What is the evidence that sound travels as a wave?usqc fe ,i1 11+nsc) :c i/*rtwocoz(bzo w-0e

What is the evidence that sound is a form of e 8 xms )14lq5stvnoi c0efo(5znergy?

Children sometimes play with a homemade “telephone” by attaching a saa kuyh;5kr(l ie/j85tring to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, lrehi558(jk/; k uaa ythe sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect tj d9jo3zut7 :dhe frequency or wavelength to change? oj:dz7ujdt39

What evidence can you give that the speed of sound in ai.l3rnuyo-y oz3)t e9d r does not depend significantly on frequency?y3.d9eorl z tu 3-yo)n

The voice of a person who h.axs/iv +l4 blcw9 w6nas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch 51 1 vy+vwcu vrzu7eg/of organ pipes?

Explain how a tube might be used w5/i6 s:n1u ivfhopu5 r3x;ayas a filter to reduce the amplitude of sounds in various freqsy i npuv6r/5oxa 1:f3;huw5iuency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12mn,t87xe- o2*pn 0s 5omce 9bii2 vxem–30) spaced closer together as you move up the fingerboard towar *8 oxvne-2obcp 5t 2nx79mmem, siie0d the bridge?

A noisy truck approaches yypr((rwa6 z 4mou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly(mr ay4z6 (rpw “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beatzw4 c4z ct7fz j70 etv+xyi5y+s can be saicey4y7cz +vjtzzti70 wf5x+ 4d to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers werett8 (zuvvk9usr :n.4 e lowered, would the points D and C (whezs(:tkv n8 9tue4v.urre destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protect mz7k+aa:i5rip /c eb,ing the hearing of people who work in areas with very high noise levels have consisted mainly of eakaei /b ,cp:z +i5r7mfforts 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 shown32lke t/qum 4pqi 6-ih in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies,pu-q mte /3ih462kqli as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t9ivt/kz:w,ul pk/u*1 (n o ablbp3t/ hhe source and observer move in the same direction, withz /h,*vttkkl ba/ uwnlip/p(39:u1 bo the same velocity? Explain.

If a wind is blowing, willn j,z0 r1bfad uu)a4+a5skb muy7pz rf/7b l;0 this alter the frequency of the sound heard by a person upjz 1 5b;f007bu nb,za y+/)mfra 4kradl7 usat rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a wxp- 8, +r0kwl0uwsaqw v3 wcr;ii5w7child 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 the child hear the highest frequency for rws q5r u3wx+ w0;wpai0lc7kw-iv 8w,the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hedp,x 0g.k w3zzr shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting0z,gdk3 wpxz .. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jus-y(loa,fp3nee )h9kw t below the waterline. He hears the echo of the sound reflected from the ocean floor directly beloweok-pf 3)lh,a(ew9 yn 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 wavelengt uk(.mskj5+sj hbw. g: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 just above a school of tuna on a09ui*+iecg jx(l(dm a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). 0*dcm9jgi(lx(u iea+How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whqy hgo:( 0vuk9wf0 q5ben striking the water below is heard 3.5 s later. How high i f0:(b9 qkqvho w5ugy0s the cliff?    m

  A person, with his ear to the gr o qp9y0l+o-iqound, 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, anlop9+qo 0iyq- d 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-second ru1 uh3ezt 5uim8rj8t t*le” for estimatin581utje rthm 3tu*z8i g 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 sound a)q sogby +ekiqz-sor .3r2(w*t 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 of a sound whose intensity d9ewj ,3s m j99 qtv yx;viydrb705b.uis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sounx6q yukgh * a*;et+i*bd level of 95 dB when fired simultaneously at a certain place, what will be the sound le eq itk+xh*;g**6yu abvel if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frol ete9xe+5, kim an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if 5elkt9, e+ exithe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is ygs8q+- bhdmx5(kg ny:4 poh3said to 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 for eacx8(+m3npd 5y-h o4b ggsk:qhy h device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conver /s.cnaf)nzsr2boo;) sation. Use Table 12–2. Assume the sound spreads roughly uniformlso sof/nbzcr;)2. an )y 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 smj )3a cy ,rex1huuu4lo n(/l-8a,bjbtrikes 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 modest amplifier B is rac l0vyg27:o cdala5a7ted at 40 W. (a) Estimate the sound level in decibels you woul alo :aag7cld5cv y072d 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 v)ki oci10i /w-zqhb*g8ghn +130 dB when placed 2.8 m in front of a loudspeaker on the sti0q+-o kg )8 i1ghi*zbvncwh /age.
(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 dtec)ub(x(a 3edakxk8(ou5xb: (z9 + +tg nfdx B. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9abob(u xk +x(zd3(e(8:kg xc5autx9d te+) nf .]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fam((xx.0pp d4h z ish8gctor will the intensity increase? Increase by a factor ohdpz(i084h s(gmxx p.f    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equxf7p9g*;b hbx a4lwtc3a 9h5bal displacement amplitudes, but one has twice the frequency owba;p5h4 glc a7* bbxf3ht9x 9f the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tha0ng. yu4w v-mlt corresponds to a displacement amplitude of vibrating air molecules ofy.mv 04 l-uwgn 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levp+7*su8hm. z kpcogw*g pu*9 bel to seem as loud as a 100-Hz tone that has a 50-dB sound levebczgpu* k97.hpg*ow*+um sp8l? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies t 7(kr sj4:ljxg ;emh h.mvh+d,hat an ear can detect when the sound level is 30 dB? (See7,jhexrljs+(gv :k dmm.4h; h Fig. 12–6.)

  Your auditory system can accommodate a huge rangexw+mqdsaj 3b+2e-g0 9rn9wx k of sound levels. What is the r92bewds3kr9gm0 wqa- + nx+jxatio 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 frequency of 440 Hz. The g-rsg a/-s+aolength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the str- gsgaa r+so/-ing be placed?    N

  An organ pipe is 112 cm long. What are the fundamenpw7ho-oo ,qi3 tal and first three audible overtonesh3p oi woq-7o, 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 yozwz(7yqte 7( f,i:ebhxj 4n r8u expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a ,7t(w bizj (e q zrn8hf7xe4y: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 the range 4vfwi0 d q*q xj3te5e0of human hearing (20 Hz to 20 vte0*eqdw4xfj 0iq 35 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 hayxhb1pj;y)r 34u6aan h s fe xh9x1p9:s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered yapb9sx)n69:fhyu; h3 ajx1 p 4hrex1 at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long af ,wvcq-6a) tn(r3q, vcsh e7gnd is tuned to play E above middle C cc,6 g7f ,wa n(hsver)qvt- 3q(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits m94exr/r c ly)middle C (262 Hz) when the tempmr 49) xrce/lyerature 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 9egt 8h zdkf6fsw60q,wbf 82b at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flut,u bv+h skc- gotvq+-/e in Example 12–10 should the hole be that must be uncovered to play D above mid- v /,bukq-+s+hct ogvdle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not l dt+s5fm l0k (wn/-ncat any other frequencies in nmf+ n/s(kt5ll0-cw dbetween. (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 8m0rqqb7jacl cwhovf *,y6ym (d. a*0both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is dqf 0 walm. abmq*cjv67c0*( 8yroy,h
(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 ew gq,u/55wxb iq4 oi8sylu,h :c)tp+$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a jv2zv8*y raa 2s1 vny02.14-m-long organ pipe at 2010na2rsy2*vav vjy8z $^{\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 kzszq)ouz ld 8)-:vlydy ik+cu,3 , m3to the outside and is closed at the other e qdkud3+u o 8s)z -:yyzl,zic) 3kvm,lnd 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 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 trying to 9)ulp4uvto z +adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stringv+pl ) o94utuz? ±    Hz

  What is the beat frequency if middle C (262 yw3;ya yxuk32 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while aqpwe0j;0 8q1m6t txgnnother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are plamqq086pw gn1 ;0xjtt eyed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a :0 z/pyob nx6;yjbz0t350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain you oxjbz0bzp;y60 :n/ytr reasoning.    Hz

  Two violin strings are tujls/y hj / qt)l21fa-rned to the same frequency, 294 Hz. The tension in one string is then decreas- r l/jy1t/hs2)qla fjed by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heardksnn jaon9-e1xsk* s5+zd (3 m if two identical flutes each try to play middle C (262 Hz), but one isznn(ss k-5m+ 3oke 9 ajx1snd* at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, ,cdp75 nglp vw-x2 -goB, and C. Fork B 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 together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded togethegxl p25pwo-7,vcn g d-r?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1 b* xck2(r;/xmrs v8hz.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the oth/bkvhmr* ;(8rxzcs2x er.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hearc l0*6mdaeii 4s three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must bel iim60d4ea*c the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. H nax;x02i t5bl,rsh 2d k(iu1jow many beats per second wiixja5tku12 b; 0s(dlnxh,i r2ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaisce (rhpgk1 i a5*io1,n fire engine’s siren is 1550 Hz when at rest. What frequency do you de1s( ceioa*gk1ih5r,p tect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yejsteg2*3 /np ou detect if a fire engine whose siren emits at 1550 Hz moves at a speed j/2 neps3tg *eof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if anb1cm 7pkr-vi-r6g7bmffzo( 4 8d iv- 2000-Hz source is moving toward you at 15 87(vfi-pfvok b -bn i rm7z4rc1g6m -dm/s versus you 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 singlf40+ fhkzrfp* e 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 beat frequency of 5.5 Hz. What is the +fhkf4 0zfr*p frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrapshq:b* xl .cy-3 0if0l ted*ysonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received so fdtlx:yq-3h0. yp* bsei* 0clund frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As yfbf7j; *bxo9it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency*oybb f9;fjx7 does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movin4- cq,ta b r-.)jknhfl*spfx.g flat train car at a frequency of 75 Hz, and a secopt), -kxrfbhjnqc- 4 .l*sa. fnd 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 measure blood-flow .mnkt-57uhc.5wh cft 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 artetumc .fhw5c.-k57t n hries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves oz4-/1jl u2r0 fvfg7li vdlm)yw em8n .f 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 7wli6iv1q nnx c 07x0nHz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,x 7ql 6v07wc0xi1nnn i 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 mmpc iw jm6+rl7r+h,c /oving on land if its 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 where vnq /x 1w50(qasr3u jithe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction oqq riv3u(5as0/n w j1xf 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 the speed of sound iq .5zn368dv en.fgllws only about f35qv8gzelw ld6.n.n 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the sho9, bs(rs*oxg 8cr7by 6azo,ltva7xw 7 ck wave angle it pzcbo7,so7r7 ts(8 b6 ya,g9xv*x w larroduces
(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 o/:4wsah u9tug* era :$/theta$ 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 ab)n::g4ljl;)xee th 8nxww cx; ove the ground flying faster than w;wxgejcn :hx t8e)l:4x) ;nl the speed of sound. 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 sj: m 897xz1lxt xd.vtlends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is.7mzx9xx l 8ttdjl1:v the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are t 58epe rwmad9x7w8tw9 here in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.1jxv ) hj0oh/4r k2isu It consists of many plastic pipes of various lengths, which are open on bots24 rjvhxuj1/0o h)ki h 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 me+ -5rl7ocnv. w3wc mbakes a sound close to the threshold of human hearing (0 dB).cer 5co.w7 bvnw- lm+3 What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-d*( q zhq (s1hqyfsp(n,B sound and an 87-dB sound are heard simultaneonqz1(qqsh(*(f, ysp h usly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the op01(fl3/u k g+ qwil eryxvoc f3dr0i2+en, is 105 dB. What is the acoustic cy33(kll w+fg0o2r 0e1if +rui/ qxvdpower 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. The power out4-0q2n9 v g :ntummhjiput drops by 10 dB at 15 kHz.vniu4n9h g 2j:qt 0m-m What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviced (wr j(bsi:2/0fvl qhu/3icg s 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 ear at a distance of 30 m from a jet airplane 2f3 gr siwu0(:j /diqblvh(/c engine?    W

  In audio and communicjpdvj/d+:u m 5g z+ -:o8amvwwations 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 freqka 80 odu.l4tjuency 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 fundamj qb-licf o3 (9.dnh 9:t/ynjsental fr-/.dj:3i9l9 to hsy(jnb nfq cequency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with q;o l;/c 4bbu79fezb d-2kyspwater (Fig. 12–35). The water level is allowed to drop slowly. b9ey7 z c4fq-kosu;p / d2bl;bAs 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thatua ;gt3g5zc: c is open at one end and also 75 cm long. How much tension 5cg za:;gc3t ushould be in the 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 as one ful../9klfyc 6d ,(hwwep hut yn9l 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 -cteb t mhq :(2)vifn*in the 500–1000-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 fnm) i hvt-c:bf(2*etqinds 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 stationa2 d:q8qsvepx /ry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train appro8 2/ pvxqsdqe:aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After xqg)5z*9mxjwnt0 puis ,(: jgit passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)0t9pwisj xu5)( g*:g mzqx jn,?    m/s

  At a race track, you can estimate the speed of cars just by listenin;,nqlct 7q6xg g 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 (frcqqng xl7, t6;equency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Ty+iww7-kx5 b hhe shorter one is 2.biwhk5-w7 +yx 40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as i5+3,phe95a 8imzxp:ada2ifh za s+mv t 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 whzhie5 2dz:f+mmxa,h5 pa98+ v3ias pa en (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 flow in the aorta is normallyeyl x(96/y;jg fa/tpw about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a spex l(gep/a;fy/ wj6t9 yed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a l y4; 8qgtlt9rmoth 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 af tyq9lg8l;4r tter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound8tg 6i9l sp0vp pulses as it approaches a moth. The pulses are approxilgv60sp8t i 9pmately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signalsun kbvy;.2pv / from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that /yp .ukv n2b;vonly 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((mv +;dn7 hntnr z/qo1st: mkce of standing 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 frequenm ; n7tmntz(vsh1+(/dqkr n:ocies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a *-ca *rskb:ailong, slender aluminum rod held in the hand near tha* :ks*i-b acre 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 hearingxu :/hzjdnr0unp n373 for the human ear at a frequency of about 1000 /uur7nh :n n3d0xzjp3 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 the soni) )f f/kuno2br4z hq:dc boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? h4ku)brzq 2/ndfo)f:    $ \times10^{4 }$ m

  The wake of a speedboat is j zz1v0r:g5 e 4-q0mkvb-hgyv15 $^{\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