What is the evidence that sound travels as aq 6yb q5 5/infdv,3tmi wave?

What is the evidence that sound is a form( ebf0zn 7f b;hwcizy ,i2nk00ow.9zl of energy?

Children sometimes play with a home)r 2f dl ).bzllbns0p2made “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at th.0r ) bz2lnf)db2 lpsle other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passez/s,sv eapl).8o:5me kfd jd+s from air into water, do you expect the frequency or wavelen: essd5pl.ka8/zo m,)fdj +ev gth to change?

What evidence can you give that the speed of sound) b f zk;u.m/-pap7miw in air does not depend significantly on fai;bw /)k.pf-z7p mum requency?

The voice of a person who has inhaled helium sounds very high-pitched. W3klvdzak ,6bp(l5enn 4p7 d 3bhy?

How will the air temperature in a r(a+. ea+t sqwzoom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sou2mu (a 0pdob em;)oga1nds in various frequency range;u )a0mmdo (2a opb1ges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move fg;uf rf1 6.n39bgaojup the fingerboard toward tg.6f;f 1 ufbaogjr9n3 he bridge?

A noisy truck approaches you from behind a building. bxylmo1 cdxyz/,s2q- , i(wtn xx x+h/3n)k/cInitially 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 high-frequency noise. Explain. [Hint: Seex+,3mw) dx2sbxkinzc/1-(lxyqx /o h/ tncy , Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereasw*x .t46bs pu+ kt1x ;j)rnlhs beats can be said to be due to “interference in time.”t.r1)kssx ljh;t x+ 46wu *nbp Explain.

In Fig. 12–16, if the frequency of the speakers were lowerth*6 eu1pd4 q9,tok2 oh 34agssm 2ujue7l g2wed, would the points D and C (where destructive and constructive interference occur) move fartjoe ,7qd2h la2gkw 6tpmusu44e *t19h 3ou2gsher apart or closer together?

Traditional methods of protecting the hearing of pg-;hpy6zoa 3 miqh; ey(k.ja,eople who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wornqp;jh3omhi- e,.6ka a ;gyy (z 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. Eachnq1* zg9 0/ /.jgfsm*cxp ur (gpw:bmo wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (ab/1mgxpg0q( 9 *u: wf. gos/cp nj*rmz) 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 jc oey5wg3 y95same direction, with the same velocity? Exw3jcgeo y y955plain.

If a wind is blowing, will this alter the frequency:/q*crlvf 3 6oav08 ffzoqo7mh/xtm9 of the sound heard by a person at rest with respect to the source? Is tqxvof/cf9z 7m:a mo0h q3 /86 ft*lorvhe wavelength or velocity changed?

Figure 12–32 shows various positions pwx wqk0c3i(2of 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 qp23(w xkc w0ithe child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines thwj;y zv3gc)( -jzmk2l e length 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 ech-k(;l jywm)2g cjz3 zvo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just bg)e0x72uk uqpfv .t9oelow the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and v2puxe 0kqo f7u9. t)gdoes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt1b qquoj7sof.u(n x88 lrd8/s hs 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 jus x ,rb(yjsi4;z9igzb1 t above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time ey14b zrg bx zis9,ij(;lapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the tosseu3i 2. juz-p of a cliff. The splash it makes when striking the water belowu 3z s.ie-j2su is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone 5)mujth1 / lyastrike the concrete pavement. A moment later two /j th )1ymlua5sounds 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-suge o*,(p u0m(+set/occ 1k pcecond rule” for estimating the dist+t, e* o g m/cs(cpku0ceo1(puance 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 iqbz2.kc t - uw8n7r.vpain 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 intensit0ohk+ 45-lck+rr ucox y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of lnnz8y4rwy*/ 95 dB when fired simultaneously at a certain place, what will be the sound level in*l 4z8rwn/y yf only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from petszb2y tjo2428)l xan airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person)824sl 2jo2y p bttezx 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 sigq/4kv0 ;g*xl r.civrvnal-to-noise ratio of 58 dB, whereas for a CD ;v irk .v40qg *lrcxv/player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking ing o*bo7m0*ltm normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly *t0 molbg*o m7over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose e-1f ),oc*v j lgbeve2nskb .0g f:2hxarea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is ra*4us qr(grp;zw* z j3if12v dm/pes, sted at 40 W. (a) Estimate the sound levws ; ijz1/pq sme**u32 g(rv4spr dfz,el in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plg z6+g d/+hnp g7fwg82s xol;8kw1rxnaced 2.8 m in front of a loudspeaker on the stageog2+ hw s;6xrpfxz1l+dkgw8ng /8 7ng.
(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 leve0+j ah+v (rnbkl of 2.0 dB. What is the ratio of the amplitudes of two sounds w0h b+jk arn+v(hose 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 (dtmo17 cs1h- ter rp2intensity increase? Increase by a c-h7p(o dmets1tr21r factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, fiwvrk;ev aw7) :(385w upulwkzv07ibut one has twice the frequency o kr5a)f;u7vp w uz:iww0v3l7 wik8v (ef the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in m4j m11kpl- o s4/bfxob.w hs4air that corresponds to a displacement amplitude of vibrating air moleculefxp1 m.-b4mo lsjk bw/4hos 41s of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound lvxhl,h*ix: q -evel to seem as loud as a 100-Hz tone that has a 50-dB sound leve*-qvixhhx, l:l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies t:xpro nk4, my3hat an ear can detect when the sound level is 30 dB? (Senm rx:y,4ok3 pe Fig. 12–6.)

  Your auditory system can accommodate a huge :w j qc zq+4ooa5fb,,c(azj7trange of sound levels. What is the ratio of highest to lowest intensity :4ao ( jctf 7a,ojz,qwc5qz+b 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 of thm qx qko0b*(u4e vibrating portion is 3q u*4o(kxqm 0b2 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundr2 y05 uz/x0g1)clwwuph ;li e-i.ewyw;m9i gamental and first three audible overtonehw) 0cwpl ix2/59;-ewulw1iiyey g0rm z gu;.s 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 froml l)q xq2w k895rc8dev blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clo92q 58r dlkxl) wcq8evsed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pi/wym,i- meed; pe organ with open-tube pipes spanning the range of human heaim;ew y,e/md- ring (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 frequenck41wlg7de -0 nho y9fzy of 540 Hz as its third harmonic. What will be izdoln- 7940kgye f h1wts fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and epjd b:x*9ip/:v+ m5 rvzvr) bis tuned to play E above middle C (3dpm9j 5vz: r epbr+bv*/v i:)x30 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 middlei frl94)3pris C (262 Hz) when the temp9sp f)4 i3rlrierature 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 at9:jeiwexq, zvir6 4*:ejt/vyv i6 mu:qunk +9 20 $^{\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 1cglt0e hpoz )c -tmd5k-s; 7y+2–10 should the hole be that must be uncovert;e lyz -)mh-5 ckpc0 odtg7s+ed 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 Hz, 440 Hz, anac -4m 3+b t3eqfsgwy.d 616 Hz, but not at any other freq .yqsg+efm3b-ca3t4w 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 1.80 m long is open at 1 sh(cs,und ja20eol6both ends. It resonates at two successive harmonics of frequencies 275 Hz anus2,6noa (0 dhjlec1sd 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 b k 763vsx9-lvj4 dqrxu 48zfet02c gd$^{\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 f8c,w:g 2rkbsad/yu+x ua; t 1vor a 2.14-m-long organ pipe c2kaav 1,d t;r/ s+bux8w:ugy at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximj m oo+q:h 53oss;9i3e)gobiwately 2.5 cm long. It is open to the outside and is closed at the other end by the ear); +w9o5s3ismgooje iobq:3 h drum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.bazk ;veow oic6uk+1ab) d*720 s when trying to adjust two strings, one of which is sounding 440 Hz. Howcev1 + 6ka*b2)zokbu;doi7a w far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 9g jgd1qm3sjldz5*mw4)ura..bo o l5Hz) 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.i a0 23akj(k lccdsz*q5c -(fy5 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 occuc da (li*3c5z 02(-qcf yjskakrs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35y vc3;8kn-w2vrng 6tc0-Hz tuning fork and 9 beats/s when sounded w3rk8;c-gtvvwn 2 n y6cith a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequen ;trc0ho z;s +ltid2sgk 04no-cy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Ret ocgs-+ nd04k20hos r;l i;ztcall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play m)f 6* pvhixsr/:cz2yriddle C ( *sh 6 irzrx2p:cy/vf)262 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B.;p0.wjzgn4ggdf 7d g has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded t0ngwg. 7z.fd; 4jdpgg ogether, 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 m from oneq;flu8j 1xmsf *i-zl,- upgx. speaker and 3.58 q*ilf;mgx fxpz. -suj,l 1u-0 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are sup*3oxvjjdc.8psgt( 3+ djnisn*5sz0 aposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when thesd pz*s08jsgnj*.jxctn3+o5( 3a idv y 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 :hln zp/72euf in air. How many beats per second will be heard? (Apehf: lun /z72ssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ zqj-e1o,bj izbq- z.+ency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect ifjzibz,+qe-z 1o q j-b. 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 frequka,9u7 2yey zmency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed z2a,euk7y9ym of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20y4j j,o: - iux:44vqb6x knsz6op.oeq00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are thy6u -4 4,izpxq :nj:v 4ox6bkje.qoose 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 singlez7-09o-5b4 djaiqapu5gpfin frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a bea-gfo ji5 a459uqp7bdzp n 0ia-t 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 a-v0pnt sm o6tq7zy 5;wnd receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency?0p z7n;m-qt s6t wvyo5    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits z1j;0ooli 5+qo+wvjc82 quor an ultrasonic sound wave o1 v 5q 02woro8j cqu+loj+iz;with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a m//rxaug5, o*gbrl,h koving flat train car at a frequency of 75 Hz, and a second identical tuba played the sa,ghrora g,bu/l/*xk 5me 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 usesb j *)vp:es)pbxabj4cv*w92 wzqt-*d ultrasound waves to measure 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 *v *a2c)b wwpbq )-xb vspt9jedzj4:*/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves ofs -h)5uvbdput:yudj(z90 0e,a esm3j 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 of9nae o,5/ncnqesf:y ; frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers ;q,ec saof5n/9n:ey nhear 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 qbhtc:t y: v45 ;f;f* dvj7opgits 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 / 0avc0sem )vq2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wv0ve /cq0mas )ave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where a(c74 ku p;g*i uq fdye7h:yo/the speed of sound is only about 35 m/s 7g/ypkye *74fuacqoi(u: ; hd
(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 1al nz5wzs.n 2*wts6fa tldg, feb*kcl).5) tocean. Determine the shock wave angle it )lfgn) sewst*c*nlzlw1d k5 .b , zaf.2at6t5produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle v*(jnqoat zzc+2 :x5e$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and (zdrys7 5- fkpay4g 9gsee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you h5p( ggy7za-f49ykrd sear 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 sona) w0:hlwhm1jjdt* *obr device 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 desjb0: 1wlh)wh*o dmj*tigned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in thew eimg (z -a f4(w0+y5res1iqay2u;qv human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sehp 7bqq7 5+xb;vxe,z jwer pipe symphony. It consists of many plastic pipes of varivj5b 7 b;+xe7phz,qx qous 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 threshold 9woyu3t oi: 78nts2 waof human hearing (0 dB). What will be the sound level of 1000 such mosw7it3:9syon28oua tw quitoes?    dB

  What is the resultant sounws1twycnq5r2u( *hs*d level when an 82-dB sound and an 87-dB sound are heard simultaneouus1 t2h*wcnr y5w (sq*sly?    dB

  The sound level 12.0 m from a louds;* v-0zkf.besw:dtmg 7;t au:g rlj 8jpeaker, placed in the open, is 105 dB. What is the acoustic poweu0;jltfa7:; szt*g 8 v-be:rgdwkj.m r output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz)a,s0n )o-z7 hcxaa(d ga4lzm. The power output drops by 10 dB at 15 kHz. What is the power output in watts at (7zc,0ad4n gam)aoaxh- z l) s15 kHz?    dB

  Workers around jet aircraflw00*l y7i2e3aj8xndv -en tet 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 intercepted by an unprotected e2 -jyed78ivwlxe3t0 l n0nea*ar at a distance of 30 m from a jet airplane engine?    W

  In audio and communic.ig2wx)422to6ugl. ntgro cq ations 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 tune;vhh10c6 ajej fx5+ ljd 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 funaxr27p,xr7l(w c 1afkq,vl2 uk zgi4 0damental frequency of 440 Hz andlp 1q,kvl(ug x0 f7w7a, 2ax2ir4kzrc 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 vibratibi .pw8 lt08t;xvj)j fy; ;gtmon 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 with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuningvx)ltf8; j0tb; ;y gpwt.ijm 8 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ophx-uhcy*t.hh-uu(6 yen at one end and also 75 cm long. How much tension should be in utuuh hhcy --*6(yh.xthe string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate a. cnt0v:yqaym 4h6d j-s 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 ra u*yo9j/z wj;2s/7en z .qfkxbnge coming from two sources. The sound is loudest at points equidistant 9qj*kwnys ;jof72 xezu.z/b/from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statiox4isvzej6/5xjwpp6 2nary. The conductor on the stationary train p iv6 jp5esw/zx462xj hears a 3.0-Hz beat 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 yocux n0/, g-qoru is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant nuxqrcg0/- ,ovelocity)?    m/s

  At a race track, you can estimate the speed of cars just b+a n+cv;dbfp8qa 7xc,jz) 3 oly listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car7n,vb ;l38a+ocj)d + xfap cqz 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, soum) 1x6n0xj+sbtq vy p4nding together, produce a beat frequency of 11 Hz. The shorter otysxpmj+)v0 n4 x16bq ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite pcyd6yk1hc 3a:)z g z)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)c3 z1:6c pd)agyz kyh listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aor9-i r:yikf ;ctta 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 iftyr: ci;9- kblood 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,ppj5nua kev/vu1ca11))9tpmp l /m/ lzo:qb moth is flying toward the bat at speedet pju5)b1 a mzco /vpplm,v:alu/ pq)nk/191 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it m eb6qyb 5wcc(+hw(q3 approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before+y6bhcmw ((q eq3cb5 w the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ol)1rpdbe+ .9s szke :jne 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 popullbe+ :sde1rz 9.sj)kpar 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 presence of standip(mqriz,):ado w fp1d. mcy4 7ng waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standin d imoq)cpaw 4f (r1z.pydm:7,g waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involvm27mmd.yz5 ggv l9 b)h,pbz-o es 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 d 5mzoyph- l2m.bm 7, zvbg)g9to “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 thres8(tp1 ui xmvj1hold of hearing for the human ear at a frequency of about 10i8(uvxjtp 1 m100 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears t gvm+dutx* l/jx+:,suu)w cl 2he sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alti,us)x+txlm 2+/duvl :gcuj*wtude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 g2zpc8 ja5o7 br.x6od$^{\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