What is the evidence that sou/r4m:f mbok 9mnd travels as a wave?

What is the evidence that sound iljj*nqo,c6;retm2. s s a form of energy?

Children sometimes play with a homemade “telephone” by attaching a )2 pcy xus7e l1a4r3pustring to the bottoms of two paper 4ex uyp)p a7132s lrcucups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you l gk*jetod.91,. umtrexpect the frequency or wavelength to ,l9j.kmou te *rd1.gt change?

What evidence can you give that the speed of sound in air does not dep0kcyqmmg (8uwg78c 2wend significantly on frequcw2c qm8 y7u gg8mw0k(ency?

The voice of a person who has inhaled helium sounds very high-pitched. Wjv) iau*u r,d4,p4doohy?

How will the air temperature in a room affect the pitch of o jm:qlzfek/j(0v t f7w9m-m,h rgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude ofgi (k g*72rfxj sounds in various frequency rf2*rkg (gi7jx anges. (An example is a car muffler.)

Why are the frets on a 8: qy r:u3yqt3dmvjw+ guitar (Fig. 12–30) spaced closer together as you move up the fingerboard:qw:yyj8+ 3r muq t3vd toward the bridge?

A noisy truck approaches you from behind a bui.dox 7 o.aaawgpwi.6.lding. Initially you hear it but cannot see it. When it emea7 xw6 .. agaodi.pw.orges 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,” whereas(3v*)rl m kc/wlu;vr f beats can be said to be du/3 *vw rf;clku(rv )lme to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were w7 72kubdgh1 slowered, would the points D and C (where k2gw77hdb us1destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of proteczky :-o/)mi8w x qf2lbting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headpfbq ) wz l8:/oxk2iym-hones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown inj4jhsrr00qd 2 itdme8(mn r /0 Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with q injerjr04sm 80/dhr0m ( 2dtslightly 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 souro:vd1xs/aj sauv 6 tdd)5 :d,nce and observer move in the same direction, a/sdd),d6d sx5:uvj vn 1to :awith the same velocity? Explain.

If a wind is blowing, will this alter the freqqc p8ch 7sku4q(o.e v/c qey/o*5 ov3uuency of the sound heard by a person at rest with respect to the source?pv 3*ucyhoeq ckv8 4/ue 5(/.ocqqs7o Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monin jy4(-l+j tl92 zv0idv)xkp ktor is bl0k+ jt 4z2d 9jvl-ikyxpl(nv)owing a whistle 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 7okecr9h p:fx) 1k* 4 xywilp(listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears th7k9 *xe p:fh()ol1 pwx4 ciyrke echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of ixg b9ohd-3x;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 b9xdg- xh ;io3at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ai w ;csfv3w.xf 6gsa+(or at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a fog6i,wvg 8nsjx(4l4 e:zwghf)wr j- d;mgy day. Without warning, an engine backfire occurs on anothe ,rwhivx gf(4 s6)e84wz;-m wljngdj:r 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 xqd 0ns1 dyyzr pgr.djg5or,j .qn3ti+/3a48the water below is heard 3.5 s later. How h8arq0 xjipqd ns /4 yrydo.,dg5n+z33rjtg1 .igh is the cliff?    m

  A person, with his ears.2zv xiwd deo7/h5o 0 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 5ixwvz /deoho7. sd2 0apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dist6t, tr .6dzkpl)bv0 ovance by the “5-second rule” for estimating the distance from a lightning strike if th6)k tv 6p0,lzbro .vtde temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level ofkwe.f(offuls.t v4akx 4e0)/ 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 : gkw62 bqt0taqzu21lof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound levelh pl5c y.a)fo6 of 95 dB when fired simultaneously at a certain place, what ) ofhy5cla p.6will 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 wit6 fg7lm9dt-1qt +chl 89iknhyh four equally noisy jet engines is experiencing a sound lev-chtymk61 ldt+8hq9f gl7in9 el 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 on8 n3 ymxmx4(5 rpj r abi0y4hrhr);2mf 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitie0m43p h r2 ;rxrmn()rh5a8 jyyxmin4b s of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a peelquf f 0mu)33d bly7)rson speaking in normal conversation. Use Table fdq3lf0yel uu7 m)b)312–2. 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 strikes an eardrum uu8re25bzqq - 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 2e3d 3nbgcrob9wq;: m)hu(6hw auf :d 2q*md+a50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulr 3bwumw3 a6bq:c *)g d(nd;h+ :29hfmduoeaq d expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130;) 0sd5t0albs(spxqm dB when placed 2.8 m in front of a loudspeaker on the stage. paq;bsml(s0sdx 0 )t5
(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 typicalq mb sm9cvno1x6 df .vaq2q;(:ly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whosv9q dc;qsq vaf x.n:1b6mo2m (e levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripl icpzhx: 7:)p;eni1)r 6nfn5i+ncdl qxb9ru) ed, (a) by what factor will the intensity innqpihr9;u xc)f: ncnd6il zbpi+1 r)x)n5 :7ecrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemen lw npy-y5j bbh )e8 8hera+jbxz: jt/q18j6,zt amplitudes, but one has twice the frequency of the other. What is the rat8wq+ 85p8y yhneh6,zjxjbj-tlr1 :zbe/a)jb io of their intensities?   

  What would be the soun73ju:93 s 7 cacsxoypqd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0 ax c3sus:c9y7p 7q3oj.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sounz7bex ,7 5 :fwaup;xd /6umrcfd level to seem as loud as a 100-Hz tone that hxuz6/rwx fb 775;u a:decm,pfas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequd :arp f38w8-)r stxivencies that an ear can detect when the sound level is 30 dB?i:x-wt8 )pavs3f 8rdr (See Fig. 12–6.)

  Your auditory system can accommu b ,f(e1ju,ln x;)1rk/ywnt jodate a huge range of sound levels. What is the ratio of highest to lowest/j(urxjn; knu,f,t)e yb11wl 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 lengthvao6 27u5i zc-j)luyj of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under2iovca)- 7j56j ul uyz what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are thecv)grdrewg6j:;a fr2q , l(j2 fundamental and first three audible overtones if r6jg(avfd2,ej )wqg: rr2lc;the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequekp+-aj wyzo2 , 7m5nzbncy would you expect from blowing across the top of an empty sj yz-+wpo7m,2bnk5zaoda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ3ho gyxl4r)t ws)*zq5 with open-tube pipes spanning the range of human hearing)t3z hw 4q)r*oxygsl5 (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 hm8 (guakm:hs ()q; (m.5m/p vqux uhlyas a 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 its original len/8h aum:y; kqg)m v(ms(u .uml5hxq(pgth?   Hz

  An unfingered guitar string is 0.73 m long andr8 -nt, xinu-r* zz8w1y:uxfv is tuned to play E above middle C:iz8,*1-w ft rn8 yuzur-vn xx (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of h4y(m9 hkt q6ran open organ pipe that emits middle C (262 Hz) when the temp(94hmkh6try q erature 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 ad)s1 i5oe ey;hl9qnh 8t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpil6 ( v64a 5+lyxmnhunmece of the flute in Example 12–10 should the hole be that must be uncovere64(havlmn m 5ly+nu 6xd 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 8dh 7xb i8:jrrse3hc4n resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies :h8jh7bcex3ri4r d8 s 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 isb,/v tq wbzp 7qyhi ju.576k8j open at both ends. It resonates at two successive harmonics of frequencies 275 Hz anhi/67 t57j jqbw, yzb8 pvq.kud 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 cnow2o*4mv2vx2vq 6d $^{\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 rangec shsex i77u/9l3lp v8 for a 2.14-m-long organ pipe3s7s9c lepv /lh78ux i 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 open to t47j*jea:jtrt ,,f )aq li *xcvhe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audi4:e* iajf)jqvl r, xt7ta*,jc ble range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stringols d)e1u-wp.s, one of which is sounding 440 Hz. How far off in frequency is the other string? d ew)us.l- 1po±    Hz

  What is the beat frequency if middle C (262 Hz) k )aq ezn4s094dyvq3s 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 ope8,bt(zd ar/n crates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate t,r tcazb(8d/nhe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and kd2-8uoc3 dlv 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the ck3d-d ol v8u2string? Explain your reasoning.    Hz

  Two violin strings are tuned 4. mow8aq yu df k w,83;b*st(ixlbys7to 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 playet q7x, aow4ms;yfwki 8(udsbl3y8 * b.d together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play 5* 8mv y nuo/da yrtu1()mipx;middle C (26 tuny8;v )(ym5 aupdmxro/ 1*i2 Hz), 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 frequency o+ wdqe.;nnl5kf 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundk;qendnl + 5w.ed 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 ;3r+zi pegyi7tands 3.00 m from one speaker and 3.50 m from+e yg7iip zr;3 the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratis30el*f2/ xhm d as9bhng at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?hmxh2/elaf*b39sd0 s   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Ho wtans0 4i)k67/ickxpf8;ipvw many beats per secondt v6kf40/ )7cnpi pxw8s;i ika will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cerbttxbzq z h)/2b7tnjq 7im;+9tain fire engine’s siren is 1550 Hz when at re/2;mbqbt9z7i x+ htbt7jzq)n st. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Wha: b0y(ql) oavbsk9gf* t frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at ay v(9 *fbl0qsba:kg) o speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifttz qi7n9 ey73m in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two fq77 e3i9m ytnzrequencies 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 bh7ixnqw +;7 uequipped with the same single frequency horn. When one is at rest and the other is moving h 7qbx+iu;nw7 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 yz,r q*zgvz(ue x.1ez.g h5t6waves at 50.0 kHz and receives them returned from an object moving directly(yzzxe .gevgth.z6 u1 z*,5qr away from it 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 As it f1 0 a ;mbp:v -/iiimq.;zr8:rgppegj q7v dw8ilies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the 0g;m: 8-iwii8 gvqbr r/qjp z ad:ppv;71 i.mereflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplevbxx .ru-2 s/dr experiments, a tuba was played on a moving flat train car at a fr/x 2.udxb-svrequency 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves t 9ja p-w:h.gkjb ;nz-go measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of so; nhjka gg b:-.9-pwjzund 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 waves of frequ 3b;u,uaod8 1d 2*qr)lk m1jd-hruopyency $2.25 \times10^{ 6}$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 winnui 9bqrl (u1gb ,+p-ld velocity is 12 m/s from the north, what frequency will observers hear who are locatp,iub u1b(nr9l+ g-qled, 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 l b bd)7npo (+sjc*kdpgsy3)j (and 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 speed of sound is 310 0fovi;qgg9p 0*n(,dy,fcych m/s (a) What is the angle the shock wave makes with the direction of thev(ify,*c 9 c0on,fgqdp yg;0h airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soun *9iqbj c hjpfgfh;1;,d is only about hibq 9p f1jfg,*hjc;;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. l*tl3 -weq9d d do etj1fq0+8cDetermine the shock wave anglec *o9e0wl3 d leddf18q q-+ttj it produces
(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 hgu9iwhu;9yz/)6y4 p3pwck.c fo t 7r$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above theyk .trzedi-wi +cg24e sy 6o-4 ground flying faste +.cwy4e k-zo6di-4ye is2t rgr 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 sound pulses downward 4w7l y9lnj-uj89 rpdzfrom the bottomn 4 j9u9j8l7dzpw-lyr of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the )ffqjq5 pv 1ulg46p0owm6 3ws human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called ai.d roh+h+n- v sewer pipe symphony. It consists of many plastic pipes of various lengths, which-h+io +.vndrh 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.h;l/nv.,r va w0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosrln ,;va /v.hwquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound+gq ,acos1s7dnr .9pl/ ho2 ds are heard simultaneously? gdad,1c+ sor29qpo hsl. /7sn   dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i x c*jfpmv1jy 1(;ier(s 105 dB. What is the acoustic power output (W) of the spej(vyrxf1 ;ij(m1p c*eaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 7 oymf,6jmj+ l150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power ofym6 7 jj,+olmutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pqeptm 7kfjtr:im o5 l 1sn80wx70+:uh rotective 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 ear at a distance of 30 m from a jet airpl 0 sj8im5kxmfun ettqlr7::w 1+ 0o7phane engine?    W

  In audio and communicaomuq lu(+ 1il6kg:x+stions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freqledap 6:j9l (yuency 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 jhj ccr *l4j iw47*xk2is 32 cm long between fixed points with a fundamental fre74*hk*c r 2jxwlic4 jjquency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set f-jv(q pkby; c9rxnzs;4ae22into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. vzbnp c-xq; r2seay9j(;f42k 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 a tube that ip;3 2k; )tei emc4 en9tjfh4 boeyou0)s open at one end and also 75 cm long. How much tension should be in the stph2i ue; njkmoefcey3;bot4)4)e0 9 tring if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass wasy ;w*:kv,ewzelre .4s observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two souhg5yu9j 5qym8pdp2qh17in66pb jd5w rces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the ot1idpm95b7 hd j5 6pyq58wpn26hqjgyu her. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whiri/z+quu;tp3 stles. One train is stationary. The conductor on the stationary traii u;3zupqrt+ /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 appry20imc 9 yxk jkitb .p-;lhg7)oaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume 2;ykhtj.b 07k p -xi9ylc )gmiconstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by2 ,ik y-,trfa+mmezywr2 +ret6jp) t5 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 straighta-,y+t me ),eyt2rifj6twr5 k +r mz2paway. How fast is it going?    m/s

  Two open organ pipes, sounding together, producehf*+c c 3oyl1k a beat frequency of 11 Hz. The shorter one ishy*lco k3+1 cf 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of1wkum 2umy9 2bz0qs86v8pgpz 6 iw( yg a railroad car as it moves past a stationary observer at 10 m/s 68u svum(91izy8w6 y2 mzk0 ppwgb2 gqas 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 passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s whao 72m 8m3;w ;wab0dgziixokj7 .4ntdot beat frequency would you expect if 5.50-MHz ultrasound waves wed;m. 38i7dgxiw ;4koz2om bo nwj07tare directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towards c 4las1fpwu/+ nk/mfv-me+ ( 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 reflects w+smfl(n 1/vkmu4es-pfa+c/off the moth?    kHz

  A bat emits a series of high kezaw 8vt 8jq3u251gv frequency sound 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 t13q vt8zej25g8kaw v uhe bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oq.uhlyn uw;w /0iy6 5 )st;ggine 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 w5 tsqwil;ug/inguy.hy );60 a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by tcgrs 4m)iw gt0 8vt8v 2*eml-phe presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider 824 ps m*)m-vlew0t g8ivrg cta 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 demonstrati+2iqapuq yu :ru2bh */on, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the oquiruq* u2hbp2 a/y+ :ther 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 fr*te gnb4ha nvdj4 t1 ct) u-8ce*8*5w.ktc mvdequency of abw*.c-h)1av4 dtudtck5n*b ecv4 tg8 8em *tnjout 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 sw ,r, m;x2nw oilj)izi.ye:z(onic boom 1.5 min after the plane passes directly overhea 2.z;i yxni)w jre(m:,lioz,w d. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is oc81s;igp+ v2(l3x 1km fyafi 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