What is the evidence that sound tk.5 /gl578w3i ovw1urfim zxvrzn k; 9ravels as a wave?

What is the evidence that sound is u;6qh61a5d ub gti21zvhpd)t a form of energy?

Children sometimes play with a homemade “telephof1 nue0bd0/uf ne” 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 hea f0bud/e0 u1fnrd 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 sz /ylx9b 7fiuio*l(9air into water, do you expect the frequency or wavelengi9/is(ylx zub 9*f7 olth to change?

What evidence can you givv; )o pw6 8ajsd65ytaxdnlo+4a r*dm0e that the speed of sound in air does not depend significantly on frequenc m+ljrda8onpdw6x t ao ys*;)d405v6ay?

The voice of a person who has inhaled helium ttw5q+ 1v+ug28 it bqzh. m7tusounds very high-pitched. Why?

How will the air temperasoax7 r,u2t z0ture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reducy1nl k ,a(0wvze the amplitude of sounds in various frequency ranges. (An example ya1(n, vlw zk0is a car muffler.)

Why are the frets on a guitar (Fig. 12–309kfstt)d 9hu5mou6f 2) spaced closer together as you move up the fingerboard toward the 56 o9tsktu fhm)29dfu bridge?

A noisy truck approaches ya-d*tg*ynbax5d 5 yr-3l a8f pou from behind 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 the3y* dtdpab5rx-5agl8 -afn* y high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wh:nsro kli e- s-kylzn6r0r-86 ereas beats can be said to be due to “interferencerns -8r 0ior-6 6s l:kkez-nyl in time.” Explain.

In Fig. 12–16, if the frequency of the sck:vky(+hdg k o(v0+*, a a,ni l+nlowpeakers were lowered, would the points D and C (where destructive and constructive interference nyid+,k++kl lkh,n0o (wa a(og cv*:v occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peo. ne sz-g(1) 4muv(i 9ejd thuz7mm4p*bp.qbe ple 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 th-)eqgvzshp.u9m4. b(e pznbmej *u( dt7 41mi at 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 in3w00 o s1jg6rvfr upv9 Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencie30rf96s1 pw o gvujrv0s, 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 the source and observer move inajkh ycu)/yta; l.w 26 the same direction, with the same velocity?t )6u;y/wj. lh aa2cky Explain.

If a wind is blowing, will this alter the frequency q5tutnn 3.bdr 7q+6 tzof the sound heard by a person at rest with respect to the source? Is the wn qnu+rdqb . t7t3z6t5avelength or velocity changed?

Figure 12–32 shows various positions of25p+3wg clv nu a child in motion on a swing. A monitor is blowing a whistle in front of the child on the groundc2u5+lvp3n wg . At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listesk rkyb)h og+.c,o 1z1i daw.5mq77lfning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of t)ok7zglr7 cya. o+,fi s15 qm.1 dkwbhhe lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side oz89u:l).5 qz ir egg5w.uwdbxf his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 1b z w5.:.wgrex)d5 q8ug9uilz2–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in aird5 i ;iz ne6ey6mttz )pdlt.+* 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 i +ry4hc- ,avpc3tu/qw s drifting just above a school of tuna on a foggy day. Without warning, an engictr auycvhp- /4w3q+,ne backfire 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 from the top of a cliff. The splash it makes when striking th.ofg2qk+k v z+e water below is heard 3.5 s later. How high is the k.+zgfk2vqo + cliff?    m

  A person, with his ear to the ground, sees a huge x r+qibx6jq,:stone strike the concrete pavement. A moment later two sounx qrib:jq6 x+,ds 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-sejtlv6.r( lhv 3cond rule” for estimating the distance from a lightning strike if the tempera6tlhj(.v3v rlture is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 9,x+ f5firjvadB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ;/ xrm6:izsdg( r3p feof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta 03r-.semvohzxua ;3wneously at a certain place, what will be the sound level if onxv s;uea0 h- w3r3mo.zly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanenhnpz7:( xe/,se uwv9 with four equally noisy jet engines iz 7pn/, eshnwu x(:ve9s 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 o7mjgfv 3j5p.kf 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 eaf 5v7jj3mgk.pch device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in no5by/jt65 urp /iab q-prmal conversation. Use Table 12–2. Assumupr5/-q bby6jti/5ap e 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 eardrvq+sosn cs57;v 8u .as.d 5kkcum 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 ratedqs*3w swq+uv 3 at 250 W, while the more modest amplifier B is rated at 40 W. (a) E+* sq3wvq3 wsustimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter rr 3-y 0.3 ,+2tudkiaivegkecuegistered 130 dB when placed 2.8 m in front of a loudspeaarv- k.ege2t k+iudy3i,3 uc0ker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a differenceaq(5i xo ue+z+ in sound level of 2.0 dB. What is xao(e+z5iuq+ the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what ,o( tym45wecczm 7*5df ;dsl efactor will the intensity increase?myc 7cfz5*,4s5d ewd (m;elo t Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amnwj9g:pd hf m*ou2 ftbm4(2 k,plitudes, but one has twice the frequency of the other. What is the ratio of their intenn:d4* wfho2 mtf29ugpk j (,bmsities?   

  What would be the sound level (ini+ blxxrl:hmvu)z**- dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecuh-* x*lui : xzlr)v+mbles of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound n lcvihz,ya(fh;pc1 j ;-+x:1m .jilelevel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (Shmcal( zp,i.c1 +j;e1y:fnix -jhv;lee Fig. 12–6.)    dB

What are the lowest and hiubj-g y8t8w,ke/m0 rughest frequencies that an ear can detect when the sound level is 30 dB? (See8 w/rtgyjume0 b8uk, - Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound lev5o f1*3/eki mb)ex ellpxseqb8uf+ ;3n+o1fjels. What is the ratio of highpole; f 3bs l kxon8e+efjf)*+q5iubm1e13 / xest 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 freque5la,z tnnsn-/ oi29bency of 440 Hz. The length of the vibrating portionle / 2,n9zno bstia-5n is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fun0dk)ou0pt7p eb* possk95 m r*damental and first three audible overtones if the pipe is e70odp5 *ost p)bm0 sukkr*9p
(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 across the tod rj8qsx zvr *3prrqaa7q)3 5y29rgb 9p of an empty soda bottle thatrg39qdzv) 5 *x8q 3rr aj 29rpy7bsrqa 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 organ with open-tu4 w.b8vb3h ;wlh gdm/obe pipes spanning the range of humbhvb;h3 wldmo/.8gw4 an hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harm3t)vk3c( ymwg rvu5 n8onic. What will be its fundamental frequency if it is fingered at a length ov)cu(n3mt gy 385rwk vf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above mhf:-cx;j c3k riddle C (330 Hzkjc3h: rfc ;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 leh/ *util4i(lrngth of an open organ pipe that emits middle C (262 Hz) when the temperature is uh *(i lrilt4/21 $^{\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 at32 vcs +y:wyqk gi/r8x 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiep5xrskt 1e* 6nfkk 8j5ce of the flute in Example 12–10 should the hole be that1f5sktk *nx 8ke6 rjp5 must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at yn(p 2vu ouxml(x4(gf :,cdb4264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies b(cud,(on gxpx4( lfm2y u4:v 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 resonate1(z4 ,a5vbyj wu q+gb6fmmyz1s at two successive harmonics of frequencies 275 Hz and 330 Hz. What 1zy6+m,(fyjg bqzv1mb5ua4 w 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 p+nben rror *d7u dy-.j50 xf2$^{\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 2.14-m-long orga f6axp,eucrl r a9w+23at;w .mn pip9p.6a t le,x caw2wu+r3rf;ame at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximatelszy5+4 ic ;v cgr+ s3lzfy6;qjy 2.5 cm long. It is open to 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 your answer to the information in the grqljs4ycz+;; 3s5c +6ygvfrizaph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when crcp/2qg ya z7-n 1btvy5 79jqtrying to adjust two strings, one of which is by/a p1 9 zg vqjq5c7r-2ycn7tsounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) arsq-6uz t jzd4np4oit639d) oorz68z nd $C^＃$ (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 (brandb *eji+:fx :,pp8l qpa X) operates at an unknown frequency8x*:,:pbiqppfjl e+ a. 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 frequency of brand X.    kHz

  A guitar string produces 4 beats/s when 81t(lvm y 85k5bgr-fcdu*qvm sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibraqm kdy*v -m1flv5cb85g8(utr tional frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension h 1sto- o1y m7-ul/(aw/wptpt in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playe(oyh-17p wum/t/t1a s-two pld together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes kq. ym(3n.t *s usgmt:each try to play middle C (262 Hz), but one is at g*mk: ns3smt.tq .(yu5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of rvda./3 kf w)i441 Hz; when A and B are sounded w r/dfv)aki3. 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.h.2ogu j:w. fs80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. sgu:fj.o2w h.
(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 aapf 1z v78kumw0q7te8 t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is v77 vkew8tq mpfz8 1a0uibrating 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 andwdmo poz g 0f,y w pc+/a,h+i0k;:utq8 2.76 m in air. How many beats per second will be 0cqg+;,ukwy opwf 0ho+/ia:t8pm dz, heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when alc 5w*d 2wh5izt rest. What frequency do you detect iz2dw5i* hlc5wf 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 you detect if a fire engine w9vfcy bun1y1f;3 bdn4 hose siren emits at 1550 Hz moves at a speed of 32 dvnf14fb b yc93nuy ;1m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcewde)/.wph j6w, (em r*b+k+ik,upboo 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 closerwi( u+,) ,+kkbhm6ow*ew de/po p.jb? $f'_{source\,movine}$    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 pg7 *j8 t1 8t0vnnhngrsingle frequency horn. When one is at rest and the other is moving towarn8gngv*h80r7pt n1jt d the first at 15 m/s the 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 outhj+ox yuix7 s*e8::jb ultrasonic 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 sound s bx7:+ohu*ji:x8j eyfrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emit -2dl6 dh 0+wew(khxrjs an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the + w-e(l 6xhdwkj2dr0h reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat)ivh1b1lrz -14iqb,or df4uwkz 0gs7 train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the di1k b 0)gb -fzw4,4hi1z1 7rvoqu lrsrailway 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 wave+s(uz lpy7a/ko3p*u (nejnk 7j40of js to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and tho +jujpj sn07pk 3la*yun(oe(4k7 f/ ze 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 directly away from the sound source?   Hz

  The Doppler effect using ultrasonic erg889kq2x e bwaves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind vell,myi; /5j.k xdf iu8jocity is 12 m/s from the north, what frequency will obseujfk x;8iy .jm/d5l,i rvers 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 - jaxvj s;g2m*we kuf.na65q3its 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 a/8ntlmh/abko l8g8s3 i4fb( rt Mach 2.3 where the speed of sound is 310 m/s (a) What is the anglemfog3nt8h4 r /8/kasb( lli8b 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 k l,frwhtp n 04xzc bxip-,02*thin atmosphere of a planet where the speed of sound is0xhxr*k2-l p,p 4wf0i ,bzntc only about 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. Determinkfj*t5 degkf/e-.nf/+z kf, fe the shock wave angle it pr+ f .ffknzkek-gef//,dj5t* foduces
(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 a bp7s(h,aq/w$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pm jy8-8im:fs xlane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has t8 m8y-jxmsif:raveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dow vacssfk be; zk0:4kv9r/ 4h+rnward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed szk bv 4/40:9ska ekrr;v fc+hto work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thehgu)gw. )x 1yn-/0qv8 j6n emwpvhgm 7re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disp.3ce;r qa3e/bds zh8ulay called a sewer pipe symphony. It consists of many plastic ;er.s bhazc8ed/q33 upipes 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 frobv16peveknkgvfa(y .6 3* k+nm a person makes a sound close to the threshold of human hearia1+e(636v kn yev *fgkpnv.kbng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and s+a4squ dl7/jn m; .auan 87-dB sound are heard simultaneously? qu4u+ ;saj.dmals 7/n    dB

  The sound level 12.0 m from a loudspeaker, pl2e6;k egfngg 6aced in the open, is 105 dB. What is the acoustic power output (W) of tkfgnee; 2g6 g6he speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ok wy( *o0zcw2q3hr jp)m* e:(rnplw4eutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is(qorze (we30 *wc*w2nyj:k)pl mh4 rp the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thyab4vlr6r -, yeir 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 ea rr6y 4,-ayblvr 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 engine?    W

  In audio and communications systems,z l jznzcg96g*. ;6pyy 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 n* ,zud /.eul*ftf. 2e4iba qxfrequency 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 poinx1vove7gil7w z, ,vc0ts with a fundamental frequency of 440 Hz and a mass per unit zclv ,71x g,o0vwvie7length 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 vertisjj:3c.m c e:ycal open tube filled with water (Fig. 12–35).s:j.j cc:m 3ey The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near ycnsv:- y(;vn 8yq(usa tube that is open at one end and also 75 cm long. How much tension v;us y(q:-(c8nv y ynsshould 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 obseri qkbjd(zk, u;aw*j(, eeu+8zved 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 thklf q)mwyp/45e 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 finds that the sound level is minimal at a point 0.34 m farther f/ 54)mylwfpk qrom one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Ov f0me73ohfu:3 oaryy5,kq9 or)qxr;ne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What u0 ,a:73xkfy v3 orh;9oyeqf ) qrmr5ois the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachepqb oy s/f c6mn40ecd- y,47,gufye.fs you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constanyf -, ny,ues6fcmo4 bf4.qycegp/07d t velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the q c/( 5p)wrr.lds7 uaedifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by rlsedr5/ aw )u.( pqc7on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thv5z-b v(+)+fgf +z py6ggs jyke shorter one is 2.40 m long. How long is the ogf5+zgk f-s( 6pg)+y +b vvjyzther?    m

Two loudspeakers are at opposite ends of a railrogh9dukj0f 7ox- edr(. ad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sounh7u9f. de0( gojd-kx rd 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 the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in th5wk71ioy7 hlye aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultr7li17h yy5owk asound 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 m:ytv +n0fznml2pm 2 *ioth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave ref y +m0v*ft22pzlimn n:lects off the moth?    kHz

  A bat emits a series of high frequency bp0qfi4,,6vbx a6vbu,s0:ym 8 nnsnnsound 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 th 0 ,08qinm, yvsb6snbu4pxf :bn,avn 6e echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send sig 2*alsyej3z i)frt 8 q+wmjj38nals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep soundy*f+ 3jm2) e88slritazqw 3jj s. 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 en2ih kfa c;.w(8n(v dbe compromised by the presence of standing waves, which can cause acoustic “d2fn( (8vh.ac eiwk ;dnead 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 in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singif:893dtox)h :szzff k ng rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a ) fxfzz :os :9hkd3t8f90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the humaw b4nk.na b.afj*2dz6n ear at a frequency of abf 6.zbn2kan. 4b dawj*out 1000 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 sonic boo4 m;9uei0rla*t .m z2 tsawv6im 1.5 min after timrtt;u09 6a.vm2l 4w*zi saehe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat oibrpy8 6i *7ris 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