What is the evidence tta np24+m* hwbhat sound travels as a wave?

What is the evidence that p,j1p s,7lu q kh sy5k;bnm8qr 4z5k9vsound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to th-a+ * *wyz8chwx.gj eae bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the* c8e-aay.gwzh*wxj + 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 yoltl9vd 2,/a t t:y:zdj/kpx1z u expect the frequency or wavelength tovzda/:tt:pydlz921lkxjt/, change?

What evidence can you giq7m:yhfzh2tcqz + k2.lm.ay.ve that the speed of sound in air does not depend significac.m2. +ytkmfh hzl2:q7.zqyantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitcf3zrosbd 8dogaex)enoj9cf0*5 2f:( hed. Why?

How will the air temperature in a room zlay1v30lwg+ns q0z5 affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the an-*cre2:vy0xzbi dkjum(zp/rv k18+mplitude of sounds in various frequency pu(z:x r 2ir+v0-jdmcvke y81kb*/znranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–kxmpg dnt*:59k gv v+sq ;+0gjp.rex730) spaced closer together as you move up the fingerboard toward the bridg;vm9 *kxpq0 vj+d7:ngs t+xkpre.5gg e?

A noisy truck approaches you from behind a buildi/9 qmhberv 2t-5.lnmx c 9*fh3qqkh:b ng. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the h /qb.bnxrhhmt c9k 9 *5q:v3lef2-mqhigh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats bwr*jkq0hm)ke1 bxqg. dh++zd 1:)dhcan be said to be due to “interference in time.” Expla +ed*xb0qg ) )j hqdrh1 kmh+d1zwb:k.in.

In Fig. 12–16, if the frequency of the speakers were lowered, would the 6c2r f.4x,3*qz wn *zgcj gcarpoints D and C (where destructive and construct f4rxg ,zq6nc2gj.r*cca3z*wive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areassef ifyypc24aw 7g-y,5mfa 812n3qjm with very high noise levels have consisted mainly of efforts to block or g5ypic,qmw8y3m1-ffjn2 s4y f 2aea 7reduce 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 can0f8 v +*9;c/ebdyef7k8bnx l n+mig tu be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig9d il7nf+e b0yn;xt*m/8 vcg ebuk+8f. 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 direyy g9 ow:bc9jtd :t.5wction, with the same ve. t y :99yodw5jcw:gbtlocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a perjmul:g/(s :5 jhthsy0 son at rest with respect to the source? Is the :y: jhst0ljgh5 ms/u( wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ong npd(rxg5 7gs/d9yje .e:u-k 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 freq5jg/y:-e r u.gns d dgx9ke7(puency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of he fug:j5j7a 3fsr shout reflected by a cliff at the far end of the lake. She hears the 75ja3:jgfus fecho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side .yg wk0 ,d syxz4f2af+of his ship just below the waterline. He hears the echo of the sound reflezayd f+2.wg0y f xk4,scted from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air 4hh;xga e)r;(fsix/ * )uzveu n ;lul.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 fowj rg wk6(8 mq5rurn oz0n),/bggy day. Without warning, an engine bj8r0 )u5, kr6nmrw (ozqw/gnbackfire 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 fromruq zehe;l r2d q1t+07 the top of a cliff. The splash it makes when striking the water below is heard 3.5q7 er;e120 dlzu rq+ht s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concm)w2wbxm gh +/;,enavrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 1+/2awwm h,x g)v;enmb 2–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one wlgs ;*mje( t rs:r vj.g38e9pmile of distance by the “5-second rule” for estimating ther:t3 9lwgs;s (j8mv e*jr .peg distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain t)le mlwmy x2rfo0cv*b0)/ ;xlevel 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 inten z5(ygd7a)ocakxz 0b;sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ajz t.b.76/ invk mk4eat a certain place, what will be the sound level if only one is exploded?jm7/ kt..zba ei46vnk [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four7p;mzn8w uc g;gw (ksaa3;mwf 8u;w3t hoyb37 equally noisy jet engines is experiencing a sound level bo nwgbwzmw(m kfu8cys7;8 33w gt7h3puo ;;a;ardering 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-:dl.e+ tdllv4r8 ag:.h+lm hx noise ratio of 58 dB, whereas 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 dB = m l4:dg8hre:lxlh.lv .t+d+a    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal cor7-rg.wu xzty3qfe0o, 6+ln+ m6qbh(ffaw) bnversation. Use Table 12–2. e0-tzuw3.wb +axr q)f6 b,hl7ogf+mny6(qf rAssume 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 wh1jt;-*gqh e8hlu hv w;ose 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 modes25iz)uzm 0 ae p 1qilg4fn:p3e6lvv2pt amplifier B is rated at 40 W. (a) Estimate the sound level in decibels y)2: z g 6u vpfal emeilvp2nqzp0153i4ou 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 when placed 2.8 m i8ko 1m1be1ji mn front of a loudspeaker on the sta11 8m eokmijb1ge.
(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 ofd)u s cs6t-l:smy lz62ku(2 yi 2.0 dB. What is the ratio of the amplitudes of two sounds 6zd cs: -l(y)6u2tsls2yimk uwhose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wavdfkj2 d-cm* 5 -s4 +ky1,n zjvblf5ewyoy5 (fce is tripled, (a) by what factor will the intensity increase? Increase vyck5b*5w-ms54 dn+y2dzje ok - ,fl c1yjf(f by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displace n n/wxd:i for;,p rbb*s,k:f7ment amplitudes, but one has twice the frequency of :k7nirb/fd nf bw;:p,rxs ,*othe other. What is the ratio of their intensities?   

  What would be the sound level vch(kg6u3 a8o(in dB) of a sound wave in air that corresponds togo3 hu6ckv (8a a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must ht(kz5uw / xlj;ave what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 15wzkj/ul x( ;t2–6.)    dB

What are the lowest a6lj4pnt xk; w9nd highest frequencies that an ear can detect when the sound level is 30 dB? (See xj 49wltp6k;n Fig. 12–6.)

  Your auditory system can accommodate a huge ranrz d1n o;khl14i6hn 4vge of sound levels. What is the ratio of highest to lowest4zv l4 inhndrko;1h 16 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 /ouo635j (ux2f kt3y;fkjgs1kjeid / of the vibrating portion is 32 fi5 k6 je jj /313/sduyk(utf ok;og2xcm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm longth7urvq9;2 wu . What are the fundamental and first three audible overtones if the pipe isu2vqt7uw;9 hr
(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 wo q9ie yen* 1;-zj0curauld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tuc1e j9un0q a;i*ez- yrbe?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ do w6 i*n2m,owwith open-tube pipes spanning the range of human hed*62,m i ownowaring (20 Hz to 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 kh 7b*5eig bkcqpx6(2Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a lengtxkhcbq pg 72*6k5ibe( h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to playrnrj9blfrdii7 5n: i y8q2x 40wac3i3 E above middle C (330n3 j: b5dqyr7n8f lwi3i i02ri9xcr4a 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 opi u/d)*fvlhj ephx ,16en organ pipe that emits middle C (262 Hz) when the temperature p1u ivhx)he, dl j/*6fis 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 27 q8w bwt . u*d2gz3dwqa4f5kr0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be thar9i*kys4l o5nt must be uncovered to play D above mso5k *yr l9in4iddle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but4bfkdowf/i;. *.mhio npp s 2( not at any other frequenciesfppbh.i* w(4k/.sdno2 ;of im 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 resonates at twohg 5 4p-ha ps7t0/gby6 j+ttxr successive harmonics of frequencies 276 s5 /phyg pt4+h0jgb-axtr7t5 Hz and 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 :i:x-l0bgg ;mxtp1*rfgr2s iv : u4hw $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-l twle/xm 732xaong organ pipe 72 mta/3 ewxxlat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It igw*;dq1mly8xpvzbi rzx/ ohhw0b y)*( x*g 1: s open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationshi ;wzxzyoyg xrvqg(*l bd1 /b* 0i8p1hwh:x*m)p 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 u8c l-uq-:gc69 ) 8iiq-lfikjwwrr+pry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off:6wicfwg)k-jp - 8riquri 89u- l+lqc in frequency is the other string? ±    Hz

  What is the beat frequ.l3*t-lxll kt ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5tv(*uw 6k0pq(vmw z9ayy,d1q kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs wq wtum(dzvy0v6qpy k1(a* 9,w hen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string prodi-+4mx e4fk-6 jxitifuces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequenj6 -me-i4+xtfi ki4xfcy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The h1mj tsv. cete 237xw+el97qatension in one string is then decreased by 2.0%. What will be the beat fre+v2x19wm.e alqh3 ets7tce j7quency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each 2n,hwuby -ayqmd 4 / q2qnwc:(try to play middle C (262 Hz), but one is at 5.0°C and the ot4yq:2cm-(a /bd w 2,wnyhqqnuher at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hasjlzng,ch 24tntbexu8-3 n /* a a frequency of 441 Hz; when A and B are sounded together, a beat frequency o-83 t zuna,nb4lgx2t /jcen *hf 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 bg oym b tfw*ws 8jic4d-t36 *; q,max+;o5xwjm from one speaker and 3.50 m from the gq+bmxs jo3ib 6c y,*4 5;aj*wwmx; w8tdt-ofother.
(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 t*7fjvmss6r is-f: w1dr d,(eko be vibrating at 132 Hz, but a piano tuner hears three beatsd*(sjv: 7kr 1wfim,d -se6fr s every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How manys53;fnr h r.j :boqd9fglh.)y beats per second will be heard? q;o5h 9yhj3:rs lrfgf.). dn b(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ceroxommtab) 24) tain fire engine’s siren is 1550 Hz when at rest. What frequency do bo)4 2a)to mxmyou 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. h/ds rrg8:l.j What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at asg.:8 rjdl rh/ speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in wt 3 +g spu22ja/ste8(z/p ftdfrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ex gjttespp3 /28uws/td2 +zf( aactly 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. W)gtsq 3fp7dzz d-d 6of7-5mtdhen one is at rest and the other is moving toward the first at 15 m/s the driver at rest heo- f6pz-d7 f)3dg7ts zqt5ddmars 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 ultrasonic sound waves at 50.0 kHz and receives them ret1 )t* jb;k ul elaomfhoy24,t7urned from an object moving directly away fu 17olt )hmafe; 4*ykj,lb2torom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b rl y/huj,yz-2yh:d+uat emits an ultrasonic sound wave with+ u yj,uzl/y-:h2y rdh frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimenrl:0vfu ojmx* u.-e/3bc nj/o3uzw 5 nts, 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 10 m/s n0ov nwoz/ 5:fubj3cj3 */-xeurml .u?   Hz

  A Doppler flow meter uses wg9wf g8ii 8qhhli*72 ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.58w2f ihiiglgh9*8w q 7 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frsqe+5yc( tb e8equency $2.25 \times10^{ 6}$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 winm7 j/ v;lp-up8edmc.ad velocity is 12 m/s from the north, what freque -a8.pdlmcp 7;j/mevuncy 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 speedg10 sv3* exxtuyu5jmye 0z5l , 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.snm .aesx7ex.obqla+t+sa,t *q n; 5 310 m/s (a) What is the angle the shock wave makes with the dir. aa mq5+aeqnt*;t.,ox x +bnesls7 s.ection 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 atmospher :yml-at 7)swde of a planet where the speed of sound is only abowtsm:d 7)ay-lut 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 ae5-,tz2c dvq8500 m/s strikes the ocean. Determine the shock wave angle it prodt d2 ,e5aczvq-uces
(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 8roe w g6*lpajp+2xw( $/theta$ 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 above the ground flyi37i ug ,+x guc5ag5nrcng faster than the speed of 5g+3a5,cx 7n ggiu rucsound. 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 devich37 w)sbm3vu-na w1qie that sends 20,000-Hz sound 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 betweiw)h3 nuw13qs vba7 m-en pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible radc+u k(wls9km ogf ;5,nge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon 9j ,kb0xfm1xa);9uv;aoq sx fy. It consists of many plastic pipes of variousokafs1b0x,qu j9 v;)x;amf 9x 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 pp+fhh5v/k/7 nq* qpv from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 105+/n f7pq *vkhhp/q pv00 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soudt/k+2anra ka :y z:*nnd are heard simultaneously? /: r+kt2azy d*:nana k   dB

  The sound level 12.0 mr9 e w0vtp.6lbfh0sz( from a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (Wztrb009(vs p.ef w6lh) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W out8:skq u1yjk9nxb oj h421)jxqput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output2xj9j8k 4qs )qk x:no u1yhj1b in watts at 15 kHz?    dB

  Workers around jet airc4t3n-,t n vydk 9izw,i yff5t6raft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power f9f3tn5 ikt wnt-dy46 zy,,i vintercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, tfch 3e *7ogfa.he 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 gtqkb3dms , n92.iptnsiq;zp8d) 0f8 is tuned to 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 between fixed points with a fundamental f u0771iu,s8hb ysoipnrequency of 440 Hz and a massbni0s7pu7huo1y,s8 i 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 +o4sq5*u5lzfa.it fnvertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water levefqot 5af .i*lzsn5+u4l 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 nearjee oifoxqe o9ba.u j ,3w*4+, a tube that is open at one end and also 75 cm long. How much tension should be in the string o q,a uji3+9xo 4 jowefe*eb.,if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was objkt*mus.j8; x a o/h .do*.uqoserved 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 in the 500–1000-Hz range coming 4wb qnw1po)b5 qyi5*7mf mi6rfrom two sources. The sound is loudest at pointyb)5*fio5q6bw 1im rq74 n wpms 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 trai+mubg5z 3mv66 cn(yxjb7 7ahc n is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other 6uzh7 gnyxvjc56mam73 (+bbc train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appr rv4 h4t-xtzm*oaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (as*ttr44 v-zxmhsume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just o+rm*8,5 ni d bq mfaark4g4s9by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certsak g4r amb8*d9mi4f,+q o5rnain 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 ai0lxi )xskq7 : beat frequency of 11 Hz. The shorter one is 2.40 m long. How long lqi)x 7 i:skx0is the other?    m

Two loudspeakers are at oppo()o,n 6 z-d)lnwhej alsite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the spon 6dn ),jl(zl-ea wh)eakers after they have passed him, at C?

  If the velocity of blood fo tjb9lq aq;m9kf8w6 5low in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-mqwt q jkl659 9f8bo;aMHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tw033: yv2s htthnv -seo c-y(coward the bat at speed 5 m/s The bat emits a sound wav :cttw s s32(e0 c3y-oynhvhv-e 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 serieswikqz)v3h1yp d*kx :5 of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long5zi :whk qx1vk*) 3ypd. 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) was once use9dx f7wp+5;9tjawmvs0 ba1mr d 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 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 thtva f5x; wrda91j9+ mbp0ws7 mis horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo rcent / a9ywq1/ctu:2 +d:zw0gc m8felistening can be compromised by the presence of standing waves, which can cause acoustic “de29zwfca /t+gcu8wq m1dc: er t0/n:eyad 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.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, c)mem knyld, b-d m9s6c 2;1bzrmic9 d6alled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emr -kb2cz dilcyed)69 9bdm m;1,6nmsmit 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 t5kx.wh coki68:7 nou;( cbyobhe human ear at a frequency of about 1000 yuockboi.5;78kb hcx6n :(o wHz 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 a-g (-p xlewa9yf*uh :observer on the ground hears the sonic boom 1.5 min after the plane passes direc(fhaa guy9p*:x-e lw- tly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatdvdvkm+/lmup8),8yj+6(ru p gzq je( 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