What is the evidence that sound travels as a wavm l )zd1;* *h akbnum3rd2ch-se?

What is the evidence that sound is a form ofk6i/idn uw. rk zpe93a7e8uu2 energy?

Children sometimes play with a homemade “telep .: jdv2glscs:uoty4 m p+9a0whone” 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 b2uc0.w9 :mtd go+j p ys4lsa:ve 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*6 o,tn7jl l9jwl n-ou water, do you expect the frequency or wavelength to chal lt7 6*ono -9nwjuj,lnge?

What evidence can you give that 4 wj3 )d*weyfwthe speed of sound in air does not depend significantly on frequency we4dwyw3fj*)?

The voice of a person who has inhaled helium sounds very high-pitched. w 8l+6zdl3gpeh.b0k 4httg d*,alr) pWhy?

How will the air temtg rkv(o2 u;g2 n6 qon1*en9)rpth)c6m jywl,perature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filte 5 f1m ycctsrf,*b2v4wr to reduce the amplitude of sounds in various fre yv 5fb2,s*4cf1tm rcwquency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 122unoh/;n v+ 49d +yd-vud pkhu–30) spaced closer together as you move up the fingerboard toward the brid h2n u49ou+ k/uv n-;ydhdpv+dge?

A noisy truck approaches you from behind a building. Initially you hear it :/j nw4t t/, erkuj4rebut cannot see it. 4twu,r://ekjt4 r ejnWhen it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”s7t9o b1k jg*2krm 9sb 4o:rzt whereas beats can be saikrb9skz *2s: 71bojgo49 ttmrd to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, eqxa3c37a;6cdiw zb r(ziq(h( 1-stjwould the points D and C (where destructive anzq x-z ahi;3j w6r( ecai3(71(dqtbscd constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people wh)gz(/ :dibo vko work in areas with very high noise levels have consisted mainly of efforts to block or reduce noisb:/id)k (ogvz e levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eae -ry tw4.e whw4az*i6ch wave can be thought of as a supeawh ti*r6ye .w4 e-4zwrposition 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 frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer moveli- x8v74xbt0cn vf i, in the same direction, with the same velocity? Exp -8tvn0icl7xi 4, xfvblain.

If a wind is blowing,q0.q3/svdox o will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengto/vs3qqo.0 xd h or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor mi5qpi /m3(s0 ;rnu.ju l +btv9 qqh)nis blowing a whisqilmhs mb0qu;ju3r/9 q( n5+t.i np)v tle in front of the child on the ground. 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 ecrko/d2(6zv0p ;jn2gh-rxa yl j;eo y( ho of her shout reflected by a cliff at the far end of the lake. She hears the dx/oyh26yrz;(o 0jkvn (l;j-g2pr ae echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinek*qzjf2 u 40n7a5e47ksb aefs. 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 (Tablej7 5fak* 7ub0fee4 4zksan2qs 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave /i-)b pe2xdiklengths 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 drif83m(k dy 9dnxdting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another b8(d9ddmxky3 noat 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 strmtr,: d;i ,thyiking the water below is heard 3.5 s later. How hi;ity,,dm t r:hgh is the cliff?    m

  A person, with his ear to tvesrd.r( s4gj y*njm 5wg-cqy0 6 o+j1he ground, sees a huge stone strike the concrete pavement. A moment later twnos1ey 4+(0 rcy w.js g*65vdqg-m rjjo 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile w/ qiqqy*:af6rpe zl.(;ecf 7 of distance by the “5-second rule” for estimating the distance from a lip q7aq/qy e(c.zfel:;rw 6fi *ghtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity op(y ; ej312pu mzfywa9f a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity iqgl/u*j z;9 yns $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a s:* pdvp wt e,*ldz68hdound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Addpzhd*6 dv8l:,wde p *t intensities, not dB’s.]    dB

  A person standing a certain dist6g z m3sy:it8ri-/vpcance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would386m/gi i-cyzv: sp rt this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas fos+g *gstq1ya;j z( .otr a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 jogq *.tta+1;zs gsy( dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from - ,0s/:ctefnw qtn(y ba person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered o0c /f:(n ewn,bytt-s qn 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 ared+t6o)ru0tez8(* gl1 v zgfpea 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 amplifief *ffc:cbi-(wcy3b 6er B is rated at 40 W. (a) Estimate the sound level in decibels you would exf( cby6ic3e- :wbfc*fpect 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 dB when placed 2.8 m in front oasw+d4z c3wd 9f 3bhh,h2, s81 kbudrkf a loudspeaker on the 42u,h1h9c sswkhb+dzk3b f,38 drawdstage.
(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 ljo v0 mmczmqvruv*we 6./ (o :rsd)4:level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amo(m0rdq ujv/e)4r lc: o 6w: mmsovv*.zunt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sowq.z bl sdr*+(und wave is tripled, (a) by what factor will the intensity increase? Increase by a .sdwq *r(zl+bfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have *p 4okj6b5v6 wq6ynv bequal displacement amplitudes, but one has twice the frequency of the other. Whatv6j6 nq6pv k*b5y 4bwo is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air th0 h 5+*at uhuoq+qwlpprk5; r)at corresponds to a displacement amplitude of vibrquqpr5+wh5kr p0*h+ a;t )u loating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what souz/zz e6dnk(fmqt+60 vnd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)z6kfdzz0(/vqtem + n6    dB

What are the lowest and highest frequencies th6mz (nd:; lj*9kye3 x)suwwj 1sjx2dhat an ear can detect when the sound level is 30 dB? (See Fig(139kj:zyme2ljw*sjnd x h ;)wds6ux. 12–6.)

  Your auditory system can accommodate a huge range 7 1vn-b4(cupc ibwn 6lof sound levels. What is the ratio of higheu46in7 n1 cbp(v- cbwlst to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of y;jp7+trljon,z qw8g (t30 vdthe vibrating portion is 32 cm, and it has +q ltwg,p0r8z jv73dt;(nyoja mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thb2wll3v d4u3a e fundamental and first three audible overtones if the pip v334bdwlu2lae is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from b.4jsb5: ubua glowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubegbbu4 j:a5u .s?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanna j;l ,;fl2hvking the range of human hearing (20 Hz to 20 kHz), what would be the range of th afh;2jv;, llke lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has acfp,;oix4h +vhl :fw (7u2ob f htun3+ frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of ixcf tu4vhlbp+;uf3 f2o, n :howi (7h+ts original length?   Hz

  An unfingered guitar string is 0.73 m long ae;hyql5s1(8zh - u+uvgfwiw0 nd is tuned to play E above middle C ( -g +l vs(508qezfihh;1w uuwy330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an ope u;a)k6 g0mt cp5.khaqn organ pipe that emits middle C (262 Hz) when the temperature is 2gc tq;6 amu).h5k 0kpa1 $^{\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 20*/3gm4gp q :o/mjs nc,j ym1oh $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–tg:cxg ; l;vr+10 should the hole be that must vg+;tcg:x ;rlbe 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 264 Hz, 440 Hz, anbv7k v:3 0hhhgd 616 Hz, but not at any other frequencies in between. (a) Show whhvk 3h70hg:bv y 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 awba6qmd7q0c7tls-e ;aw2 y*b t both ends. It resonates at two successive harmonics7e tl wbaswc0 -qbq 6d*a7m;2y of frequencies 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 yhx5nn,67e 1aqtmk-r $^{\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 t.dwr f0m-vb ovaawsp(t *d4)ll)1so7he audible range for a 2.14-m-long organ pipe ad0wa(-l)wo*7fbomdvs 1 tra. v psl)4t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm msu3 h+6cb9vm 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. Wh9m+36cmhb svu at is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trv+.*1g,ta n xz rn(r+krl/yf uying to adjust two strings, one of which is sounding 440 Hz. How f rr* + ,.aftx1nvgknlz+/u(yrar off in frequency is the other string? ±    Hz

  What is the beat freqr2pyqpt g o vj,(du1pbo95*k.ox2.zbuency if 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 kHtquo-:t3q pp+s,e ya9 z, while another (brand X) operates at an unknown frequency. If neither whistle can be hearqtuos- qy3a,e+ 9tp p:d 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 sounded with a 350-Hz tuning fork /i4a9tpd3j stjdm03w and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Exw3tdt/ p0 3sdjm9i4 japlain your reasoning.    Hz

  Two violin strings are turo -zbz0pl6v 2 xzxck ow.p))0ned 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 strings are played together? [Hint: Recall kpw)z 6lb0.oxr 0vpo-zz) 2 xcEq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle wofq6 m: 5(mfpd(3uw (x2 okntiv:nq+ C (262 Hz), but one is at 5.0°C and th (:nqnmu wdm:ki5fvx+powf6 (q 3t2o(e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, 3 / f-x/abct.u6 kmbwnB, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a b6c/ ka/un.-bbtmw f3xeat 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 s kifrj b.0t0c+tands 3.00 m from one speaker and 3.50 m from the otf0 rj.c0b+i kther.
(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 tn:+e emmdxi 1k oxjo0+c 76d6no be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a+xoji: dn61e6+om xdnkec7m 0) 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 k29daf :5 zvocin air. How many beats per second wo5caf2 :v9 kdzill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequen. 1;goryq2g :. qqbcyncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you drg1q o.qnygc 2b :;qy.etect 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 you detect if a firb;vz94tj h f4ue engine whose sirenv4f4t 9;uhbjz emits at 1550 Hz moves 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 ph8 c*4y p3fzsis moving toward you at 15 m/s versus you moving toward pp*4 fs8yczh3 it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn7r(7g g 3,ztj zaccxu4. When one is at rest a3acgxct 7(, j gzrz47und 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 receives thedab2iqhi /.9 v1lai2m m returned from an object moving directly away from it la1vd/a mbiq.i 229hi at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s o 9wp2qd2msu5sx-s,j As it flies, the bat emits an ultrasonic sound wave w p2owju,xm5s9 d-q 2ssith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimmg(fs biu;w 52h sy-j:ents, a tuba 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. What beat frequency was heard if the train car approached the station at a speed of-s5 yush;i 2mf(gj bw: 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bl yw t wr0w1ac2hv9(.hlood-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 1 hw car thlw(2.v0yw9frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrc vdct4c,o*4c 2h haz,asonic 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. When the wind velocity ib+ ;* nl6xt re 28)esvfoq9mcqs 12 m/s from the north, what frequency will observers hear who arft r92lqe8q;*6 nv b+sxmcoe)e 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 l2tr :onlx1i.j .i:/,hafchh if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speem cxd;vk/ 0sa.d of sound is 310 m/s (a) What is the angle the shock wave makes with the direction akv/0sm.d cx;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 at)k h) mjj+du.g3n ,uz-ccl6lomosphere of a planet where the speed of sound is only ,lodmulujc+c3zjh- g 6n).k) 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 strit4 (xaj8 3v 8g*ynys1aedh6zpkes the ocean. Determine the shock wave angle it pro yysa6 gh 8xepz*n1a4jtdv38(duces
(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 td15k b89/suptl6 :ovan ,wcs1w i)sg $/theta$ 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 zicn,m 2,l; fhkm above the ground flying fasm2f li,n, z;hcter 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. 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 s i .el;xid1pb+e(j9ao0sjw d;ound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for wh apwejbso;; 9lxi+d0ed.i ( j1ich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ran jwots1y6z.c qz1,l0 pge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonj f2p mt2pk+ ybhk)q*2y. It consists of many plastic pipes of various lengths, which are opb2fkhk+2pp)*mqyt j2en 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 close to the threshold6qfahlk3: 4z) q 2itl;s jszz: of human hearing (0 dB). Whajlzz:l2 hkt ssf z;a:q6)q43 it will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound ans/b k l3ianm4*68zrdod an 87-dB sound are heard rkz64*bonmld3/s ia 8simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 107hd6c4ym:j8xvr;q m a5 dB. What is the acoustic power output (W) o v7 dxqm4r8cyhajm6: ;f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The72ded+j (jr*ff7rhee/t . f4ujdm v2g power output drops by 10 dB at 15 kHz. What is 2dj+j 7f(7rhve*4 g/ tdff.rjedue 2mthe power output in watts at 15 kHz?    dB

  Workers around jet aircrawvs/ 4y; 8ea1ga *wtmjlo+puy1ri *x4ft typically wear protective devices over their ears. Assume that the sound leaui*yg jt811/*4lv spm xy;w+r w4 oaevel of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, e 73m1yj hjj,x*coxtc*7vo f( $\beta$ 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 tip( ph4ptyv 1,rdob.,o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fu1sfpg ,1lsxh4q;.2zyp uljg3(i i(f5hbw ju-ndamental frequency of 440 Hz and a;i3, jx( ff.ysizguwlqbp sl(u 1g 5h241h-pj 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 aboyhv+i6 j7gllz vo-9d3 ve a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the dihvzy+3dil j ov6 g-79lstance 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 stringyzuf+. g gv5w0t63 vn1ol vvj- of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance6ou1f.zvlvnv -+t j5wv g3gy0 (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatrjffsy)3 lx.02 kmq y3n6x m3me 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 sources. Thebw+zq uko7x ,8a7lm3a sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and fiak3o x+77wul,zqam 8 bnds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. .n.l9q hprrv:vb5if 6 One train is stationary. The conductor on the stationary train:h rri6l qfp.v5b9v n. 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 whistle as it approaches you is 538 Hz. s3ioko:rd5v rt7u g0xn)am: rab2 q8; After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocitymdr:rsv)ona2i8 k0oq g:;a7 x 3ubr5t)?    m/s

  At a race track, you can estimate the s pnch.a7)/5*jplhj * (cwgabi peed 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. How icn )bpc7 *a.*(/lw5japgjhh fast is it going?    m/s

  Two open organ pipes, sounding together, prod hi2l:6-u ) zhm5,vd.nn bll tpkd+nd-uce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How loidl- h+tvznuk25 nmn-hd. dbl,) lp:6ng is the other?    m

Two loudspeakers are at opposite ends of a railrow4wi+ z5i3ty9 eq5ed yad car as it 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 w5+9yz y5it3wi edq e4frequency 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 the aorta is normally about 0.32 m/s what beaufn ob3l( 0if*t frequency would you expect if 5.50-MHz ultrasound waves were directed along th3ul0*( fbofn ie 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 atv+/lf hkr 5*jz5h fuxq3uvn48 speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s Th lr* k45/hu+zunhq8vf53jf xv e 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 pulses asgx.p4+0c21 jp yepot s it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns befgcs.po+jt4p2e1p 0yx ore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine villlh-ypmyd6 +b 7o5zzi0o t 4ra4age 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.) Modtrdy zz 0ha75l o+ 4b-4o6ypmiel as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standjk0 5pdrf -i:w:cio* ring 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 fundamenticd r:-kjo5rp :f*iw0 al frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves 7 ahr f1lfw-t:91p ;jqbva/,wyq jv-o a long, slender aluminum rod held hr b7ql:--yw ,/vpwot;91avf 1jfjaq 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-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 human ear at a frequen5enegk klg)cm+).vtl1h+u d4cy of about 1000 Hz .) kev4) mh1 lkd+5gg nul+cetis $I_0$ = $1 \times10^{12 } W / m^2$ 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 s:ifw7ga+bz,)tx 9e 6lhfdlh5 onic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu:, 9ftzg6 xlwa)db7+feh l5ih de?    $ \times10^{4 }$ m

  The wake of a speedboat is xevw*zqn)om 2 k;2b4o 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