What is the evidence that sound travelhx.e( ( wwc7dls as a wave?

What is the evidence that sound is a form of e)rbb641 ,ayhn1 w -ysawhjssc -2 dzj/nergy?

Children sometimes play with a homemade 9stfr r s1-f3mnds+i6ql tu( 7 lzq+r.“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 the other cup (Fig. 12+i qtr1rd3tfsq9.srs -fmlzu6 l( n7+–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect th icpax 21ja0g0;mm a ,cfk:3jfe frequency or wavelength tc ff i ,jcjm0g2a1:3 axmpa;0ko change?

What evidence can you give that the speed of sound in air does ncgag+jn-- ,)7k8 yx ay3qeb qhot depend significantly on frequenc)7 xna,q8+-y-bj eyg3gkqac h y?

The voice of a person who has inhaled helium sounds very higt,tg3 geg.w .jh-pitched. Why?

How will the air temperature in a room2mgc x)sj/q4 a oyxr:m:-c1 w 6abxwx1 affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude ofhiph0u v-zx 38 sounds in various frequency ranges. (An examhx vi- p8h0zu3ple is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together atz7 n:+ kulfuzy 5y/-ss you move up thezy+suf k uly-nt5z: /7 fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Ini:noi hvr:n;d,tially 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: See Sectir;h ,n::oi vdnon 11–15 on diffraction.]

Standing waves can be said to be due to “interferl5bn*uzw b wrczc -wxh 4v976:ence in space,” whereas beats can be sai z -r4x7cwcu: zvl5bw*6nh w9bd to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were d39pav/gcd; o lowered, would the points D and C (where destr;9ocd /g v3dapuctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peomhhkk+)74d ( pe jyjq3ple who work in areas with very high no( jmy3j4+kpd )eq7h khise 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 noise reduce the sound levels reaching the ears?

Consider the two waves shown int(uw,:e h 4sdyqbn-)l 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 whict-d)e 4n :qs wblhy,u(h 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 a2esx 36: ksijil2iq gnfw/ v4mj9by9:nd observer move in the same direction, with the same velocity? Exfw6ii/sjq ix3se:b9gk9n 2:4lvjy m2 plain.

If a wind is blowing, will this alter the frequency of the sound heard by a n0rkgr kr*rbu3+rb.p o+ x8c1person at rest with respect to trn u8rrrgb3.pk1r oc0+* xbk+he source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swiqm9td /*nslrt *55lusng. A monitor is blowing a whistle in front of the child on the ground. At which position, A througndu sl9* q5* t/mlts5rh 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 listening for th:. agqu8xw*yde echo of her shout reflected by a clifqdwga:x y.u*8f at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h, jkd zqvx01/his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly belxqj vkh/1 0zd,ow 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 ai34*7krf t blbvr 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 dri1f6d ;y d )zob:ecyr)efting just above a school of tuna on a foggy day. Without warning, an engine backfireocd)d)y:;ez b6 1fyer 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 frcku)d 0 wluf9x(c8b2tom the top of a cliff. The splash it makes when striking the water belowcf9 ulwd2 b)xtc0uk(8 is heard 3.5 s later. How high is the cliff?    m

  A person, with his ea/cupl0q wid8/ r to the ground, 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 1c/p8i /u0qw ld.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 dist pdmey l,:*gqem85lq5 ance by the “5-second rule” for estimating the distance from a lightnin*:dg lp5 eqlyem ,mq85g 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 level of 120 ,1n: xm jn l8ybm pvf .7ht7a/p5/vbhzdB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leve2xzrz;c.,o 0zbs8eetl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fa1g - nhch wx1i)gk27rired simultaneously at a certain place, whakw1x2 gha1n-7rc gih)t will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from y0;*8tnpu 92uebl x 1 -siwqzsan airplane with four equally noisy jet e*z2 9e y;suu-pqw8bi 1 nsltx0ngines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 tc0+i e fs3o,1 pj4ejcdB, whereas for a CD player it io3+0 e1je,jsfipc 4c ts 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 aqh9k if: d3n: x67uwo18vtohk person speaking in normal conversation. Use Tablvx8f7n 9ou k:ht:odw3h6 q1ike 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area zan, 6 rnim-,tis $5 \times10^{ -5} m^2$ (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 2vgnnd3f z 25xy5ty:,d .o1iq a50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibel3i5qa :5tz . y21fdvy gon,xdns 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 registera0n*, up,0 ap0bdij zyed 130 dB when placed 2.8 m in front of a loudspeaker on the stage.ua0 ad0nyb,p *ipzj0,
(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 dis d7u*cm)u w,fpgv6l )fference in sound level of 2.0 dB. What is the ratio of the ampliv) gcw*f) sl 7p,um6dutudes 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 izt7 r i-3rnf.tntensity in 7t.nif rt3zr-crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onwa 06 .kctnwts-qu 3g5e has twice the frequency of the0cw6au-t3g.5 q sw ntk other. What is the ratio of their intensities?   

  What would be the sound ,a.fin:ond.6 jg *ebr level (in dB) of a sound wave in air that corresponds to a displacement amplitujf.e :id,na 6*r.nbo gde of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whv/ubt,. l)qy1;vq j gjat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sj ,v /lqbu.y;v)1gtq jee Fig. 12–6.)    dB

What are the lowest and highest fr8r k uck; wbo2yd.u-)1ryl db6equencies that an ear can detect when the sound level is dd yk-w ;2u r6lck.1oy b)8rbu30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound level.hf6c yu//j8h pnhbv+s. What is the rathy.vjhu6f8b /c/n p+ hio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental u+w2:2cwa fkl frequency of 440 Hz. The length of the vibrating portion is 32 cm, and: f+ cwl2uakw2 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 fundamental and first three au pj )g+/s,,qm, q3wur s,sxdizdible overtones if the pipe is pqx/jssigmq w , ),su+d,3rz,
(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 blowing acrose8sa uweqtap-71 k72xs the top of an empty soda bottle that is 18 cm deep, if you assumed it was x1sa7 ptq 72wa k8e-eua 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 spanning t9mp 9)f(/opmj k oal+ohe range of human hearing (p(/ poj9+ofmak9 lo)m20 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 Hz as its third harmoahi zk9ubu2/t61a v e1zw(/p tnic. What will be its fundamental frequency if it is fingered at a length of only 60% of its or 1vek/ htw(u/a1zia6p9 2tzbuiginal length?   Hz

  An unfingered guitar string is 0.73pzgf-8w6mb)s wy1:)vlw6ct p m long and is tuned to play E above middle C (330 w)l-s 6tp1w byp cz )mwf68:vgHz).
(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 thzrd/w/:-aj xmk .l;omat emits middle C (262 Hz) when the temperature is do-zm/ :.w;x r lmjk/a21 $^{\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 ymf ta +s 6mag4m/- 8bx(8zggx20 $^{\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 sh- xcp06yktfw. s )f8siould the hole be that must be un .s8ckf6)-xyfpw sit0covered 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 ca e:6q4u/ rolfgn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any oru l/o 64fq:egther frequencies 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 t cv t5yg rh;gg-)pu40two successive harmonics of frequencies 274r t50uy-vgh;) t pcgg5 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 2-2mvw yrejb9$^{\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 wgz hmxs3+prkk78aukp hogl),9 qf 2 5*ithin the audible range for a 2.14-m-long organ pipe at 20 hk2pql)8x+u fp5 r kkog,aghs 7z3m*9$^{\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 ok,wh 4vly1o -(qkvqp//ki9hyutside 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 relationship of your answer qyyh kk9iw( v4lov/k,-/hp1q to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tr 7y mjmdvup() /h7jf0qfg2 v/gug+cx-ying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is thej0/fumfv2)vhjmx7yqg -g7ug( c dp/+ other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and g yyiwm(8(+qc $C^＃$ (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, while another (brand X) operaa1,pg *bz4ps wtes at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating4z *wp1pabsg , frequency of brand X.    kHz

  A guitar string produces 4 beats/s whrteghc1 vl i+y3qz26 jn.n k9.l5 2xcmen sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibt+2ch926 qr znlik .c1nyjlv .5x3gmerational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. ,+i(oefzm k, lnj zx,,The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings a mzz k, ,e+fn,(jlxio,re played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hex(5ftld :x/kw ard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and thexx 5dt/klw:(f other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44i0qz8- pf+4xidyp x.l1 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 freque8 xly0pi+.xq d 4ipfz-ncy 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 apar7:pzx nq(q:qxd2u04gjh s nw 3t. A person stands 3.00 m from one speaker and 3.50 m fro(2sgq:dq730xnw hq jx n4u: zpm the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be +t;q ck.slf6hvibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratik+qh.t 6c lfs;ng 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. y64115hj nmbsv zygfh +bo(x-76 m in air. How many beats per second willz6(+y4nvb-s1g b1mfoxh 5hy j be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency upq,b /sb; t9c6 b*cynof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 muqb 9cb*b6n;pstyc,/ /s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine w m9m8von9zt7bl ddnszu2 882whose siren emits at 1550 Hz moves at a speed of 32 mn7o8umtn2 z9dlw 9bsm2 8vzd8/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 200:0 ;tc :absfyn0-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cly0 ;ca: tfbsn:ose? $f'_{source\,movine}$    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 fre;80 xh6krouuu;d 8fsvquency horn. When one is at rest and the other is moving toward the first at 15 m/s vdrus 0u ox;uh;88k6fthe driver at rest hears 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 kHyzsz, bb(hw x39aj7wr y;v7u3z and receives them returned from an object moving directly away from it at 25 m/s What is the reca y;r b,uj3h79zs vbz(w3w x7yeived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, ovr3j;rh c +:v-cww:p the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the rorc cjv w:hv:;3 -rw+peflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mov ex6lyl9i)9s rea z:g4vg l,/qing flat train car at a frequency of 75 Hz, and a second identical tuba played the same toneg96llq x:/gasi e)94 l v,yrez 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 s-czk*hnu ) 7d5kyl8e p*v if9p .pq-ewaves 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/s directln ihpuke-qc5f* d*vk7 z8-9ly )s pp.ey away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencydhq9v6/cdh hx e99dl3 $2.25 \times10^{ 6}$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 5 kups9d84he9 a70 Hz. When the wind velocity is 12 m/s from the north, what fpd ue98k49ahsrequency 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 spego2 zr5u8v9pyi :cn 5ted 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 p8e de wa2.o/*pilal8 the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction 8 p i8lwa l/oaped*e2.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 atmosphe*ewvp*qp 0* *2elne :n3i7 c0zsembg hre of a planet where the speed of sound is only about 35 m/se*zp7e: qvn0n23w ic *elpe **smb0gh
(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. Determineupcwp *(0cs kbah05g /8a kh2o the shock wave angle ic2phk 05a*/sgho wa8 k(0p ucbt produces
(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 ,wu1lm- 0nbx r$/theta$ 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,f ilch, 3/k7euqg 1av km above the ground flying faster than the speed of sound. By a1gqi ecvfu7 k3, ,/hlthe 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 thal a (id/gkx57zt 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 workigk75 xza/ dl( is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in thp+v v4 a,j3vrr/r9t u50r wlkae human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of b4t wij;2meu uduq48 7many plastu2 4duqe7um4t8bwj; iic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makkrfsg(jb pp45*i 2 ei/tlnq:.es a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mol q tne:gib j452.(s pipf*rk/squitoes?    dB

  What is the resultant sound level when an 82-dB sounded k i2*h5kat8 and an 87-dB sound are heard simdk8* k itha25eultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed 1foyqv5mf1 5+ 2kg yx ap/ +aklg6q8ihin the open, is 105 dB. What is the acoustic power ouv1+2qh8gfk yo q/+iafk1 g m5ya5 x6pltput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power o.il( fe3 3zrwfutput drops by 10 dB at 15 kHz. What is the power output in watts al3fw e3(zr.fit 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. A jqf7 27rbjx/yssume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear q2f/b 7xjr7jyhas an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicationa bu7gs.0pcqg24 e0yjs 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 tunedy:4of, nj r r/o2kwiu/ 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 fundam04p5w- zicj/pzikm-mental frequency of 4k5i0jc/4z-zm -pi mpw 40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vii, -ocn3g) zdgq -rmk(himr8pq1+2y fbration 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 8 qq(gph)nz d r+oi3 iym-12,c r-gkfmfrom the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tu+6yu )h,r7hknx)98wuvn e djlbe 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 fundamental mode) with the third harmonic in the t9 uvdh,ne6ujw y)n)x hkl7r+ 8ube?    $ \times10^{ 2}$ N

A highway overpass was obc;220wsq 9;e xuadzwm served 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–p8+ xohgx3. -* hjhruu1000-Hz range 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 farth .hu g3- 8ju+xhhopxr*er from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The csgmn r a. )5g 0(gwgbo328thchonductor on the stationary train hears a 3.0-Hz beat frequency when the other train approache50gghh3tgg. )82wonrb( mcsa s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.4nvnsjhu(, j)n oa+m ) After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assu+n vau)j(4sjh), nomnme constant velocity)?    m/s

  At a race track, you can estqg (ux.0vy9-zjt59lhl 0 i- sfqpm (qkimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. l5gkx f(sp9.ih q tq 00jq-m9y-zvl(uSuppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, prodo7chy1ntm 2wc0f 7 jt9uce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the oth2ott 7m9f0nw 71yhcc jer?    m

Two loudspeakers are at opposite ends of a railroad car hra7r oqt *p( u69gol6as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequenciort*h9(6uorl aqp76g es 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 speakers after they have passed him, at C?

  If the velocity of blood flox7x)-e7m ,z(ublpv zow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MH v blz7( ezo-7x)mp,xuz 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 sn.w5 (r jumhctvlt4 /(zt9k i2peed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound t/ 2zucr9iw(j h(kv4 5mnttl. 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 his)kwo4x o7-i tgh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chiiowk 7t x)-so4rp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig txkr /8;6t6ds.8dz-esgs whr. 12–38) was once used to send signals from one Alpine villast 6grz t.x8dr86 ;se -hds/wkge 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 this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for srke4o9kw3tikd qq4hmks i)+w319 4 oxtereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long,19oq tshkk w i9qx3r4d 4wk+ei4)3okm 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 gbbc 26 jjme41j x)pvgd2h4hb((twz 8“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.164ebxp) ( 28ht mjdggjh cv2jb(wzb 4 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 jw6:lwy,d 6 m(jsrfn ,for the human ear at a frequency of about 1000 Hz is,rjsw mlnfwd,6 :( y6j $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boombd1qb hvf2pgn5j,5 - h 1.5 min after the plane pass pj5 1,vqghhb52n-db fes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo; htswq qj/ 5plqk/eof; i+7y*eg(y4kat 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