What is the evidence that sr2o.s x5 lh(sqound travels as a wave?

What is the evidence thatb/:f,ime dr .o sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to uga7)kl 8m(mi the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig.87 g miml)uka( 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 wavv rqsqeej s c42p pmo4pjg)+v-q/ .1v 6m1fs0gelength to f p2q1 ers0v/4 )sc. 4v6-mpjgseq1pj+gqomvchange?

What evidence can youg*lb.+ 2af msa7a lgy61i( wvz give that the speed of sound in air does not depend significantly on freq(laaz +2by*mi .ggfwav7l 16suency?

The voice of a person who has inhaled helium sounds very high-piu2mtx0:b*q vcxo: of92c,wez tched. Why?

How will the air temperature in a room affect the pitch of organ pi0hwg5 7bgm/f8ran4w a pes?

Explain how a tube mige 02(;szxe bkl+j, hd m4g7icght be used as a filter to reduce the amplitude of sounds in various frequencyegjzs+ ;mc0b(7kgh4,dxel2 i ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clo(+7tbenz,0u3hijr q gus y8u .2azkg1ser together as you move up the f7i q1z2un,+ hea.(sgzr3gut 0b8ujky ingerboard toward the bridge?

A noisy truck approacd js 0xji. *pev6t+igj0zp( m3i 8-qxwhes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the hijp*iii06.- (s0xd mg qjz+twe jxvp 38gh-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in a4cwuza)6 0eo space,” whereas beats can be s a4ze6oa )w0cuaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frw xhd(ek u2yzw/(2;mmb82, lzrlhwj (equency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) ej z w22; khb8rlh x(y,z (/muwd2m(lwmove farther apart or closer together?

Traditional methods of protecting the hearing of people who wod;yy,fdln--adz25k( z *u rf hrk 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 headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the e*dlkh zy, ;zyr-n -5(fufdda2ars?

Consider the two waves shown in Fig. 12–31. Epx,wz1 ons7xv2 u wbzuw08z8.ach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves2,zw18 uzb nxuv xws 8zow7.0p, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in 47 2g lw1yyoeothe same direction, with the same yy41ogl oe2w7velocity? Explain.

If a wind is blowing, will this alterp2 qc i4be3hxl8i m1t 2bps.;k the frequency of the sound heard by a person at rest with respect to the source? Is tq2hcpilib3.s8t42 m kbe 1p ;xhe wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on ag8cjm yi)u086ga;(u.db6ok ;zh anh ie+zhk( swing. A monitor is blowing 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? Exp (6 8uijzz)c (i +6g;yhmagkhobhad .k8ue0; nlain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoulah(sga z. q+3m/u6h nt reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the3h6/nqu(a hzs+l.a g m lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears tl.+qms5jfws9- 942 m f jhk tug,io0yjhe echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Am 9j.y,0g sqh+mkwjfijol u924 -ts5fssume 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 air at vl;(0g foyce120 $^{\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 drx o8lwsxqrhsgzi: 03is /*+ i5ifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfi rhssgx:oiiiqz 3+x5 l0/sw*8re is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splfix 9o q69m*tv4.dd epash it makes when striking the water below is heard 3.5 s later. How high is the*md. q9fxvi4t do9pe6 cliff?    m

  A person, with his ear to the ground, sees a huge sts r lx(3muyaaag26t a8 9pm4k zih:7r7one strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other gha aym7r s9ka6l( zt28riup74a: m3xin 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 o-cgfn3d-rgr +5/zk vz f distance by the “5-second rule”r+ k rvf5nzz3-g/d- gc for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lepw,fid+trw: fo5a) 1x vel 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 soun2kuv v0rel v/x0x;:kz d whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouso( *5zrwarj v1.5fc gd ,0vqdwly at a certain place, what will be the sound level if only one is exploded? dgfwo1.r c(a550q w *zv ,rjdv[Hint: Add intensities, not dB’s.]    dB

  A person standing a certain di+w 8ib72zxv9oatr1 c ustance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this personu7 xiv9cr1 +8 at2obzw 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, wd84fr.p2mo (g 3y fo;wj9hl/ y4 zmgb8xu il)ihereas for a CD player8ymryh2d g/uplz;8 9oi 3fmj)f owxg i44(b.l it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speo4h f, cebj7+daking in normal conversation. Use Table 12–2. Assume t74he+o dj, bcfhe 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 whose area is v/y4q6rprh w0 $5 \times10^{ -5} m^2$ (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 amplifier xhxiel: 1o 0ty2m d)i:ax(s1aB is rated at 40 W. (a) Estimate the sound level in decibels you would expeaold( xy1::xtsea12imh 0 ix )ct 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/31* 3fadj pnkhu. o m+ l/(:ksnm5zyd hau8yh 130 dB when placed 2.8 m in front of a loudspeaker on the 3*1u .md kyfno5au+p(3/njs:dhz8 /hh ymka lstage.
(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 diffeys9u*5fx k fn1 *tjfz+rence in sound level of 2.0 dB. What is the ratio of the amplitudes of ft kx1f5 *n+j *fuy9zstwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of al,yf)*xoh 2nt)/8ni t 3 z m7s8yzmmco sound wave is tripled, (a) by what factor will the intensity increase? Increase by )) nlcsn7t 8zzo3m8yhy f,x2itm*m/o a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqb yi:1sgbj-te wrie)4r7smd:4t; if y8 2fjf2uency of the other. What is the ratio of tfe sm4b tg2ef b1:rwj2isi4:7yij-d);y tf 8rheir intensities?   

  What would be the sound level (in dB) of a sound wave in air kg2d0u fl+3u g87+2irlkvc(7cmggsk that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hs7 8gg3u cm k(0+ +i7v2lgdlfck2k gurz?    dB

  A 6000-Hz tone must hav8t)y75b fsie t/vmrv(ud5gb7 e what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–uvbb /y7r55e87i vt)(tg md sf6.)    dB

What are the lowest and higcr3n c/ljqw 80hest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. qnr03j8c/cw l12–6.)

  Your auditory system can accommodate a huge range of sound lejbxo *k rv zzvcq*,xx)3:*v 6dvels. What is the ratio of highest to lowest intensityq *6)3bxj zv xzc:*dov*vkx,r 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 fundamentatv:t3r-xc. by88p auil m*1ctz nuf:8l frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must thzv8u3 lcymrti-1t8 f:utnpx 8*a b.:c e string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firs(*+d4e qee vfot three audible overtone(deqevf oe4* +s if 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 frequelko, 4e(g(df k+7p xyuncy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed,gl7oe+k u(px f 4y(kd 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 pipes spantw/9 -1qububi ning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of/uiqb tu1 w9-b 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 will7g 0ikj2 ibu4o be its fundamental frequency if it is fingergib2 ikj7uo40ed at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middlv*5 s 9/o(en(d9pqnnkous (y8p yj vi2e C (330 Hz). v(v8yk9ds* py (eq /ujnn n2osi5(9po
(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 pipe that e ze *j*fqxod8 ll(r98 cy*c0ygzrc 2y+mits middle C (262 Hz) when the temperatuyel+0yqd*cyo(rl8c j*9g2*rz z xf 8cre 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 atebh9q4d g;qx3 20 $^{\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 shoulgr8+xshsc (*ld the hole be that mush sxr8+ *(cglst 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, 440 Hz, 1d2u68 b hvx.7mihxo rand 616 Hz, but not at any other frequencies in ivo8 h2r.1h 7x 6bxudmbetween. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resona* yok8lj)eps7 e sy65ptes at two successive harmonics of frequencies 275 Hz and 3307se sj56lk* )pp yeoy8 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 0n*hugtf 2rb z: p gp1m6)stw3$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long oe.c ;00gl1v)j7rmwwa k6m ts ergan p1v6c ew w)kglmr.as jmet70;0ipe 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 ope)5jxo8hw vdh+j* .mcvn to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answ ) wxjhvd.*cmjv+o 8h5er 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 strings, om2 j b(x9tqtb+ne of whichb 9b+t tmxj2q( is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anbcuneva;1xhmzbuau s(,/7i q h*x2)n4 ,ssf4d $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (br2rssto1 dbqe-jcp pfmo k 973,0zy19jand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shr0-jspfbe1 os9p, r19q2jtkz y dcmo7 3ill 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 soundlj*/ox0 h48 y9swwa mjed with a 350-Hz tuning fork and 9 beats/s when sounded with *w0xj4lhaws joym98/a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu(ddjhrz1qa * ;:e hc7qned 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 p:he a( qr;1dd7h*jcqz layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C ( yb8dangko3 a9itg 29;262 Hz), but one is at9goa;b 2 a3d9i8kytg n 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 of 441 mn ci+ 8enfzgt,(y2y( r)p,9 m+fzgwu Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the,r,f ( 8)9ufy( pnt gngy+cz2+ziemmw 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 standsh:5rpt73ecjw ,v, pjl 3.00 m from one speaker and 3.50 m frovwcle3p rt:j5j, p ,7hm 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 6t ngpnx, 4 4b:hq/vc/virsrq hk5r7 .tuner hears three beats 4t hscbvhng6q/ 5 pkqnx7r:4v, /ir.revery 2.0 s when they are played together. (a) 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 in air. How0-xxj ljm ,s/ :ebjk7v many beats per second will0vejxjb /x:7l k m,-sj be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren iwy517,agb kcbs 1550 Hz when at rest. What frequency7ba 5,ycw1gkb 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. What frequency do u*pbx /9eqsnrt *))mb you detect if a fire engine whose siren emits at 1550 Hz movesp bm*nte s 9br/*u)qx) at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if axtw6da knkpq5j4: r.gd0 /yb- 2000-Hz source is moving toward you at 1a0j:-/kkxdp5t qdrng w4 y.6b 5 m/s versus you moving toward 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 rm3ii8nb26nd,fp sc3b b -3- phey3wdequipped with the same single frequency horn. When one is at rest and 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 yrd 8c- fbs3wihpne63n- pd2i,b3bm3 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receivmmh,98zumj n hwx2 4x9 bahq1:es them returned from an object moving directly away from it at 25 m/s What is the received sound frequej94mnh9x2h:,h8zb1wu qxa mm ncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ultrsk itzj8qg2:49j g: v,blriu1 asonic sound wave with frequency 30.0 kHz. What frequency does,rvg2 qu1 sjl:8 t 9iibg:kzj4 the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dpe/j 5f2 vcyr0tru6jnf1af 5(oppler 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 in the railway station. What beat frequency was heard if the train c1fjru65 (vcjf/ rapn eyt0f52 ar approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Svr96a5xaf g/q uppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood ixa9a/gq65v r fs flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of fao2 fcb*0.; 8abbpt t 5ntuomk/h.2 rcrequency $2.25 \times10^{ 6}$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 emov9) hvi*tu e7its sound of frequency 570 Hz. When the wind velocity is 12 m/s from the northut)*vhv7eio9 , what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if +tfji,-:upsb9 jimz4 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 whe;f*y /mlfohs5re the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplanem5sf*;oh/ ylf’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,ny s: qvi*k9ex;;n e o;cwcs9 the thin atmosphere of a planet where the speed of sound is only about 35:n, cov q;xescny;*k9wse 9 ;i 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. Determine th rf/ jtme.za+.zvl-gga*,h8 be shock wave angle it produc/-lh.bz*afr, ga et+gmzv 8. jes
(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 j v .*3rbynt ,1bfdxz qrjw;h)v0wp58 $/theta$ 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 abovee4(l+t k*f24sqksijzhyg s(twf3o 5 . the ground flying faster than the speed of sound. By the time you 3*s 42+s(o jt4igyf(fkksqt .elwhz 5hear 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-Hzu2j/c6ylje1 ajx v53l sound pulses downward from thev3 aj/ 65j yx2ucljle1 bottom 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 human audib/*.z jewz w6ec; qex-qle range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a 1+ b * wdgto63xlkzn t-ylw-g9u7izj9display called a sewer pipe symphony. It consists of many plastitzxl6wj+b liuy7d gkn3z-o19 9w-*tg c pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to 4;lkvpx t:*-7g zoktl the threshold of human hearing (0 dB). What will be the sound level of 1tk*oz7tg;x -p: l4kvl000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound /f.0w1hq+p evm j rkj4and an 87-dB sound are heard simultaneously wjmkjh+v f1e4pq./r0?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.)-q9h8jzjgg o3:uh wf What is the acous q-j9wgzguojf3 8 ):hhtic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 100t+7vqy 5v dsv5j79wdd0 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 w dvy5v9v 7jdq+t 5ds7kHz?    dB

  Workers around jet aircraft typically wear protective devices over thei-ya8tf( k ,y0c2dxst fr 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 hay0 ka2(8tdctsyxf -,fs 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 systekx g j+(os*n br486mexms, 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 cwpthvcl: b: 4suc)-g r.. -jea 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 9ls86ma ynekt/- vin) cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length o9y6n/s nemtkiv8a -)lf $6.1 \times10^{-4 }$ 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 inj41t:u cs5(it;njd-rmf ak u4to vibration above 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 distacuj tadsfnr4-4(5j1u :tik ;m nce 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 open 2**4nx6lfrk gw0 bq (zf7pj kpat one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundwq6 g *pn 4*lkk2 fr7b(xzjfp0amental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to ret1sxqu: q1 h(bd7b789ojixi hsonate 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 sourcesv d66i6jnkhmxf,d2j9. The sound is loudest at points j9nv,6mx idj2kdhf6 6equidistant 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 other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One*c-(wx n6 m1ofque1yv train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when t (wm1n cv6ex- 1o*fquyhe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it apprc;8;lalmzhdf t rutm(+ r ww :89)4jdsoaches you is 538 Hz. After it passes you, its frequen: l+m8r ldmrhst4dawfu(t9z;wj8; ) ccy is measured 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 ju2dh99:3 (m mzmzbyp1*7ni ipzpj * qvest by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppo pmny zi*2j z:7(p39vbzim peq*h9m 1dse the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of3;-vr ftn euk4 11 Hz. The - uenvf3tr k4;shorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a +rs8s 2gc4cks railroad 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 frequenckcsr+ 2 c8ssg4y 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 w/1l-5yc5ybb w wzea0xhat beat frequency would you expect if 5.50-MHz ultrasound waves we5/wy- xz5ylb 1aewb0 cre 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*w07wuo-y n nl ,;rjzn speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat ey- w7zj,n ;un*on0lrw mits 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 soundc ljrd3ony,x ny 9 4f-189bsud pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo 9cyrdb39lyoxj s,d -8nf4u 1nfrom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Aw jnlcd50fm+2( beh)x lpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 w+djc5 b)mxl(0h fen2m 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 th l6; y3z(n7jlj)kf ljee presence of standing waves, which can cause acoustic “dead spots” (lnlz e 6l )j73yk;jjfat the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long5mn+p1 9lqi l7oa+myzeo) ;sjxo2ib) , slender aluminum rod held in the hand near the rod’s midpoint. The r9mj7enoxq+lop)1ay) io5 ;im2 lz +sb od 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 humanp z rcc;4+ x:yeiuck24 ear at a frequency of about 1000 Hz 4p u;c r:k2+zy4e icxcis $I_0$ = $1 \times10^{12 } W / m^2$ 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 gr(a7fejce1r)0a n/s gkjg) h)tound hears the sonic boom 1.5 min after the plane passes direa/gsgrt ea)e (nj1hc)j)k7 f0ctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboab0hhc xlbc -kdb(eh,c. .bt85 t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h