What is the evidence that sound travels pn*5gtr)m 9fdas a wave?

What is the evidence that soun5z 6 dqvtuxpr ./i9swf+ lae6nihv6 3;d is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thez.wlp *e9iv7ltp*z ak1,1h mx bottoms of two paper cupp v,91xwmp*ih k. 1*ztz elal7s. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or wav,a /t), jfwexjelength ttfe a) ,/xj,jwo change?

What evidence can you give that the speed of sound in air does not depenr,flk; 3xanp)m vz3 (ad significantlamvkfp r x3;(nl)a3z, y on frequency?

The voice of a person who has inhaled helium sounds veryzu3l+o3dc+ ze pgz9 t9 high-pitched. Why?

How will the air temperatujv.k: w3s: ddh r).xafre in a room affect the pitch of organ pipes?

Explain how a tube might be used as a fil, bsifo8mqu:k h 6n..ydv1 1rfter to reduce the amplitude of sounds in various frequency ranges. (An example is a cqidu.y6,rk1h f8vo:smb1f n .ar muffler.)

Why are the frets onv/6*i nu a0f7oc87u h: fvtmb3kz wv v8l;xqi; a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward tuf6v3i/bw 7hx 78ozml0nu:c;8 k t vi;vvqa*fhe bridge?

A noisy truck approaches you from behind a building. Initially you hear it but cct, ox+e g6pgj; kyoa:.v;du4annot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you he odjgovcx6 ey;u, p:;a4gt.+ kar more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said toyvv e-baato3ux84 *g) be due to “interference in space,” whereas beats cv4b3gaaux-yv) 8te *oan be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wou97 m tmwet5i4sld the points D and C (where destructive and co t mwi95es4mt7nstructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas)vqvr nx 8u)g* 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 electronicu)vxvrg* ) qn8ally, 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 gc5ov-myo4* f Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with syv4o*o 5mf -cglightly 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 ne y gkl2fhk1*.sje /.and observer move in the same direction, with the same velocity? Explain fh. 2/len.y1gse*kjk.

If a wind is blowing, will this alter the frequency of the sound heard by a pereh igc93/9/k rgytp.rson at rest r9r tkh/c.pi3 egg9y/with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moniiw4j rant 2(0ly(d*xqtor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highes* nardxy( t0(wqijl 42t frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening sth ouej(7 )6ofor the echo of her shout reflected by a cliff at the far end of the lake. She het7o 6e s)(jouhars the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his s c4pscypa1lm 4 ii5jz 5,:v hte7f0au8hip just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 4u i5:vfl8hy7,4cza j5s tpi0cmpa 1e1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2ri e+1kyaf fen6fs)0avfb0 7.0 $^{\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 tu u7cjc)a4t(rp na on a foggy day. Without warning, an engine backfire rtp4c ) (jua7coccurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.; 0duk4(k/six8z f ixv The splash it makes when striking the water below is heard 3.5 s later. How8k ;x fxiz0ks(/ 4vidu high is the cliff?    m

  A person, with his ear to the ground, sees a hugzh *lbb-zjw35stwj e,( zmb)qek5e4 8e stone strike the concrete pavem)-ewejzl8 ,4 kbbqm5*z(stjz35h bw eent. 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 impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanc9l)xv*:nuwc/c5/y/ gl8 bh 1bodjr3u6k gre je by the “5-second rule” for estimating the distance from a lightning strike if the temperan38 /5l *//9:rybrweo 6jccbd jlkgu hgv1u)x ture is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB7om h,dk(jrs6 ?    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 6 2oka7y;jy1 n/p4ueh .tgiss whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce agp1vagziipo n /4x;- n7a)m2s sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only on4 anv 2s/ gnapxzm1;o)iig- 7pe is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certab vyq0r1 . xzjax 4u+rnt/7h(ein distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? njtauv/7e0(4rr.yx 1z q bxh+[Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noi0mwzrdc4g:cd n :5d5mse ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the baw:c n dgmc0rz5d45m:d ckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou8d q :3uu6 e2u;s4 hpj.ivfcwbtput of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a2p6d;sh:jeqv3 4wibcu.uf8 u 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 st 1sid r0dd 7;j2wcnoz.rikes 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 ratevr 904 uo7l+jqxt1f gud at 250 W, while the more modest amplifier B is rated gvol 7t+rx01quj 4uf9at 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 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 placmymb --q(9x tved 2.8 m in front of a loudspeaqb(y9 vmmtx-- ker 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 of 2.0 dB. What dsno92l(0h3. gbu u;-ni yhoris theubn.il oh yusgd-20(;nh o93r ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledk2o,w942w hxnlk5nu6wpq 8i:-j wp sp, (a) by what factor will the intensity increase? Increase by a fano-:wxn5,spl wikp2846wkj9 h2 qup wctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but c*f0q(j mx:kah4 imr9skn p07one has twice the frequencyf khqr4cx90npmsim j 7 *a:(k0 of the other. What is the ratio of their intensities?   

  What would be the sound level 6;i0+zh *kmaoj8l l izu3dye3(in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules o;0yd*kz6+oma e 3lijzli8h3u f 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leveq )awqa+g)2b0sbbm ap- na i++l to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See+aaqabp+- i2+)nq bg0m )s bwa Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deteqv-hz 7uc u+c/ct when the sound level is c -/7hucuqv+ z30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soundz *( z.oc/lyc,wg(mk a levels. What is the ratic /(m., og(ac kzwlzy*o 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 frequency ofu+7ajy;inuhyy4dm.xo5,p y9 440 Hz. The length of the vibrax9uy ymhi.,n uj4;p+ o ayyd57ting portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the f8cix7*lj uvai3g3 7dj rt 1-/ zesaj*xhfzg).undamental and first three audible overtones if the x8f cza3-xzd h 7*)3.*lu teaigsvrg/1jji 7jpipe 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 blowing ac,b99,ox (1xv* rgzojifrw h :fross the top of an empty soda bottle that is 18 gvhj:,r19xibfw*9, ( rxoo fzcm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pip o.4x1opr ch2nes spanning the range of human hearing ohop x.n4 c21r(20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What kh5ojz s184ak5ug+ bf will be its fundamental frequency iff s5kk+4uh8z5ajb1o g it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long 6m-1-sum .r fsoft.aq and is tuned to play E above middle C-q o.u fr 6tmsa-1.smf (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 an open organ b ntnxg;965*zyi e sc9t8mxvmaonp 06i3bu90pipe that emits middle C (262 Hz) when the temperaturen6pnv39gtzbxt5i098 0o9sm n 6beyu *x;im ac 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 2v-;m9wt )yggy 5awfe 6-gf lm.0 $^{\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 12–10 shoulgl14uyvyia+(9g,,d b f)eebad the hole be that musd4l,1+ig 9ub,gyb a ()aeye vft be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, (trhe4-v gp0hi jk9o+440 Hz, and 616 Hz, but not at any other frequencier9(0p +h-eg4kj vt iohs 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 iyd p,e:i.--bf*c mk.mby)i e8x -mza56tud uk s open at both ends. It resonates at two succeu f.6k5meexi)mi8 p m , * z:cby-d-bku-adt.yssive harmonics 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 2q 3)1odi iof9nxupe 58feys/$^{\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 a3d0 zqhw2w 30;uhv8 z gioazu,re present within the audible range for a 2.14-m-long organ pz0wadhvo0;8h z3 3i,g u2zquwipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lo;2a ls-kb r(m68tyxgs ng. 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 wav6sxy gks am(tr;2b -8les 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 s4*t;; 3u c-gucl axicto adjust two strings, one xucacts ; ugi*c4l-;3of which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (26ho5 g./btly z22 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 kH16s.l rnz kvoqs3x5 h*s1y u(iz, 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 the operaty(uroz kx5sl*h.s6is q11v n3ing frequency of brand X.    kHz

  A guitar string produces 4 beats/s when 9o2zn-vozfhcf,;d8 o-fr- jg u9 a6kzsounded with a 350-Hz tuning fork and 9 beats/s when 9fnf--hzg, 8 fuv ;ockd6ro9zjazo-2 sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in *a 9mhtf2m4i8)gyvvoa tg- 3aone string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: R2-g8a4 vfta9 gi at oymh3*vm)ecall Eq. 11–13.]    Hz

  How many beats will be heard if two idef/5to*-te cfentical flutes each try to play middle C (26 f 5o*tc/ee-tf2 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 f g/* f1eynfi;3ef+dgqrequency of 441 Hz; when A and B are soundeifg*1 fde q3y; +/ngfed 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 m from one speakw9e -rq18oiu ner and 39 q8r n-e1oiuw.50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunerxjip9 . :)flr pm3ytr, hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, .pil9rj: p3t,x )f myrwhat 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 -cd l)bz/- cptvt,w ,fof wavelengths 2.64 m and 2.76 m in air. How many beats per second will p)/fv-,dcbc twl -,tzbe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cer 2c :1q9erd( wrrbo,em cve,;gtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed vb:r cr,2;gee9 rdq owme(1c,of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng fj(6oj tf73osm(cpji-t ;9tkine whose siren emitstj96foc;(mij ft7 o- pk3(jts at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shif ts gaa7tmcu:0by+8 b(t in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward gbc:+mu8sa( 0tba 7tyit 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 fvkh p o25lk-.hw 96yovrequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beatv5h-2 ok6plwkh.vo9y 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 atbmqzk b9-41z (joj e/l 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivjqj / zb(k4m9-lz1be oed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5.x z)yg 4+hxfip2t7hx;os cz 3 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the ref7x)ps3x z h4g tyzhi2x+;f co.lected wave?    $ \times10^{4}$ Hz

  In one of the original D yn pidk2+0o/coppler experiments, 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 +/okycp nd2 0iin 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 sm 1tp:u 3 8gdccc40x -pecfd)to measure blood-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 i-s4cpcp8x0tgm:1u dd c)fe c3 s 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 fozqe tx+t5*b/wqk0ty ny7 n* 2requency $2.25 \times10^{ 6}$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 emyd+ aevqcv5:b4h )ke89afqf 4its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observeyv fdq4 bafe9h)a8kq+ : 5e4vcrs hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spu)jk) pxlch n.um fk i*j1;yrwe7+f4+ eed 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 spefpqa. 5 *mty/nn u5;fmed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motioqu f/mfm ypat.n5;* 5nn?    $^{\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 planetw)w c, iw:(ta3xli1g5woji. y where the speed of sound is onwi gwt j,i5a)yw :13cli.oxw( ly 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/sc,b9btl u (7ff strikes the ocean. Determine the shock wave angle9flf( b,bt 7cu 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 5 l vk79*v,vgrlwi wy*$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground flyip qt8;zbrs8p -yw5 ;vwng faster than the speed of sound. By the time you hear the sonic boom, the plane has tr qpt;wvw8- 5rp 8y;sbzaveled 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 sonargttm ju+.8 (xksa23ni device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum dxsin8tkua.+t mj3 (2gepth 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 human audiblhw+ ev.yh5j(+r( 25ukcij dmle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer3*ms m c9;rzvj pipe symphony. It consists of many plastic pipes of various lengths, which are open on both endsmr c v9*sz3;mj.
(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 soundl2z c, 7)fjymzii)beo l/2nl8 close to the threshold of human hearing (0 dB). What will be the sound el/7n)zm)cy , fz2i8 l2joibllevel of 1000 such mosquitoes?    dB

  What is the resultant soun cp shhpfq*w8-t:(. oud level when an 82-dB sound and an 87-dB sound are heard (f p.u:w8sq tohh-pc* simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac kc -iggt9zedru nrf:.:75 3kyed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in alzrtc-gf 59kgd7iu ky: :r3e. nl directions?    W

  A stereo amplifier is rated ate igpmrl6(25j6 5u(ycnu m+pa 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?p5 emynpim 6(u(ugj2r a5c+l6    dB

  Workers around jet aircraft typically wear protectiv, th j00 *n:9t3lrf, vcgbhjowqwt.- ie devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 d vnth3.wj it ,cjr9lbf-0q0o*hgw:t,B, 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 syste m3w+kt)g9txz 4gxcw.ms, 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 frequency pzjiw9miwb ui:g-unq//q+/o;mt w+ r)/ m y)u1$\frac{1}{2}$ 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 fundamenta*2286tgk1grttmgq pw no6p+fe0 zx-al frequency of 440 Hzn ktp82aqot fmx*we0rg2-1gp6 z 6gt+ 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 abotdztbrm s+h+ x3l/w b j4t/ j9jwl3t50hh+ rk6ve 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 imd0zx9h+b6k/h3+tt l rjbhwj 3+5s t4rw ljt/s heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is:02 c x6yhlfjinoss:8 open at one end and also 75 cm long. How much tension should 8 6ifys2o 0j:nsh:xclbe in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ful4vjaw77w+(aqkp ghg r yir1 -c)6,*fd9 xnzzv l 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 npev g,y 09:eth),/mnwvk -jws7 x*oyfrom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at,y )wp ewyno0n/ es,t9* vg7m -:xjhkv a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-H*k 4 iv(.gxipqz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Whqgi*x ki .p4v(at is the speed of the moving train?   m/s

  The frequency of a steamq-,jo2m81k an+lnqy.sig 4n v train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measur,1vn-q qalk +myoi n82. 4gjsned as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jfn20ro vlop :mfiq8)3 ust 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 m:flno 0o rqi83f)p2von the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produc.//9 rrna ic3afqyp1b e a beat frequency of 11 Hz. The shorter one is 2.40 9iarnyp r/a ./ b1cfq3m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a statit.xi+vx5 yzyzl:ka ( +onary 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, i++z vx5kyzx.yal :(it n 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 normaq eb1jgz;n ljpdd ;ya3mk h/d5/*/n2dlly 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 red be3mg ldd/hy;db51/2pnzk*j d/qna;jlood 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 towar5 -amo1hf4h mi9up;hud the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequencmhp 9a- iu5f 1h;uohm4y 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 as it approaches a +d+r -rywe6eu)kk3fg bh+wh 8 moth. Theg)68yhe -wbe+ r3 k wk+fhdur+ 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was o.+x2kzyks,4xu8jxov h (m)hhpf n5, mnce used to send signals from one Alpine village to another. Since lonmh),v 5y j( h+hxz4o,xxfp8s.u2mkkwer 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.) Model as an open tube.

  Room acoustics for stereo liste;d:uysdfc 7 1nning can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculatscd:f u;1nd7ye 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,” inbz4b))c rld6 4it .0xc6+fbax5yp av jvolves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to vbtzb)rad06 l.)xf6bj45y i x a+c4 cp“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 ateou noa w3m2c;p/g6k* a frequency of abe/ w; ogu*ock3nm6ap2out 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 a7 lr5bhnlrwl5-zb f 67t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane p7nr 5r-5lbb fl6 hwl7zasses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iswcmr2;i-( p ay.6flte 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