What is the evidence that sound travels as a ms0xhc t 2bu060sf57akkwht1 wave?

What is the evidence that sokuqvl)/ su8 y sc3kagpvtw:(p (yk0;-und is a form of energy?

Children sometimes play with a homemade “:wuw42v:h: c m5wb8od 0vnwi rtelephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard a:iro m2w:h 4nvw5w 8dvcub0: wt 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 87935 -pziey*ty ti,nwxh jgmair into water, do you expect the frequency or wavez8t 3g,75-9jimypyi * whexntlength to change?

What evidence can you give that ta/.yq+ qov3hq bv . (8gypr,wuhe speed of sound in air does not depend signif+ wa q ./.qyu8,bvprgo(qhvy3icantly on frequency?

The voice of a person who has inqtc0/qr7ysj : h67jx4decou0 haled helium sounds very high-pitched. Why?

How will the air temperature in a room va*x2bxbq 68i affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soc5c+fp cqo+ 2 lng .lln,fj08bunds in various frequency rang.+l+lg2 5n8qc,pb0ocl fnfj ces. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog5fux6 -kke+7jqd7ha3kq f;b rether as you move upu577 qe;+k6kxa f qhdbkr3f -j the fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially y/ qjpjhmel; 8(ou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectionm(/jel;hp j q8 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereasr(xu)pt upn .7tvi/boh ox58/ beats can be said to be due to “interference in time.” Expla)rvx/ut npo/5 pth bo8ui.x 7(in.

In Fig. 12–16, if the frequency of the speake,2zj 0a)okwzm rs were lowered, would the points D and C (where destructive and constructive interference occur) ko0zz2, )amjw move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with v3-vww:b8rxe 6nek: frery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noi v-ek8f:w r6 b:rw3enxse reduce the sound levels reaching the ears?

Consider the two waves showno:u v1*o-zasy in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of thos* -1ou:z ayve waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift iv:a5vcjr (sjk49; cfv f the source and observer move in the same direction, with the same velocifv k:vs94a5cj v jrc;(ty? Explain.

If a wind is blowing, will this alter the frequency of .ubn;l wdk3-c h(v6 st41gp awthe sound heard by a person at rest with revkp lw4b6un.a3t;-g w(cs h1dspect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child i0cxzwcauy*2*kwo+3c 42v3d + ybr.i e stuy 7on motion on a swing. A monitor is blod.4+eb c wcwkz+2* aoy02c*yixu to 3uyr 7v3swing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by dhrj)zs, ,y1 ylistening 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. Estimate the length of thezdy 1,)j s,ryh lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hrq9y;/l ):rzkmra h)4j 9dm f zhvpm:(e hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with deph zra9j h :vypfmkqz:rml4);r9 (m/d )th.    $ \times10^{ 3}$m

  (a) Calculate the wavelength-;ftsos76/h7mctruxd o -nv-s in 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 ko:) .c4xdngm foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time el:gmno .)kxd4 capses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the j0hynl f9y6 (rg hg23s (7vrdstop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the hnghdjyrr3 vgsf7( 0sl(69y2cliff?    m

  A person, with his ear to the groundwpk) ru4k vcoz58,.u 4iam0nf, 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 other in the concrete, and they are 1.1akk5np0 4 48mr)ociw,fu.zuv 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 “5-second rulef j 2q0oqf.*jc” for estimo*.q q0fjf2 jcating the 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 sou (rvw9ns/rt1q m0:z/ om0 grnl8; znnind 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.3k mt;j mjf4zoi1r1u of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously67( cmsp4 fzg/iglxgz4d. .xju /yki3 at a certain place, what will be the sound level if only one is explod z/zgfgp3mk(. id7 cjs /.xxyliu4 g46ed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with -ciys0y m. r;e2 ;x fuap)ixko8o:bv 9four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wouleoyv-ic:2 pm) ;uo s8rxiab0 k9 .xfy;d this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said t l/s9/ru*x)h,fq80a ub.wz q. y fzktqo have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise fouz.8),/hsq btx *9qzuly wf0k/qf a.rr each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakina:+oup9uoc 1r 514vpfsipr z5g in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered orp auocu951i5v p1zrf4+sp :o n 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 str:9.g vaf+f ;0:x nrn0l sbfh7mminl (dikes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modese.i:vqko;ck0pu5 m jfe/:/ a8gp jxa9t 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 loudspeaker connectgi .pekf8co/9 j:xuvjmeap 0k /aq 5;:ed 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 regist0/zo lxe 1cqb)fnd jybl +:-f,ered 130 dB when placed 2.8 m in front of a loudspeaker on the ) + jolx0cl/:fydnbqfz1e,-b 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 dBzx u .j 4wna9*48gw+suzh a/oh. What is the ratio of the 4huz *8w/aou. xns+gj hwa4z9 amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inten9vc*xs0+ng -k3 3djc tr2;k3oaicab usity increase? Increase by a factorsdocr330*2 ncj xu9kc t3- gkiav;+ba of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one)l4d -wr,vap6 gfy i8k dyg *r/24ii2xp -ujqu has twice the frequency of the other. What is the r* uk p/24i,uxvir-qr wi f 6a4pj8yy dgd2)g-latio of their intensities?   

  What would be the sound level (in dB) of a sound m+4b g:(s ulcnwave in air that corresponds to a displacement amplitude of vibrating air molecules:s (+4 gncublm of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev)1p s/xh bh*88pknkwvel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6*v8 xhpk h8k)1w/n psb.)    dB

What are the lowest anuuzrh,fxfz+7* g :*a yd highest frequencies that an ear can detect when the sound level is 30 dB? (Seefg7urax ,* yzzhfu+*: Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whasq.m/ ;wnw7swm .a fd7t is the ratio of highest to lowest iwm d.s/;qf. wnmw7 7santensity 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 funh1jvlpx 0++th6k .wldy iw :t*damental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string16tw wphhjk+d0ll y.i+vx: t* be placed?    N

  An organ pipe is 112 cm long. What are the funap)m:lz (u (imdamental and first three audible ovlm ()( umapz:iertones 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 from blowipl7 mulx:o dtuz9;n l1*(1 xy.s b fqn4i:hp(ing across the top of an empty soda bottle that is 18 cm deep, if you assu9ixq.*n; b:(l4dfo(1tzpslmnui7 lp uh y 1x:med 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 ss1:zbwy5 3:ctzcc7eupanning the range of human hearing (20 Hz to 20 kHz), what would be the range of :t3:cw ebs1 zz7ucy 5cthe lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string5(d(a8d k upsaxm,* +wva,v zn has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originan8kuvdvmza,x (+d5*ap(,a w sl length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle b(a3.a/hjzx*3m mr vs C (3m3/3x z*j.( bhrsm vaa30 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 emits middle C (262 Hz)*mr yn7h ;q5go when the teryg*nmhq 7 5;omperature 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 a i tldq8)f )bdstjwr*uw7( d()t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute ig/ ;ihzj9f5dr n Example 12–10 should the hole be that must be uncovered to play D above midjz;f5 g/rhi9d dle 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 616m-btl2 .yvinbl65p iur38rl / Hz, but not at any other frequencies in between. (a) Shom .ylp-6 nv3tl82 r/rb ibi5ulw 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.tw76 8c:aao-23*sz bdgs ghfc80 m long is open at both ends. It resonates at two successive harmonics*s dt g b ao6c3w-:7zcf2ga8sh of frequencies 275 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 8b 2v;x 4eo+lc+r qe(9obyphj$^{\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 audaad(:9a ogan5uto 16 hible range for a 2.14-m-long organ pipe atga(1oa56 hdtno 9u:aa 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside an1 .l8mxmec:im h n5-q: ;jbslld is closed at the other end by the eardrum. Estimate the frequencies (in the audible rangeh1lm ;lnq e.x:8-sm5lib jmc:) 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 on(. f 6ncl5rn-4a eivyvlqe*-ke beat every 2.0 s when trying to adjust two strings, one of whi lf yev(56n-.4kniv-e*lqac r ch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz0d uuzbbmwb4y1ueu h0 in 6n1c it::y16w,l+s ) 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, whilegf).8 e:m/ tbr giq,8iofgob0 another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of freqr.ibm/ 8:8g fo gibf0eo,)t gquency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string prodlqa:2oc1 f2wzgw ncl+,-7 pztwd5 rrxn /ab (3uces 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning forwfg x l wca+wc1-o/z3b7 z2p 5q 2ndatnr,(:lrk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to trov s* h v2lvo)/v1q2au; c2ghee(s3whe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the 3ol ha q(;2h 1v2g) r* so/vuecvwv2setwo strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac9 ie emi26 p17w3kuetbp z3vr7h try to play middle C (262 Hz), but one is at 5.0°C and the other ai37i me2 7ep 19r3 vezbukpwt6t 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency ofsixw328fmibi vwb /a45hr6n5 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 ani ib5a4vbx h5r s6823iwwf/n md C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and 3xzup38 rm2; zo.50 m from the puo328xz;m zr 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 suppo9bcpfct -1(c4/xpfet.e0k nrsed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency opnx/cer pbt k-04 ect9.f1c(ff 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 many beat9spv26 /q)q h cu1lgrys per second wils 1hv2cpy lqu6gq9/)r l be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hu8 0 jxv:r-mrhog(7nf 1q g:i9r x9mliz when at rest. What frequency do you detect if you move rrxm 9u q0nhg i:fl9v:( i-j78grx1mo 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 y z;jdpnage8 bdx/vi/)0w ++gvou detect if a fire engine whose sire80w ;)d/ na/zg++ib vjd pevxgn emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towardfg cb (00nqax9 you at 15 m/s versus youn b00 cfg(qxa9 moving toward it at 15 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 aj3gr0 ctlxi 6ri:y,/ w* pqb:yt rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequec: ,ii/0jwrltpg6y:x 3b *yrq ncy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrq9anf u)n) bo7a ezc m*; (up;db+6sssasonic sound waves at 50.0 kHz and receives them returne mqon;us 6buf (nzbap;7d) 9*se+sca)d from an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat kvsg5ej2k; m ,b)4upaemits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear ijkg; ma5ev4,)p suk2 bn the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movt+ ;,( bda-6rxpjjmqbyp, vs+ing flat train car , tbxbr -6j dyajp,mq(;+vp s+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 ?   Hz

  A Doppler flow meter uses ultrasound waves to fn zn)46l; 7w9vq nli u:iq4dvmeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s direizi) 4vn:9l ndf4q 7vlq;u wn6ctly away from the sound source?   Hz

  The Doppler effect using umv7rcw -)1tp-) ovih zzsaj,4c( m p48zc6xdultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity id ;mmc4nn)u8l2b y f7es 12 m/s from the north, what frequency will observers hear who are locatbn7f28cue yd;4mm n) led, 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 its2fy-ta+fz.yxwnv28b speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 vmj8 clsmtzk /a5,g.wk (8.pjwhere the speed of sound is 310 m/s (a) What is the angle the shock wave mak8.l(5msckaptv. /m jw8, gj zkes 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 atmospher :+:gfd epp5nze of a planet where the speed of sound is only about 35z :n+g pd5:epf m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock,)l jzi5 j x*2fu) you1bxyjl- wave angle it produces2b j1yx)xof) 5lylj,ziuuj*-
(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 6viu 3g 5tlzk7s5t9mt$/theta$ 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)l()zexavnz *xy0r )j the ground flying faster than the speed of soun )avyxln)0z ze(xjr* )d. 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-Hz7 u:by)+ixpvazoy4 ;d t6k oq, sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth fo),q64xvy:b ip uakzt ;o+7oydr which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octgkqgp s wg2846aves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calr-n m:4b*zywabo nh-(led a sewer pipe symphony. It consists of many plastic pipes of vaznn--yr (* :mbhawob4 rious 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 close to the threshd i (tkgf +5r1*u,unmnold of human hearing (0 dB). What will be the sn (u5rkn+tif um ,*1dgound level of 1000 such mosquitoes?    dB

  What is the resultant s-p-,o+x+ob.h c kb xfkound level when an 82-dB sound and an 87-dB sound are heard simultaneously?,obx x+pfb+ok-h k c-.    dB

  The sound level 12.0 m from a loudsc1 3 fem,mc-dtpeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it ra- d,fcmemc13 tdiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drorga+u,+ v6xg nps by 10 dB at 15 kHz. What is the power output in watts at 15 kg+ v+6axr,gun Hz?    dB

  Workers around jet aircraft typically wear protective devices over their t, ai)na x81biears. 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 intercepted by an unprotected ear at a distance of 30 m frb n) 8a1,itxiaom a jet airplane engine?    W

  In audio and communications;2be l3baf6,0gj32 h2nl pw7sr jgwa r systems, 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 to a freqb4 i60eugsvy0sdk+rw mgp(9 +uency 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 betw/mzlpw4 ) uu6aeen fixed points with a fundamental frequency of 440 Hz a)uz6/l4pauw mnd 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 intc9 kr)7h.nzx s-n7c xyo vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate wit7zkn9rx.sc ch7)yx n-h the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar strg t dme8z51kd s r72bps)jv+t-ro6jl9ing of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamj-rze 5s1)t b8s96r2d v pl7g jt+modkental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obse1oj sy*b b;1tbrved 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 rle:;j lh5c2xfz mxhuw)-5l d1*cf.nlange coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the othelj hnexhc:5m1 -z l.fcwdl*5u); f2xlr. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stam/xtg.nd;zau2 ,is 3otionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches iduam/s; .zongt2,x3. What is the speed of the moving train?   m/s

  The frequency of a steam traij :qatajq/hbo41,rehep 6hg.; o )lw2n whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train mq6)a/o4ljqh,w 2gjere:;ptb . oh 1haoving (assume constant velocity)?    m/s

  At a race track, you can estimate the sphx6o i7) k1w/ha85g)c m kd7 uq+lknzgeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on /d5l1hinq 6x) ga )c8h 7kzom+wgk7 kuthe straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetaez zr8/ 3q*45 vmqkjqher, produce a beat frequency of 11 Hz. The shorter one is 2.40 m l /qvzzek m5 *j8qr3aq4ong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movesf45fkq8p nmcf, mo,8sh, kho3 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 ,fm kf5 ,onqhp3fh8,sco4mk 8A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normall82t8 2 a41tkt imxmoh2qlxh fb,sd95dy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed alonbltix ah8x9 qdm t2 md,t12k2fo58 4hsg 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 motixuq2f , ai0vf /. ndj**7axaeh at speed 6.5 m/s while 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 reflects off the m 7ei f,2 /ajxqixd*nv*.a0uafoth?    kHz

  A bat emits a series of high frequency sound puo/ g*1uj empn:8j l)eulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3eg8nl:p*ju uj1 /emo).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) was once used t th*q i1q tnt1h9:kg.vo send signals from one Alpine village to another. Since lower frequency sounds are less sqq t9gvk*:11it thhn .usceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presen wc( v+j6vify)1.svm2m qgsaex- q;.u* 8z hlnce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cons j 61zv)n ai ;gq. yfs*cve2xm-svhq(m .wu8+lider 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, called “singing rods,” involves am/2d r3/wk j;4yo k+1iigxkaqz50 hx u long, slender aluminum rod held in the hand ;khkij5dr/z oxay2k i 1m+ q/x 4w30ugnear the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the huq5xy:k n66a,pjn n 4nyman ear at a frequency of about 1000 naj 5n,xky4pq6:n6yn 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 atsud,c 4g0vre . Mach 2.0. An observer on the ground hears the sonic boom 1. 4gecr0,vs.ud5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1e z 2n ,u q894g2nrhaaag(cbm25 $^{\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