What is the evidence that sound8(2p3lm wfjt;0zhec e travels as a wave?

What is the evidence that sound *z(b rc+0 tha+oyf+r dis a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string toctf:e)0sst+ vpyp5p x p.19eq the bottoms of two paper cups. When the string is s:ses9v.t pqxy+)1tpf p ce5 p0tretched 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 airgms)edff )*y - s+u1gl+ ltgh1 into water, do you expect the frequency or wavessh ulg)ym1 te*)ffl 1dg++g-length to change?

What evidence can you give that the speed of sound in air does n87y;.di1hk fp);fmo ;y k*cjp/ nfoduot depend significantly on freyc*ohy7o 1kp)ffj ;d8.f kmd;i ;un/pquency?

The voice of a person who has inhaled helium sounds ,sr,m(fesgn* very high-pitched. Why?

How will the air temperature in a room affect tkdxsi 9iw e)w;j;+bi 4he pitch of organ pipes?

Explain how a tube might be used as a filter to:u.:az oxizw2ic5u3q reduce the amplitude of sounds in various frequencu zi.:a:3qc5 x2uwiozy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12t(3a : 6qvhynu-h rco8+er8nq–30) spaced closer together as you move up the +nrhy-orauq c 38(h ev8tn 6:qfingerboard toward the bridge?

A noisy truck approachedgt ;44a3,t0pjoi s93jxsaw z s you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is s3s 9ws g4t,a0ojtzi4aj3d px;uddenly “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 sp(cea cahqx.a qzj1., d0 d6zf)ace,” whereas beats can be said to be due to “interference in time.” .ja0dc)dx1zz e cfaq (,h qa6.Explain.

In Fig. 12–16, if the frequency of the speakers were loweredpsd,mbc3 g3k 9 n5h/kf, would the points D and C (where destructive and constru3sn,cgkb h/f3kd5 m9pctive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearine;usnyk2 x f35g 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 t2yk3 fxenu;s5 he ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. /;p7agvyvm z gud(a:5 Each wave can be thought of as a superposition of two sound waves with slightly differ;z(vpg 57mdv/uaagy :ent frequencies, 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 mokgvkn,e.sax ,irn *h u6.v9edjq ,-:ove in the same direction, with the sq.d9vr,v*go6u-xk ,.en, ahsjnke:iame velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by nc/mp)+ 3pj oc0hof3ua person at rest with respect to thmo+ pnfp /jcoc)u033h e source? Is the wavelength or velocity changed?

Figure 12–32 shows various p 5 xi:0f.oyrgc*eeir*biy7 -positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the groundgxioic. r:pf*y5eey7b- i* 0r. 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 listening for the ewompg/p zg)cq8+bd5j25yw- ccho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 sp g 2-ywobqpz5jg8 5dw)cmc +/ after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the w0cf4ky kxjct;gx9e1;s ) ngz;, mpsi- aterline. 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 cs;), f1;jzisekgck ;0 gntm- x49yxpis 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ai)2o3qsft( wv8b wc/ gnr 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 n6x0 e vudnh:0dp8yk:/7obojjust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much jn8 hep7ydd/ooxk vu60n:: b0time 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 makesf goi/pr i:7u5/z-j+m 6ebpge when striking the water below is i+ zueb//-e:g o7p 6mrjf5pi gheard 3.5 s later. How high is the cliff?    m

  A person, with his ea,tqd(mf-fh : pr to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the tdmf(f,h pq-:impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error madg8 yz4r)elg9jr(*k- x ud+wjae over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatdkl*(8j4j )z g-wx ar eu+gr9yure is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level i/ lu7-dp;bqyof 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 uap puh+g, :uk-qwd7-sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultau9)f7 ncxt -feneously at a ceretf7 fxu-9 cn)tain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fou d2zye*agxk z93l92gy1oh l(sr 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 b1xzahl(2zody 929 *es3lggk y ut one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have4q h24pebaz-nib w-ip,4wo o. a signal-to-noise ratio of 58 dB, whereas for a CD pepo-bz -24hi p4 .w ban,qwo4ilayer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe o:cs,qzw)ma vp.m(z/ r output of sound from a person speaking in normal conversation. Usq:pzvc )/mzw, aosm( .e Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave sdua-lggvqm*-qi bw3d8a,e/ u m df*.:trikes 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 2/td* *v ir.m1vfhk,k w/ww9gj50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to ,w1grw kh k./vfw/j*vtid *m9 each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in froh dolds+6c.: /zzm 0tgnt of a loudsd:h+z.ol gz0 t6sm cd/peaker 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 difference in sound level ofyyz znrq42,b8 2.0 dB. What is the ratio of the amplitudrnzzyyb2 , 48qes 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 whs p3 ,jf9 :l6itiwd2byat factor will the intensity incre, w :9ipyst6b3d2ijlfase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displa5fk f; 096(v,tbv ;picptr fxncement amplitudes, but one has twice the frequency of the other. What is the ratiofxf 5k ,0npt;v6tvb(pc ;f 9ir of their intensities?   

  What would be the sound level (in dB) of a soua jk:5i8x*zo dnd wave in air that corresponds to a displacement amplitude of vib*k5i8ajx d:ozrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to 3 cegm i2 maw-sq4 q t*;qa(cc3u9gyz/seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sei;e 93cgacmyq-3*cgsqa 4u q (mz2w/te Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detez*;mpwqtw2 i: ct when the sound level is 30*zmpq2 w :it;w dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is tke z: +cjgfa4p(k- rn7he ratio :pg ezafnr4c +jkk(7- 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 frl fl u99u1cd /kpt24kmequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. 1p 9uulmdl c/tkk2 f94Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What arc5 rzkx5l(l.pk 4py+p e the fundamental and first three audible overtones if the 5zcyplp.xp(k lkr+4 5pipe 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 wox8n/ v*+tase- ss oz2sb3) qqiuld you expect from blowing across the top of an empty soda bottle ttbs+s/)s qiaxz-soq8e *23nv hat 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 orgtd2:wu pd7b+ ian with open-tube pipes spanning the range of human hearib7+udi:2t dpwng (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 frequencj8)28m* kq4 wwxyk aqsy of 540 Hz as its third harmonic. What will be its funda2w qyak8 q*)wxmskj48 mental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle *o6-k/pkp icc C (330 Hz).o-*6i ppckck/
(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 1 h3 xz)sr:6 wh(e6hmpia+oej pipe that emits middle C (262 Hz) when the temperature 61joh()raee3 shimw6 p xz+h :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 at 2b )ps(4jd b4uq0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthiw xeo3iro0bxbl6* -2piece of the flute in Example 12–10 should the hole be that must be uncoveredobixb0 oi*lrw23 -x e6 to play D above middle C at 294 Hz?    m

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

  A particular organ pipe ca rfht vx2ybomyvvau - *f;05t.7dw0.fn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequen fov2vrt05;u07*mf.vxay dyfwh - .btcies 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 resonates9ldn d;a lm+5i at two successive harmonics of frequencies 275 Hz and 330 Hz. What is n ad ld9mi+l5;
(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 +nsb3max, j+umfp 1m*$^{\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 audibe7y g ci;gu//x67 qrurle range for a 2.14-m-long organ u7xe67/g/iu c;r qrygpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is s ayow-qwy,y1(tx ;tl da60c 80jmua4open 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 gr(1d0ts lywa ;t owx0-4qy8uyjcma, 6a aph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 ;t+ 98caj 2ee7ftjv lrs when trying to adjust two strings, one of which is sounding 440 +e2aj7t9fjte crl 8v; Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andh,.9 oqltwugr6e3o3y4 z ( /3nstjv wg $C^＃$ (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, whzwtw8h*e.*. onc o)z vile another (brand X) operates at an unk to.z)hoe 8vcw **.nwznown 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 frequency of brand X.    kHz

  A guitar string produckt rkw9gx 37ylb 4p*w2es 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strink3wwgpx r9y *b 2tk74lg? Explain your reasoning.    Hz

  Two violin strings aren./ cgtu1hl l1mu h8 mitsmetc(+(/2e tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strm+1sllht/c(guh8c/m2n ei emu1tt (.ings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical ,,0w +neyej ciflutes each try to play middle C (262 Hz0 iwy,,e+cnje), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a .;:b-/snq,:rfn9izm-s otv2od ruipx7v; o kfrequency of 441 Hz; when A and B ard:r fn;rsk u:9o7 oi.vitqmo;2 pnv-z/b sx,-e 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 together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 mx- 0eh q1et.8siz6qfd from one speaker and 3.50 m from the othexehtqqze.1 -8si 0f6d r.
(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 suppxfv*5rux 7+g gr* 7 i/kru:darosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibra/g7u 7r xki : 5+fdxg*var*urrting 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.luyfj(7 f q9a)7jf4;xs0fm rl o9: aqr76 m in air. How many beats per s9s4jlf()qoqa m0lj fafr :fr;y9x 7u7 econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaia yg,3; cnb zztgi4 czm*;0wyji7a+l2n fire engine’s siren is 1550 Hz when at rest. What frequency do you detect inbz03a y tj 724wc*la, +mig zz;giyc;f 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 f r9i ntm:zcp1tw 3t*t5requency do you detect if a fire engine whose siren emits at 1550 Hz moves ncp* tit :91t5wmrz3t at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward r nr41suw(e.fo;qhe-ki5 w*ryou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactok 5e;w h1rrwn4efqr (- s*u.ily 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 frequency horslxm+ zanqizx , ;b2m8s8 1uq;n. When one is at rest annix8b zl;2u q8;m sqax+1 zms,d 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 frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receisvkt4 t:roit 7b -4ph0ves them returned from an object moving directly away from it at 25 m/s What is the received sound fr7k4 4t-0 t:vsopithbrequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a s jhwdg(3v+f .nmque5( peed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hea5fq+djm vg .(eu(wh3 nr in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tu kpa7me9de-**pmc *:dgrm )vrba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. W*vp-*7)d* ged pa:ekm rmmr9chat 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 speeds. Sui/uw3fsnd q lbvb -qrh;g::n3ts 6*,ippose 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: b3ss;*df/:-nnh3,ti6l bwrigvqq u large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultra m grkyk k8-s6 5kstb,2jh:a1xsonic 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 se/ lyi-ajt 1wg,h .yi*ound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, wha h/yijyw-1g ,le .i*tat frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving 36ym*vwy7pq j :iq4jmon 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; bt*qwwvqy +- 2.3 where the speed of sound is 310 m/s (a) What is the angle the *vbqw -w+t ;yqshock 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/djhjzp +(9m e of a planet where the speed of sound is only about 35 m/sz (9hej/+j mdp
(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. Determine13 dbo3u xkrc1iw.3kqz 6ur vb 5y4j0v the shock wave angle it prodbv01q6u.z1ov 5r3uyirck4jd3 wbkx 3 uces
(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 n io+ huw,v6)4k6cygm$/theta$ 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 *vg0co+3(gyt m ,;er u9dgj vu1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance ofu3gu c jg yg ,mt(9dv+ve0o;r* 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 wlx. r:xcyt*) that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 x)wrlx:t*. c ym, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in .org2 d)f 8.att7zz ;tknr4qkthe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displwg c*b;4k9d wya6oo:zay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both e6*dg ;4kz: o9 cwyaobwnds.
(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 s6voz/e5 lbg.ftra1z/ . 1zvw makes a sound close to the threshold of human hearing (0 dB). What will be the sound level 1a5t/zgz.w16o /lsbrz. fe vvof 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sou*bzy9pu n913em ;zualnd and an 87-dB sound are heard simultanea3nz*9ypmb z91uu; elously?    dB

  The sound level 12.0 m from a loudspeav u t3y-nm:kh:6 ot ae,vb4hitr(*k-lker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direhkekvit :,n43a bumy-v: *6-rlth ot( ctions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output cb6p-h(rc4 ux kp m3h1qgfq0 8drops by 10 dB at 15 kHz. What is xp 0b6qh1rf pcc 4g(mq8hu-k3 the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typica 9;sni:pjfg c7cow rw*db a,:ae;d.hy y;3 .rilly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected eai9wir : c *yr.eoj; gb;dwnycad7;hsf. p3:a ,r at a distance of 30 m from a jet airplane engine?    W

  In audio and communications system yev2jt(.gv, js, 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 frkxgkd, f3i*sl+-3 0-wlqi lrrequency 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 lonojre4g)r7 vr p ync41,g between fixed points with a fundamental frequency of rj7 n)eg,yro cr p144v440 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 vert.tmefw:n:ozv 9re)ny q+( /y qical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0me :vet(q: nnof.y)9w/rzqy+ .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 open ati.h-knbj- zkcv,w4 - j one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmon- kckb-v whi,nz.j4-j ic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonat odf:iwoig7uipa2 gz p88; x.7e 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 comicj(f xgr kkvsb4u 7679ng 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 is49sbjkr(6u 7xf7 c vgk 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 xz,3glw;thcq+pglu ,a,go, 0stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the maz;qwgto, h+,, p3lc ugg0xl ,oving train?   m/s

  The frequency of a steam train wmtag4or+ u4z5histle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. zrg+ ota5u4 m4How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can es qcz 6/g(smhq.timate the speed of cars just by listening 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 (frequency halved) as it goes by on the straightaway. Howz6 .sgcqmh( q/ fast is it going?    m/s

  Two open organ pipes, so1xo+ la +tx:rp8 bv5gev swf:8unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 mgfxw8+ao: be+sl 8ptr v1 5v:x long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves 648 cm zos-g :fujz:xtwa*w +ypast 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 the speakers, at B, and (c) he hears the speakers after they have pf :*c+oj6xw8 gz: maz4-yutwsassed him, at C?

  If the velocity of blood flow in the aa jpqy/b n91m5c+ 9hckorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the redcn9h a p1/j bky9qm5+c 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 mot1h3dk ppylpv+hecahk 0v -p::-gg )-nh is flying toward the bat atk3 cg-h-p l: 1pv -0 hpnkgvp+e)yd:ha 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 reflects off the moth?    kHz

  A bat emits a series of high frequency sound pek ,xi6m5 a0gxulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How fa65ie,xx gm0ka r 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 toj/tpe )iq(y-bi7y e+r2ftfi1 send signals 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 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.) t ( -+bpye ifrtiiq21y )/efj7Model as an open tube.

  Room acoustics for stereo listening cv:irnwl2 tbd7ga 0,j 7an be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Considr t ldwg0,7 2jbin:av7er 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 “singing rods,” involves a lonveg*n rn sf k((60jays 1ays srx49m5*g, 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 90-nas9gy 064 s*xn( r*y(kefsvs5rajm 1 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 threstpbh22 b*wy;s fz) je.hold of hearing for the human ear at a frequency of about 100 b; 2f2hewtbps)yz.j*0 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 hea5adma9m4d oz rh*u b1:rs the sonic boom 1.5 min after the z 15ad 4houmdbra9m*: plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbosomfp qx f7 74 9c(vzns8zf(7cat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h