What is the evidence that sound travels as a wave?m5fqj3j: b3ryd*fje 7

What is the evidence that sound is a form of energy?m+cfimq)l4l jj 2(j782r6q egq1 b jus

Children sometimes play with a homemade “telephone” by attaching a onk- ;tc- dptabmo.9)string to 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. 12–29). Explain clearly hok--tt 9 op.dma;cb on)w the sound wave travels from one cup to the other.

When a sound wave passes from air into water, d7 4 t2szb+h+nub5taqdo you expect the frequency or wavelength to 7za42bd5+nshuqt b+ tchange?

What evidence can you give that the speed of sound in air does not depe6oa5h(8atl xr5ziaxz716v nknd significantly on freqv t8lnxaax7z6h ko6( ir515a zuency?

The voice of a person who has 0 klc2ik i p.*zi8i i20dp9uck2udmj*inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect theuw:g0qqj )e 81hyo:d t pitch of organ pipes?

Explain how a tube mi 3-v3rzw4t p,dttck/eght be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car m3t/ ,- ptcwz 3edv4krtuffler.)

Why are the frets on a guitar (Fig. 12–30) spasesbos1o2 j;/baf/0v 6 qps9j)gf kh+ced closer together as you move up the fingerboard toward the bridge;svfjfhk12s pq0/9oabs+ b )sgo6e/j?

A noisy truck approaches you from behind a building. Init(3ukasfu si/ r 0it 8eo+tj*e6ially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you aj( u *sr oue0/tieif38t+k6shear 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,” wif ab7f* udn kwg6,g/(4gs 3hmhereas beats can be said to be due to “inteh 7( fs *g6d,nwmai/g gu4fkb3rference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were8w9tlj9tvz3d l.f o+ c lowered, would the points D and C (where destructive and c3c fd+ v98 ojl.l9wttzonstructive interference occur) move farther apart or closer together?

Traditional methods of pro k1s01fu7ykpk tecting 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 headphoy0ksk1kf1up 7 nes in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought* ;mp6 ju vtbx./1bkly of as a superposition of two sound waves with slightly different frequencies, as *tvbl;yx. m 1kb6u/pjin 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 sktok pt; 5 6rs9(yjue;ource and observer move in the same direction, with the st;5 (y9p;juk kero 6tsame velocity? Explain.

If a wind is blowing, will this alter the2jxlm ,o r(lyq-jc04g frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity ry o0 jg( qlml-xc,24jchanged?

Figure 12–32 shows various positin0ia bsy n-3u)ons of a child in motion on a swing. A monitor is blowing a whistle in front of the chil03niu b ay)-nsd 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 r bvmd) 36*,he2(yvlq/ ;ejr no c8uuylength of a lake by listening for the echo of her shout reflected by a cliff at the fbdj)y r8 qve* nhuu6r2/;vec (,3lmyoar end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the weul s2-ny3xw- aterline. He hears the echo of the sound refl23enwu y-xs-l ected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelqjp035cik- s8jn1 n3 cnkyi-h engths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is driftifa8 fxfn47:3 obfw n7dng just above a school of tuna on a foggy day. Without warning, an engbfod73fw 8a 4nn:ff x7ine backfire occurs 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. The spqpr gl7k /jef0, k,cfa+h no75lash it makes when striking the water below is heard 3.5 s later. How high is the cliff? 7j/g0, ,aqrn7pfokek5h lc+ f    m

  A person, with his ear *ev au.f1t. * pux5mndto the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travtp m1u5 vfa.u e.nd*x*els 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 distancx .jsz+ox.rg;e by the “5-second rule” for estimating the diz.gx + rjoxs.;stance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a so6/v+wociw +a c2.fuar und at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound0zmb4 /fngy. w whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir1t31-lo shc/da tun/ked simultaneously at a certain place, what will be the sound level if only one is ex/nh1u3-t lc skta1od/ ploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nois8m78z15fwwqrg:kkt b w o,(luy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would thi8wgb7q tk, 5u fwrw8 :zm(1okls person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, where sn7)rr4qz du;as for a CD player it is 95 dB.rsn4;qdru) z7 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 spea.(u kcm4yb; ceking in normal conversation. Use Table 12–2. Assec.kmu;( cy4bume 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 whose area iseg8,fl, o4y ls+d5vzlul1; u c $5 \times10^{ -5} m^2$ (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 morxw e* elqblb -niz+7(-e modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m fromlez+ nw*q-x-i(b 7lbe a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of ( ioxza;zk/sw/i*gl q0hk-9i a loudsiiigh9w -sl az*0qok /(x/z;k peaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a u-u4ibdz/a r84ag0 qrdifference in sound level of 2.0 dB. What is the ratio of the amplitudes of t8z ubi4/r4u-daqg ar0wo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave i9*ankcf ( jj,ls tripled, (a) by what factor will the intensity increase?lja9 k*njc( ,f Increase by 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 fresf96ekdge8 ym w+y) ox tq34pf bpf)1;quency of the other. What is the ratio of theirp8 x96m )+feds43p q y1gfotk )b;feyw intensities?   

  What would be the sound level (inyy/w mk3svd// dB) of a sound wave in air that corresponds to a divdmk/ys 3wy/ /splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to rdubo ;tlmc s(3f5vn53:bd* wseem as loud as a 100-Hz tone that has a 50-dB sound level? bwot nd;3*clr3d v u(m b5s5f:(See Fig. 12–6.)    dB

What are the lowest and hi:xkgh+ca73e 1acrz qb+ )p) etghest frequencies that an ear can detect when the sountec7x+ark1 q h g:3cepbz ))+ad level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. c10 3ngfa9e j4yjk + dtdu(;isWhat is the ratio of highest to lowest inte04e 9ijjant;gd(s+1u y3fd kc nsity 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 le) fjg wr/wa5q;ngth of the vibw fwrj;ga q5/)rating 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. Wh1 umnkgyl0*hvn,0l-wxn(wg :at are the fundamental and first three audible overtones if the pipe is x n1- w*l gmnvl,hkg y0wun0(:
(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 across the ;b; 0 k*lyscusf7p.bbtop of an empty soda bottle that is 18 cm deep, ifpulb bcf;*y; ssk. 7b0 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 orgahg k ;fq(s2lef9fg7-x n with open-tube pipes spanning the range of human heariqhx fk2-7;fse9( gglfng (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 tebu wi+zj csfac+3h,z53 8;jz hird harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leuf zcs;zb+ajic+3e3 5z 8 ,whjngth?   Hz

  An unfingered guitar jbnfar 0bdupfgfj//09 h/ tn0 v6m xfaz5937cstring is 0.73 m long and is tuned to play E above middle C (330 Hz). adfnrh 7/0x/jz 05/fgbjbu9pft6nf 3 v09 acm
(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 lengthirf37dsvwy88jv )k:u of an open organ pipe that emits middle C (262 Hz) when the tempd siv3r8y7uk)vfj w 8: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 at 20 2 ojoli- h mt,cif4(xc9lz6b4$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the f lp:f,vks7/ffv + gzo6hq4 :bnlute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 29lf p/:f+ v4bo:gv7 k6n, qzhsf4 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, and 616 Hz,)tbds+*k 55yeu2wfekuyzs7hzo 1 7u2 but not at any other freq7kd1ftuy7eb*z 5huo2s2 eys+wuk)5z uencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates atk7bkd lwq*o,zyhh 96 : two successive harmonics of frequencies 2hw z7h,d: k6l9bkqo* y75 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 ,d:04/;85ayfhns jrtnzt3qxo;;tw/ rt smsa$^{\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 fu8b,qa 1vfb9kxg 7v+j/ch/ fx bn:kvpq/; o1oor a 2.14-m-long organ pkbvq,;pfg bxbqo1/fo8 jv xvu1k 9ch:n/a7/+ipe 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 it(-p 3qf 00wk h,p4ls-tav mxws open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible r t4lawp,3kmht-0vp -( qxf w0sange) 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 strings, oneor9 9qxudk8jg s- 6q9w of which is sounding 440 Hz. How far off in frosrd8qq99 g -x96wjuk equency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and m fhpaksj92h-g*m :x1$C^＃$ (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, 0lcvb2haae w+au1; n)while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when p+2vwaca;nbahe1 )l 0ulayed separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whyen09o 5aos.ijg*0 sx7nil 7k z1rlw5en sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yw9*5i50l0sjgo niay1nl7 x7krs oz .e our reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension inf2czke ym 8*0n one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played tog0k*2ym8zn cfe ether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C ( pt1,2yes i6epx1 /i3,p pc uuptz2tw9262 Hz), but u/twt3e,p,ixep2tip6p9u 1c1 p y2zsone 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 of 441smp hz.37s /oie 1tpf1 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C aremtspspe3f o iz7. 1h/1 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 g/2fp,7a dt 6*lww umxd*gh5ug .o )rkfrom one speaker and 3.50 m from the otherhla*dwg7,uwk56o) ug2xg tfdr *. m/p.
(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 voifs jv)4.- ehibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratinjs)-io h4.fve g 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. How many beatgq y/bfai x12i-m .q2ts per second will be heard? (Assuaxtmb21-i2ig.qf y /qme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a c*n 4;e.y y1kst7ci jl(tg8j lbertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect gec*sk ( . ij1 y8lttnj4b7l;yif 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 qf1z*3(ya m kdyou detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s 1 (qazy dm3kf*
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in *huruomt, 8-z frequency if a 2000-Hz source is moving toward you at 15 m/s versus you movintzh -r8m ,uuo*g 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 equipped with the same single fzp+sm/( um 6zgrequency horn. When one is at m z sgp/(zum+6rest 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 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at3 )b oyo-nim2v 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is -bv)n io3ym2o the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speerh 73d /qh0bv7s3chabd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 3s/7 rbhh ah7bc0 dv3q30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentsk cn6-/ ngc fu9bm5tf6, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speect 5fn/k ngfbu66-cm9d of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow xq t 2w75lt7s.sq7ucfspeeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beatqsx27sftctu q77w5 .l frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulkol. 3mwn2r2n trasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is m g lta/m2eze c++8*dt12 m/s from the north, what frequency will observers hedg2+az lm8*+ cet/m etar 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 speed s:ivfi9x rq8. 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*cxpm.(k8p( s , ied 9omi0stp.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s momst im.x,90 kd e( sp(8i*cppotion?    $^{\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 planetccc (i-c/rm ww5n/k.n-j0 zx y where the speed of sound is onk5 cmjcic0rz(ww/ y./ -- xcnnly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave afntio+ ;a4 b:yd0: aykngle it produc ayiaoy4 dft:0 :nkb;+es
(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 mcut1dcsl8 bxp5 /6f1h0gd g;$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plan (l*j:d(g ghxae exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1(j g:dgx *hal(2–34. 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 arzfs)k ry9m0hp8x,7 n sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it ispxmyzr8nf hrk 9), 0s7 designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible ranh*arugr3 . 41ujdgy.sge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dir y: (bgfho1o1l)+ vrrsplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open oo)1blfh: y (rrr+v1g 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 makeyvb+r6p k0j 9t;eb8q ys a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosq8 kbepvyq9t +;60b ryjuitoes?    dB

  What is the resultant sound level when an 82-dB sound and a uz:yi+3z6misn 87-dB sound are heard simultaneou6zy3su+ ii zm:sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.7y:ll*mwm uad c xo 4y:m9k40y What is the acoustic power output (W) of the slkxmu*lmyy4a7:w m4d9:y c0opeaker, assuming it radiates equally in all directions?    W

  A stereo amplifier i2mu)yvoy (xpi 1mj6ppl:rgsw6 5/u*q s rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the powelgqmup2o()1yw p v x5irp6/m6 * su:yjr output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over th;uur( grnlx v (v-v2:m;-fomaeir ears. Assume that thelum:vvx r mg u(oa(f2;r-;v-n 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 airplane engine?    W

  In audio and communicatio*z7oeedw7n1ve./ 9hcj r:ak qns 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*q j qy.ue .jd6vyi8sla *n(m: is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betwe dx g2de)wzr+ sxh/ nz/0af07jen fixed points with a fundamental frequency of 440 Hz and adnx /rzeg) 0 +2f sdz/xh0wj7a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tub) b4zo2j+ 1hupri ay0te 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)rz b1+y0hj4p otua i2 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 c w9vo6lyrdm , )wa/9ris near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in tra9 voy )lw 6r,dwm/9che tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop (.l+ uj((qj f6ee5az1ku bcir4 $\frac{1}{2}\lambda$) 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 twomt7 wp)g wo bof;0: (bry)o-wj 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 a poin:yow))wj 7;btog wpo rfb(m0- t 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor m9ws0v8z - jkh(9wqzjon the stationary train hears a 3.0-Hz beat sz8j9 9mw-v qkh(0wj zfrequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 53c v - wldr*ay;o;t(5lw emov+68 Hz. After it passes you, its freq wvw+*rmyoel65o( dta;c; -vluency 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 just by listening to the dif7f xp/)w0j sapf+. n+dcip. lwe(y+h mference in pitch of the engine noise between approaching and receding cars. Suppose the sound of xew+p+fl c) f+p ./d wimn(sah py7j.0a 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, o(c.n p;jqo c)sounding together, produce a beat frequency of 11 Hz. The shorter o (. jcoo);cqnpne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as eda qm58l c6of83q:ybit 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 frequency heard by the observer when (a) he listens from the position A, in front of the car,:q 68of mdc3 5eyla8bq (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 t(pfh5h6 mhx6q gmsj. 44ws1:j dwb/k ehe aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wh(gks.ep mmjh5 w4 hd /4wx6fq bj:6s1aves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a mot,+ewv l ae j*slq7-sk)p--beig v8 sw;h at speed 6.5 m/s while the moth is flying toward 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 refl+vb7q *e8w-wg)a--, s ks;v sjelel ipects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approgz0neu-a4p6.fywqk bb2 y) w5aches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can )ea4qzw- wb6ygny0u25 .pbkfthe moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig.q.c9 ia-bfe md5+q6tw 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G f- wadqe mt5 q9+.bi6fclat) 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 byvv z0x9zb: s .h.scqq- the presence of standing waves, which can cause acoustic “dead spots” at qv-.h.sbs cv9 z:qxz0the 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 rjpqwr+6s6jk1 ocv 5( eod 60/ yul*jy (rfx)svods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other ha)kyrxojwrv5ps6uv6 1s(fo *j ( q/c0l+d6 jeynd. 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 hum/r4 x )rvkzpm7i. 3slfan ear at a frequency of abors)pr.m k7x3f i4/vzl ut 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 at3f4k+jq)suwa 6r yv4d Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the pla3k)yd ur +aq64fvsj w4ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 158fxi g6 tsk vw5v(9wh. $^{\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