What is the evidence that sound travels am swl1z 0ulf31ilru5js+g 2l :s a wave?

What is the evidence that sound is a form oflvo )ymw 7/b i;5:spxu energy?

Children sometimes play with a homemade “telephone” by attaching a stri fiti 1 7.jd*ut:u0cuu +r)jfcng to the bottoms of two papfu i.7j+r*u:t1 cufc)t0udji er cups. When the string is stretched and a child speaks into one cup, the 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 the frequencyzl q:9ft1nio8 u kb7t- or wavelength to t o qku8i:btz7f9n-l1change?

What evidence can you give that the speed of sound in air does not dr9*+o+a o8 )9sd/fnesufchrbepend significantly on frequenb* 9hr)ueo cs89ar/fndof+ s+cy?

The voice of a person who has ine9g43qe 8so6h/srr -9xw wphuhaled helium sounds very high-pitched. Why?

How will the air temperature in a roo*b*2e cdm4vrs iqe/j0g 1d5ft.y um z8m affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the b w -fgynj(.r1amplitude of sounds in various frequency (.wjn-rfbgy 1ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spyxn jf cv84uf40si(k+ aced closer together as you move up the fingxfc n(kv syi4 +fju084erboard toward the bridge?

A noisy truck approaches you from behinds9 bnfpzp31f1 a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the fsbpf1nz9 3 1phigh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas be-r3qb1 b17x nx*ui+s30oc,key ch pe lats can be said to be due to “interference br*nb13 i - exsh u7kc ,y1q+3clexo0pin time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would +fv*s wukis, ;the points D and C (where destru,iu sws+;fkv *ctive and constructive interference occur) move farther apart or closer together?

Traditional methods oh))h;/ 3hhuy tx z(cukf protecting the hearing of people 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 worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noi tcu ;3 h)h/hxu(khyz)se reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought os 39uz6lbdxn9ey**a.5;sveryx bh :hf as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencivhsb ;e dx9 x*ay3ul *:res z9y.6bhn5es farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the s k tf700x3qtwname direction, with the same velocityqxfk wn3 t0t70? Explain.

If a wind is blowing, will this alter the freqz 3. np*jmh0ahdq95oo,nk4)bbb j) i quency of the sound heard by a person at rest with respect to the source? Is the wavelenqi)mpk5hqb)93jz,bj* h nd0n4oo. a b gth or velocity changed?

Figure 12–32 shows various positv7uu:feq i q w+w8,4skions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At 8i +vq7w u,u4fek swq:which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a jsi zwml3( :j/4,cvjjlake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shou( jivjzc3s:j ,/ mlw4jting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of him-ox nka5ctxj/*,zp 9vdl/ di23eps/ s ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. Howmiac3lptk/ v* jnzp9 xxs5o//,dd2e- 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 wa7tqd8 2oin- axaf81lkvelengths 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 sc.qu7a6v/3 g5mwmuxjs1f rf x+hool of tuna on a foggy day. Without warning, an engine backfire occurs on another/ u6v7xawr31 x5fq+mug .mfjs 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 from the top of a cliffvaiy+ e-lh9qj8d8i 6 i. The splash it makes when striking the wa iv8iiy8- ed hl+69ajqter below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conc)n6mv,cb -j gjrete pavement. A moment later two sogb,)c j mv-6njunds 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-second k74kb cy,thpr4a m,6xrule” for estimating the distance from a lightning sax,4 4pkbmk7t6 ,y chrtrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lnj/yzi9ig pwn, k3v,wj*:r) gevel 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 intensit vcqo0 y8mpm12y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fw)f ;wmyw n5e9i hw m.pow.*ih8pg-8tired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not 5hp9imnw. f8whp)-w. go iemw;8yt* wdB’s.]    dB

  A person standing a certainj*boem 9s8u0 m distance from 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 the captain shut down all but one engine? [Hint: Add intensities, nsjb0* umm o8e9ot dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas 5*nyuvtta8lr k* ;o .ufor a CD player it is 95 dB. What is thet*v.ro; ltau k8uny*5 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 spj k1qq4ml5)a geaking in normal conversation. Use Table 12–2. Assume thega5)lqmq4 k 1j 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 arh:mhrs u 5*dh7 :kub:pea 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 m6.htxy( ntt1 amplifier B is rated at 40 W. (a) Estimate the sound level n(tx t 6h.mt1yin 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 5p0),8, sgulyac6z:btcb.kb h/kimsdB when placed 2.8 m in front of a loudspeaker on the stmhcz )/ :b6lkgy bp8k5scua.,bti, 0 sage.
(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 leve t-8j5hqd:poxrwi6 s(l of 2.0 dB. What is the ratio o 6(dwx-pis8th: qjr o5f the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound w o, /-ezdtf/ 41brbliwave is tripled, (a) by what factor will the intensity increase? Increase b/lb,d4 rzbwet 1/ -foiy a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement tj/x:x;6quo,fcd ub7f+p 8nm amplitudes, but one has twice the frequency of the other. What is;fo:unpt6 8 xx,qf m/+7jbd uc the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave /od e7qqd:o 3bf3it1e in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at3eodd7 of: b1iq/etq3 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as57 cm84+h3;ggbtfz srnh ny1e loud as a 100-Hz tone that has a 50-dB sound leveb 47;+cgye nh8rfnt3s 5z gm1hl? (See Fig. 12–6.)    dB

What are the lowest and highest frequencie+vom(pu lbvw /+-bj6u9 -r woms that an ear can detect when the sound level is 30 dB?+6vlmj-/wvu w b-rpo mo+bu( 9 (See Fig. 12–6.)

  Your auditory system can accommodate a huge range o(k1 zl(5 t yiw-twhz9lf sound levels. What is the ratio of highest to lowest intensity at ( w( -llizzt195kthyw
(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 o24v dp0k4-olxo+u. tya p 3hdwf the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must thxkd u24vodw pto .h+ 3a-40pyle string be placed?    N

  An organ pipe is 112 cm l pi heu+0gw)m9ong. What are the fundamental and first three audible ovew+ g09 up)eimhrtones 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 frequenc o-e+fj.od4zqy would you expect from blowing across the top of an empty soda bottle +j.-fdzeoq 4o that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe hp m8msh8285p3 anbxworgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), wha5w28h x 3mn8bap8pm hst 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 twzc;3vbjs;rpq 2 z, h/v32mfob6 imj 6hird harmonic. What will be its fundamental frequency if it qhmofps2 bv;,;6vji3 zc2 /3zbw mj6r is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned toce4n*c*.r8 cnxc;i ia play E above middle C (330 Hz).4* cnc ieac ci8rn;x.*
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whf r1, (),ays ;worlxpiox5r/ sen the teairsyprfsol x1w( r,,o; x/ 5)mperature 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 atxpl,in *y0. mav3 k6vc 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 ky5 pncan0(z (12–10 should the hole be that must be uncovered to play D above middle C at 29zk( yn5( nacp04 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, buts3 gz5q+6t),he fu2q pfxvky9 not at any other frequencies in between. (a) Sho sg2hxufef6 5t,qkv9y+q)pz 3w 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 l7q. c9k i wa a47cl1nn4v-p yxyec-6sbong is open at both ends. It resonates at two successive harmonics of fre9.i4 cc qyaw1nk-cn- p4 x7yvs67 labequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 :f xd v bl1np35,exuaq t615zp$^{\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 y wvjv)6q)lw*for a 2.14-m-long organ pipe at 2)ylv)jvqw * 6w0 $^{\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 twyu00kg 28v tzo the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of 00 kvtyzw2g u8your 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 adjust two strings, onegp73v ud4*ywu of wygu47 vd*uw p3hich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if edk8/0c ly/dg middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates 6hjt0iks,pw .j)8ner 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 operating fre,)t6 0h.inr8eks pwj jquency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9mmw37+sy u3(g6eg wf qz:ku - :rff:cw beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.f(ew::+w-7u s mkucz3mqg3f:w6 g fyr    Hz

  Two violin strings are tuned to the 2q)dga 7iu f2hsame frequency, 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?a2d)7fiuhqg 2 [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard ikfwp*t2/h ;)ui9dssor9 )jzob ;7dp p f two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C au9p2;jdrdb k 7;)t o/hp9of)p wzsi* snd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning foe y*tfw (x7q/nrks, A, B, 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 frequency7*/wfqtyn ex ( 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 apa mggc246cngve ../ maprt. A person stands 3.00 m from one speaker and 3.50 m from.2 cv.mmgg n46ega /pc 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 vibrating at 132 Hz, but ayfl,q: 33dlj w piano tuner hears three beats every 2.0 s when thl l ,3yqf3dj:wey are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in/ntih (fzf5i3vd t 0z( air. How many beats per second will be heard? (Assume T(zt nt03/z5ifv (hidf = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at d96lvk(xuzwv 8+ gv0dlrq.:b resd6+br9 dl8gwv v(lvq 0:z.kxut. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do yowfb*me60g*yy mu *cq(be3i; io7c2 zku detect if a fire engine whose siren emits at 1550 Hz moves at a speede7 2gfc3b0y*(wzo;mymqu i ic*b6* ke of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20001qe+w5zxp0vq1 z9c0qsj j z3k-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 mze0 j90xcsw+1k51p3qj q vz zq/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single freq 4wia,o y;lnl*uency 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 tha;* ,illywo4 ne frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kH h7r( e0fmon3yo ;hq6-mi(kqtyldp61 z and receives them returned from an object moving directly away from it at 25 m/s What is the receiv-oy7 0n6(l1i e fr( pmq hhom;tdkq36yed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bjlb;c9 +;ua am dp6vm3at emits an ultrasonic sound wave with frequency 30.0 kHz. Whacp39am 6;a;u j+mdlvb t 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 moving floj d e)zb+uqx sez9c588huu:1 at train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at resz 85 1s h9zucx:e)+q db8uejout 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 bl sc3 vlt4ug2 )m8y-sjrood-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 a ltur)ymsg32 csv8-4jt 2 cm/s directly away from the sound source?   Hz

  The Doppler effect us t/ jwywlafn +o/muz/ 1v22pf7ing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. Wu9mx7n4tueue ox26x:g 7ceq 2cu -n)ehen the wind velocity is 12 m/s from the north, what frequency will observerstxeeccox n67qu 4gx7u)e2 n u29em-u : 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 - +oslj.0mh 35hsqob nspeed 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 anv2wq 3r8dkc-yb:q k b*,h4d 2.3 where the speed of sound is 310 m/s (a) What is b*kyqdq 8vb-2h4,dw c :ar3nkthe angle the shock wave 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 the speed j0 o:j 4qd+ctad- kfi1of sound is only about 35 m/s +o d-qc: ik4j1a tj0df
(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 tycu+ ;tya14e rhe ocean. Determine the shock wave angle it proe+4 cy;ut1ra yduces
(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 )fqc9u 9s8old e91t h8lvu w*y$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fkroqd,+3jw0 clying faster than 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. Determi0+d,jq w3ck orne
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000n d:pr: ;:-a*;k9p vriqo(;ew tdezriw;fq/k-Hz sound pulses downward from the bottom of the boat, and then detects ioeaiqn:: -w;9k vfwrep k qz(t;pr:*r;/;dd echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how man/nmm82(tx(9+cicy dns 2qwyc y octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calledvo ;sgw,fzlsym*ufb4 te/s;q0 j.8 d7 a sewer pipe symphony. It consists of many plastic pipes of various lengths, which o* j.;u;st 8zlm0,q7/ y4ew bvssfdfgare 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 c);7/pzgow;p7gb9m ry w yf2ielose to the threshold of human hearing (0 dB). What will be the sound leowywifg79p;z7 ;m2 y/rb peg)vel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB 7cmo( 5lhh3ct.bh xt5 wv+*yksound and an 87-dB sound are heard simultaneouv(c+hxbyo 73t .tw lchk h*5m5sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in th,nlygfglx62 /z;j0jo (wa5demn7 cp 8 e open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally; cjln d8gj/lnzxaw60g2p (fe,o5y m7 in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output t- zmv3ig/4k m*tgrx8 v (g;gzn;2 m)hvuesh- drops by 10 dB at 15 kHz. What ix mzsv z2(gg/* -r3)gn;ve h8tmtvig 4-uk;mhs the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.ttm wka*r 2ntg2 i2-+(wssb7 m 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 a7- + 2ks *gwstbat2mm2twr(inirplane engine?    W

  In audio and communications systems, the gainwwsh(3g6ercwj- gmv we (z964, $\beta$ 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 h/q pib+4gnn)is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed poizef6mp/.9jtn8z1 jyvk9x6fi /p tdu)nts with a fundamental frequency of 440 Hz and a mass per unit lengt9.k)j /i p te6tnxf6du9zz 8y jv/p1fmh 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 aiok -a6s /d+qqntey3 b i1s32zbove 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 wate o6s 3q /i1ik+-q2nsayd 3bzter 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 that is openz/5u ert2 gb0g 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 tb2tze /rgug 05hird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observyg/m)yxj 2*d1 ksmeu2 ed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourc5b :8 jmq00h xhlnxnu1es. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frmhuxn1j 0hxl5 q0 n8:bequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is st uq 2z1,bzgik2hrsz4/ationary. The conductor on the statio bhzq12/g 4 2,zisuzkrnary train 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 whistl+ jl9w la)carpgqa k/sc,253d e as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving 35lkq/+ac r ad spacg2wjl,9)(assume constant velocity)?    m/s

  At a race track, you can estimat6utn j4 .4mqpmn*; o u3sg2soee the speed of cars just by listening to the difference in pitch of the engine noise between approaching and rs. u;qgo*34 s pm62j4umneon teceding cars. Suppose 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, produce a beat frequency of 11 Hzij8 xlr yw(yfr87v8u1;c-* extkj 1b 5j l:nmf. The shorter one is 2.40 m long. How long is the ot ej;lyrm vwxruk8l:tf-57x8bn * f 81cij1(yjher?    m

Two loudspeakers are at opposite ends of a railroad car as ithr w-p ddujxqo03, wst(bf /l q8:am35 moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between 3w/ 8w b5ur0 -amlhq tpq(f:dsxdj, 3othe speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow8 feo,is fs9p2 in the aorta is normally about 0.32 m/s what beat frequency would you expect ifo ssfi, p8fe29 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying a+ k5sf:5r- .hs e2tctnv +bffrj+8pjtoward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave ref8a5t vfh b+t nsj+:fpk2 jf.rr +e-5sclects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as srm; p s8k3 +cx)+8il idjq9kuhq8db4 it approaches a moth. The pulses are approximatkuq4cr3q8s;di)i8+dms+ lk 9 p xjhb8ely 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. e)ppk28srn7m 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity lossns)k m ep7rp82, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be comp (z;j z 1j)s/+llcg/ lcltne(zromised 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, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves inltl;l)/zez/ cn sj( 1z(lcg j+ this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a locdx 1)f2ao(q.s1 txp 1tb-zu+3 zo .lrcqenv1ng, slender aluminum rod held in the hand near the rod’s midpoint. The rod iso qz)c vx (-a 11.1l qtnuofs x1zceb3r+tpd2. stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for thbto+) nbs.wd(q)0eoa hgho 1 5e human ear at a frequency of about 1000 o()+bd)0wh1.onsghobt 5 eaqHz 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 thed e(t2p gbr)1f ground hears the sonic boom 1.5 min after the plane eft2 1dr(b) gppasses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 2a8ihi y3yy6p7mi+ mj$^{\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