0vx(i*y.2saqo zed ference in space,” whereas beats can be said to be due to “interference in time*yq0v2 dsziq a( xo8.e.” Explain.

In Fig. 12–16, if the frequency of the speakers were)25m b2b lxwj2u:mhjr lowered, would the points D and C (where destructive and constructive interference occur) m5lmh2bj)x mu2j rbw2 :ove farther apart or closer together?

Traditional methods of protecting thek5m,l-w unch;od )*9dtld5 f8mb( lnl hearing of people who work in areas with very high noise levels have consisted mainly of ,ou9 d; (-ltlhlw5f lbd *nmc5kn8d m)efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave canumx3bgkc(; ctevr6o a y k/a7b/8+n9u6x rzx. be thought of as a superposition of two sound waves with slightly different frequencies, as in F 7 (xo.3r a r8x9n6uxv ymb/a6+ucckzbe;gtk/ig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direction, /,ybsumre7q0 euq,y7m b/rs0with the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the w2qf:x2m; bq, vjv.jtsound heard by a person at rest with respect to the bv2w2x;q,mjqt .jf :vsource? Is the wavelength or velocity changed?

Figure 12–32 shows varme*ajmeypf/ ot(-c juk14)/ oious 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 ae-k/mm*u(ej )t4j1copoy/f the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengxb3h vs)j5+ b 9ouq5d s bav8bh2y-1ofth of a lake by listening 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. E5sb9-b oujh2 avv3s dbx5+qo18fyh)bstimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the we 0 eps*llp)i-aterline. He hears the echo of the sound reflected f)isl elp0*e -prom the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air c c40.vkn2hfe gjo7g:nf ti hr;.:c2mat 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 drift fweh9jk(7uos j 0p(y 1ivpttys.)w-qm,fe68ing just above a school of tuna on a foggy day. Withoufk0h(-p,1wymiewye o9 js.p7st(86fj qt )vut 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. T2f z0yqkeb4 dr7*4zgp2 wh6q bhe splash it makes when striking the water below is heard 3.5 s later. How high is the clif *fq hqr2z 40p kzy4eb7bdgw62f?    m

  A person, with his ear to the ground, sees a t 3, b54ajw7xuzo1 5liyay8nt huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and th5 a8t5woi74y3lb,ju atxz n1yey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error / r 0)gayhajsw8n8m s,made over one mile of distance by the “5-second rule” for estimating the distance from a lightsgha/aysrwj808,nm) ning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paivvprb -w-+tu; n 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 intensitp4zf4d n03 o;p 04gzqbet;:*/lto e xgq7im siy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta-)bh( bhig0dt3yo izuxm 9+t3neously at a certain place, what will be the souott0 h 9d 3(zih3m+)byiugb-x nd level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equaly(38-.kf29 a hjdhffm swbcw 0ly noisy jet engines is experiencing a sound levebm c 2(0hw3fdf.9aw-sfh8k j yl 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 .-*bh(ea le/i h5kg,pkuj /eb 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensiu-h /gbhakb i. j(/lep*,ek5eties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nal20g(*z j tupormal conversation. Ujl*z 2ut0 gap(se Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrumw h 0bcym)3:kc 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 7 nx .jlsb*h1aht5kh57vqbqv0n o*4 kis rated 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 a point 3.5 m from a loudspeakernv.jxtb q*7n5osk *h a0hk1qb57lv4h 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 c z5/6wapger f ey+/e0in front of a lowac /pgzy/6e+e 5rfe0udspeaker 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. Whatkmfij-t z336a is the ratio of the amplitudes of two sounds whose levels differ by thi6 akfj3-mt z3is amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavese 39gx4rn h 4 /lcem7uauw+1m is tripled, (a) by what factor will the intensity increase? Increase by a fachu ce 4wemgn943 7u+s1aml/rxtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but ogm aq,n;sx-) sne has twice the frequency of the ;qgx,-s sn)m aother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a ,wq fh;3vo, pfsound wave in air that corresponds to a displacement amplitude of vibrating air molecules,;hpq,w f3fov of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1005ga clby0mg, 7-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) 0lgmc7g,5yab   dB

What are the lowest and highest(q+ 2kxl8p fxt2v2xce)2k nu n frequencies that an ear can detect when the sound level is 30 dB?x2xqpkf)nn2x l 2ut (e +k2c8v (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levelsyivk,u *a8ca2am67 qrxwas /m m;n2x; . What is the ratio of highest to l 6aan/ a8mc;xaw v, 2yi7m sx;*km2uqrowest 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 440 Hz. The length f v -1 rgi8b:ououv3v92ye:byof the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensio:g1oyob93f r 8vb:i2-v vuu yen must the string be placed?    N

  An organ pipe is 112 cm mb x 4v7lkh w/y7e3ma+long. What are the fundamental and first three audible overtones if the p bav4yk37+ hx 7welmm/ipe 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 frequenc9xfbr .;at 5f*eoxokov.,5hny would you expect from blowing across the top of an empty soda bottle tha; ntvk5,hxba9 o f5*e.or.ofxt 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 orgaq8:2lvazvic:n gc3q5n with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the8nlgcqa5vz3ci vq2:: 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 bjjcrtowc 96b2vk6s hq0,)0y 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original len0 h6y6v, kbjrc29stjobwc) 0qgth?   Hz

  An unfingered guitar st pc+2crgf;ov f/; fqe:ring is 0.73 m long and is tuned to play E above middle C +cofq:/f2;ergpcvf; (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits0n5tk w)j xiox)), wmd middle C (262 Hz) when d wox)5),mj w0xn)kit the temperature 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 20 rytsrs,e 6s21ovm7;c6+ki nt $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec9f0byc,ukb r efo.q( )e of the flute in Example 12–10 should the hole be that must be uncovered (bkr ef)u,9 0obcq.fy to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 -vpikflo10.sHz, 440 Hz, and 616 Hz, but not at any other freq lksiv .p0f1o-uencies 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 n3ts0ece; (7zdaqd :x 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz an d7: 3;(cesexadz0tqnd 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 s0+ foq(ke-6bs +ydbu $^{\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 jn-r 8x :qrj1opresent within the audible range for a 2.14-m-long organ pipe at rj 1 orqj8x:n-20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately+(;0yhaz +(ityakv *xo 1 3hjgmio ff. 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the a iyyg.o (f+hjo+1t(0*fh 3k;xmivzaaudible 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 eve r0. )qb *rhltdy-*nxlry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other ldql*brhnryx- . *) 0tstring? ±    Hz

  What is the beat frequency if middle C (262 Hu epa;d;x6 *imz) 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, whileh8fobl.hg i3 l o*/vs8jdb83 o another (brand X) operates at an unld3/oh88fo8ib 3hg *vbjol.s known 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 simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produrr4cwqoz(,/ j/f x b/;9bepg mces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded wit4mgf/r (bej 9,p/wrq zb;cx/o h a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toe 2 hup/brh+(njnxz3; 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 to h+3nr/2(;hb pjnezx ugether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryib3 1xyj-*:gw zrj,d n to play middle C (262 Hz), but one is at 5.0°C and the other at 25i3xyjj,b 1g-*zr:ndw .0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a u9s cea 1y+yu4so4x4 nfrequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded toge1c4usyusy e+4 a9n 4xother?$f_A$ =    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 f7ebdkb2(.2uodl :a eqrom one speaker and 3.50 m from the other. k7eual2 de (o:b qb2d.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, btfd1 8 z)*luzrut a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, wh1dz)*ruftlz 8 at must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.frp sg*2e u/w8hwen(nom8 j2276 m in air. How many beats per sh gn8p2of8/es n( r2ewm2 wu*jecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequwomjsm2)3sm pjj)* :pency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if)mjmp*jmjo ss2):wp 3 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 fire0rez/) xwrh1 a engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 10h re)zw/xra
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movinas; f2:e ).mtepd piz7sekg4xt6l2;bg toward you at 15 m/s versus you moving toward it at 152lm:.6)a i;p;p fst t ee4xdbsz7kg e2 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is atgtp . n.hojgao/tt435*gpi4 2jljp 9w rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? 2n4gi5 t*t4 j p/oj.ljga9ptwpg ho3.Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound jq1wyo f1z)8mw iq-p 2waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivqqj1y) mfo-ww21 iz p8ed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the pjgc;70a ghp ,cjlb2kt;0jv- bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wav 07ckv -0pg;jj,lp agc;2hbtje?    $ \times10^{4}$ Hz

  In one of the original Doppler exp:h9k s 0sr3a oas dd1+zs.d9noeriments, 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 frequency was heard if the train car approached the station at a speed of a9ro on d+sa3:s d0s.s1k zdh910 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure b2ov2 4onz2 bpllood-flow speeds. Suppose the device emits sound at 3.5 MHz, a2vlbz 22on 4opnd 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 at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect uz/x7e+k5j 92r xwr;krwj8bhjsing 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 widk0 gc0wr2b3 end velocity is 12 m/s fro2e cg0dr wb30km the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spzx2mkx)ox b c2tr 82hb(oin+c 9ojim03 i.o0beed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 h fzbfyv;eu .z685p qqvrj0:) -ummh 5m/s (a) What is the angle the shock wave makes withv:v)8hum q 5-umrze5q6zf h.p f0ybj; 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 a6mq-h:2 w,++a fc q5gwp bicxbtmosphere of a planet where the speed of sound is only about 35,ga:5x+cqmh c +fp-iw b2 w6qb 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 shock5 w,x57hjp hhs wave angle it produchps5hxh7, w5jes
(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 el by3zup6 o1 z/he-lb z;e3,p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km aby bxz.e30-mnr kg xsdy.bs8 .5ove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distam .s8-z.0eyx.rdn5gbs yb3kx nce 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 souwsyq ,( m3r.xjnd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in frq s3wmxy(., jresh water)?    s

  Approximately how many octaves a iel ky(*a my20u*j;cgpa b2c*re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It cons:m(s,9po0iv /ss k snmists of many plastic pipes 90(n,mpvsssk o/m:isof various 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 zb f8*te erl7g)n4o.gclose to the threshold of human 4g7 *.)o8gnlfetz reb hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-m)k nwp y)+b4hdB sound are heard simultaneousw)k4)pmhy nb+ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op1e v5m 5, kstywr:phw)en, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?5tv,5r ewsw:) kpm1yh    W

  A stereo amplifier is rated at 150 W outputzqie50-b mip: ysi29d at 1000 Hz. The power output drops by 10 dB at 15 kHziz q:yipis29e 0m5-db . What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. xw.dq;wc0k u)-ra1x2 vl/wq rAssume that r )xda 2wv/w-w .cq0;kq1xulrthe sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications system0pe n2 f3i*iz-fx r ysdtc*3l/s, the 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 ;op*/ (p zttrzto a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long e7e2g2vztn 9h between fixed points with a fundamental frequency oe nv292 zhet7gf 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 watqtgg2))einm:t r l y:,b bl;-ber (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 wht : ))bq2y,etggimblrn l:b-;en the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one endq/fl +7p*aabh -a p6fr and also 75 cm long. How much tension should be in the string if it is to produp a 7ra-+p/ffh*6 qalbce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed /77/jss +m mfu+q :tuj gn8tsnto 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 in the 500–1000-Hz range coming from two sourc6(ignv8t4n+vgwd n(xdm2 5qm es. The sound is loudest at points equidistant fn68mn(g wvv d+q5x tn(g2imd 4rom 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 stay/jk6y,nr,zos rrzythd7m* )2lq -4wtionary. The conductor on the stationary train hears a 3.0-Hz bearh/-rknw*t), z rjz46l oydy,ym72 sqt frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you+n5eyc q 48i0 /9 4qbjmmtgqom is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movi5m8qtoi e9/q+cb 40y4ngmjmq ng (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just byvs,7op w *vr r;,d5e 4fjxhc;g7s9hy v listening to the difference in pitch of the engine noise between approaching and recedid p5,74;ew vgryx;9 7chsohrvfj vs*, ng cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The nzwlm ,*n4s-l5vvic4 dhvu* :shor4sd i5clm:lh - vvu4w* ,nnv*zter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastfv;mjc+,f (.dps 0 fqs 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 fronjc+ sd (q;.0smpf f,fvt 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 bl6+ xyd 0p dpznefeb610ood flow in the 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 the waves travel with a speep6f0 eexydp 1dn6+0 zbd 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 flyingefe9(b:u sl5 :* aveic 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 reflects off the mot(f e 5s:eial:ubec9v *h?    kHz

  A bat emits a series of high frequency sound pulses as ek:i;xw ldi+ qe*/eb9it approaches a moth. The pulse:kd9liq wi e/b*ex ;e+s 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 emitted?    m

The “alpenhorn” (Fig. 12–38) wi.1 tjo3 aua/h:c:xgras once used to 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 in suco 3c.j/xa:ruth ia1:g h 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 listeni7+g 5 ka oh7xeh/erv:sng 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 gx s7kaoe +75h:/he vrlong, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” vs8c8.xl wq,8abo2rj involves 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 o8j8.b lsvxa28wr ,qc 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 earvfy/ 48oqkoduv( w ;1m3;lfi 2rrxzk1 at a frequency of about 1000 Hz rl4 3x 2iozm (yf d;1 ;fkrwok1vq/vu8is $I_0$ = $1 \times10^{12 } W / m^2$ 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 hearsmjden6/l44bjeafqjp04 r t() the sonic boom 1.5 min after tfjqledpjemb jn4 /t6(04 ra)4 he plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat w -s xfaw-8xa*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