What is the evidence that sounia f,f au2w()ld travels as a wave?

What is the evidence that sout1lr- s5.lq eznd is a form of energy?

Children sometimes play with a h +dg:pf+yqsdo1m1 wk 9woui: 3omemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to tw+ ug:1+p3:w o k di1q9dsyfmohe other.

When a sound wave passes from air into water, do you expect the fre klnq-jnxon(y9w +a3)quency or wavelength tqx)(9anw jl+ynok - 3no change?

What evidence can you give that the speed of sound in air s c /;3bg.d 8xdyh*ixwdoes not depend significa;ibx.cyhw xg8 s dd/3*ntly on frequency?

The voice of a person who has inhaled helium sounds very high-pwyu nu333x+yvitched. Why?

How will the air temperature in a rojwbve so1 3j021cd1dpom affect the pitch of organ pipes?

Explain how a tube might be used as a filter c)rn d,og wwdtge 6 zh-j42y8 m86gc9ato reduce the amplitude of sounds in various frequency rangee,r9c48-6yw68gg 2)dcjathzgmw o dn s. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mor 98 pv*(w ube+dxyjc)(ty1vdve up the fingerboard toward the d8dwyub( tv9j) v*x1(+cypr e bridge?

A noisy truck approaches you from behind a building. Initially you s v)00vr yoi hi/z9rq)z-r7i ehear it but cannot see it. When it emerges and you do see it, its sound is suddenly “b r)09si)oz0-zqir7e/y v vhir righter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in sda1 c+ev 7-nkfpace,” whereas beats can be said to be due to “int-cn 7v1eak+ dferference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would ugqjh.zpq(p( 5 d/ -vithe points D andjg-v/qu.( iqhppdz5( C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i( 5+sucux 6kdvn 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 red(s6 v+k5c uduxuce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought jhd f(*(qqv8tb *3pmeof as a superposition of two sound waves with slightly di8 *bdjpm(*qtv3 hfq( efferent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer mov0qw-*rjrwd ele a 1+n/e in the same direction, with the same velocity? Expn+1w erjle d-*aq/0 wrlain.

If a wind is blowing, will this alter the frequency of the soujibv*4bc uhe)2-k )- sixu7ednd heard by a person at rest with respect to the source? Is the wavelength or velocity changedv) sekc)2ibh *e7d-u iuj-bx 4?

Figure 12–32 shows various positions of a c,5ahgv2 /nvcdwj)k 9 nhild in motion on a 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? Explain you, wnnca g9/h2j )kvd5vr reasoning.

  A hiker determines the length o1e jspznk +0(df a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouep(k+zn0s d j1ting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the eci u3fv02/sr kjho 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 sou2usrf v0j /3kind in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in(2ya bzgs1zq * 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 drifting just above a school of tuna on a vk oo,sld hq4tf;l,/-foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How,t,d4vhs;o /o -qflkl 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.l)1ii/46d)de hl ijub The splash it makes when striking the water below is heard 3.5 s later. How high is the clif eddi/l 14blhu)) i6ijf?    m

  A person, with his ear to the ground, sees a huge stone strrykm:dt43( t i.2 bxgnike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and yng( ditt:x2brk 43m .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 distance by the “5-seconyasqqvg:a(yqwe ob- e+235 t t* f+er9d rule” for estimating the distance from a lightning qfs w boya*5eyreeva3 9qgtq2+ +(-: tstrike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a snyinwsq ed4d 3l7/f6 co7 8uk(ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intenu05cu 9w me7lksity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simuls- wb.:(qx apjtaneously at a ceq-s( j:p.ab xwrtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eb /;0 lld3r;zk vkf;sequally noisy je/0 lfk;s zdev; bl;rk3t 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? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB +3wuuo+2*x(adig hbu , whereas for a CD player it is 95 dB. What is the ratio of intensities of txuh a*o32ui(g+udb w+ he 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 speaking in nortg9sug2 g9 u(lmal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on tgg(9tug9sl u 2he 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 mhcl(li xvgrb7+, ec:r)9 )tbwhose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while thql7xt -3pp0j6uxq8 iy9l pk dk09f0e /p9lykne more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m frllq plk89 9p 0-67k0fxu9/x p30yntqdjyikep om 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 oo+ fgp0yv jtdxz8*/,tf a loudspeaker on the staget0+y xz, od* g/fv8jpt.
(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 i7jz98jh n.vbgd:gz88n9 rwv ,-qezea s the ratio of thrbgd8neg,vwz8q az.vz -j8j9 eh:79 ne amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound aul+mu unvh7 k/g/5/*+*eaq diqd2lpwave is tripled, (a) by what factor will the intensi +/adld h/uu 5va/*q2m ge*uipn+7k qlty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but21ja4ehsfl/w)s,;; volxz x6h-yqlb one has twice the frequency of the other. What is the ratio of theifl16qa)oe2 ;/ h svz-hsl;,xxbywlj4r intensities?   

  What would be the sound level (in dB) ou1g)n .zwdxnmuizzd 9 d 895,xf a sound wave in air that corresponds to a displacem5wxd 1 )ngzdi8m zz x,udn9u.9ent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thatj xf2 64w,m xubmz)ol7 has a 50-dB sound bwzfx 46xm, lm)ju27 olevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an e, ewimitg t/,95u4smich 0x)ear can detect when the sound level is 30 dB? (See Fig/ tgm eit)4 9whsic0ime ux,5,. 12–6.)

  Your auditory system can accommodate a huge range of sou9kf: xueei3b*nd levels. What is the ra ue:kf*i9e3x btio 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 of 440 Hz. The length8 nmt g86mikr6 of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be86rmngit6 km8 placed?    N

  An organ pipe is 112 cm long. What are t.t v.1-clb) jestc1mrhe fundamental and first three audible overtones if the pipt)1el csc1.r- . vtjmbe 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 ex(xy vf6tn2tnw03fnt2pect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubwvtnty0n3 x2 6( n2tffe?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ withw82u9 .7aiq v xjdr w3p4whed; open-tube pipes spanning the range of human hearing (20 Hz to j3wpe v4.w2 w qiudd8hx7ar 9;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 5w8(aoe2;.c fshn ( mfp40 Hz as its third harmonic. What will be its fundamental frequency if i(f;o2mn f pc(hea8s w.t is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned*jkyuq g0jc 1, to play E above middle C (330 Hzj1g j0k,*qc uy).
(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 emits middle C (2yl*y :/ t :6qmod5didz62 Hz) when t :qldd dtomz6i/y*y5 :he temperature 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 nl8auh 0o/fb7 h)lek3u1) axw20 $^{\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 should the hole bnb 3r/biy2aok rs.,3s e that must be uncovered to plrs/nosk 2ba3yr 3. ib,ay 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 yc9(/ 5 x+eqgfnr )ei/ ytqc;cHz, and 616 Hz, but not at any other frequencies in between. (a) Sh nqg5eq9 +) ;e(fyi tx/cycrc/ow 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);;al(.qsd + elg ps1arh sw nv;zrv;-tes at two successive harmonics of frequencies 275a;ld vlw;nrpzaqs+;-;rg. (e 1)s shv 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 w u1r njblr3/8 jn-an5$^{\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 with kpfdeh 3mcq l(yfp8;b0/40bzin the audible range for a 2.14-m-long organ p3;0chpzdpq/(k 4 fy 08e bmlbfipe 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 bbm1apav;wa4 z*5c: u open to the outside and iswa5 bp1ma:azcvb4* u ; 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 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, one kwc sq3fw9l oa2-m*sux2rh4 p252pa eof whi2a2ma 9 2q-u h 2 owrlwssfp3x45pe*kcch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequen 5+oscv /xh:j8 j*jmxvcy if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHbw4z/ 3ogi:lf9ix6*xnv;lcr z, while another (brand X) operates at an unknown frequency. If neithc lx :b foi;gxr*4 6inzvw/9l3er 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 operating frequency of brand X.    kHz

  A guitar string produces 4 beatu *(), (ov4ywuc colsss/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibratil*su), vc4(uoy o(swc onal frequency of the string? Explain your reasoning.    Hz

  Two violin strings a-*e.uafb 3e55k 8vzto tpvbp 5re tuned to the same frequency, 294 Hz. The tension in one strine5ft 53v*o8apbt 5peu.-b kzvg is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutesf caz r7xoh (a3bs::i3 each try to play middle C (262 Hz), but one is fz7b 3osxharc(3: : aiat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Forh);hd,6 fw(e sjd 2psrk B has a frequency of 441 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 ar2)rsh(f 6;h djp wd,ese 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 j yj a8k;k/w0g3.00 m from one speaker and 3.50 m frjya0 8j kgwk;/om 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 vibsot(yy/ikft 4sr ;(n8+kdgh .rating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one ish+/ns8kik;tydr 4ft .( o( ygs 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 6e1 kd.ata puo8kx7g9l6xn*- tfeup )m and 2.76 m in air. How many beats per second will be heard?k )pn7eafg x.8-taue1d* xu96lo 6ptk (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engizq 0m 3k2slo8xne’s siren is 1550 Hz when at rest. What frequenc 0mzlk2osx 3q8y 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. Wh8i hn+- )xhnnyxz63vf at frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 3h8n 6nf -vzx+)yhix n32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyb0vx3.t mmlk9ba :z8z if a 2000-Hz source is moving toward you at 15 m/3 mbv 8a09.z lbk:ztxms 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 equipped with the same single frequency horn. Whe kz :-kt5(bgm6jy9 ejbn one is at rest and the other is moving toward the first at 15 by( 6kjgm btkj95 e-z: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 ultrasr6p 5qg9f xfk44ly j*jonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the recef 9yj6lp4rg5xf 4 jq*kived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an iq( +lc3sj.f hu4n3r *yrdr)b)8qisf ultrasonic sound wave with frequency hl+8*.bfijd )r)c3rs rsy(n fi q34uq30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plaikyq5/to 1dt;jv1hal wg6+4iyed 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 thoik1+yht6/i t j; 5davgwl14qe 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 ultr+ou9k w6mm3aoq: gc9 qasound waves to measure blood-flow speeds. Suppose the device emits soug9cmqkoa o :w9q3m+6und 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 is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of hqj7 fe)px26r0r;cgcv7vr / pfrequency $2.25 \times10^{ 6}$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 ismy ./ifsc y4:gu jz3h -6v:yad 12 m/s from the north, what frequency will observers hear who are located, at resj/ysu3zh yadvy-c46:f im . g:t,
(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 ifv:m-g6 p*ppj8ih qqe. o w+o6f 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.hjub96 qp*fi -3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makesp6-i9bh* uj fq with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soun:) ezebtyv-, dd is only about 3ye): zv,bde-t5 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 8 1*stwp*g e sl9m;s0sblx*q-g500 m/s strikes the ocean. Determine the shock wave angle it ltqe*gl ;1-sm*9bspsgx*w0 s 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 ifv xzi;au n,-g3*jn8$/theta$ 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 tndf,8r8s myi6m 6lbl.j *jw0fhe ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2b l6ys l fi8wdj8n,60m jf.r*m.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pul0iqr. wfrn(s /ses downward from the 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 wat.r rsf/in0w( qer)?    s

  Approximately how many octaves are there in the human audibrw0l )4(wje shp).gzq le range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispd12dtkwu .fq/lay called a sewer pipe symphony. It consists of many plastic pipes of various lengthtfkqud.1/2w d s, 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 * yv mmh*77s65dj 1mlxrw1l mzm from a person makes a sound close to the threshold of human hearing (0 dB).1d 1 *h7mwm 7mjll 5vzsyr*x6m What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sou56mq pf*0/ ;o- cax:ijp jndy uc5,mmtnd are hear:5xdipa;m,cf c-0 65 /jpj*mym tnquod simultaneously?    dB

  The sound level 12.0 m from a loud; qz;hdn*y yl2 ij4jttu3g8c5 speaker, placed in the open, is 105 dB. What is the at5du 4tci; l32 hynyz;qj g8j*coustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. ahr .s um:xr98The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15a8r.:m sx9r uh kHz?    dB

  Workers around jet aircraft typically wear protect,b- b4* p7se/ ugs/qyqqhdl8iive devices over their ears. Assume that the sound level of a jet aiie,p gqh -s/s7bq8 yqu4 *lbd/rplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gaik .21sj d9vqf0g9pqugkj4 i;nn, $\beta$ 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 frequenn.8mp*d4 fgz txuti0+d p))jdcy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental .sd9 +exjbh(a frequency of 440 Hz and a ms+d9b he(a.jxass 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 vibratio(1fab a53lzhr-qp cu:x92 pdahrf g. f4z3l 9bn 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 distance from the tube opening to the water levhh2a ub -lcrrzp 9a9gp 5zfld ff(a43: x.q13bel 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 at one a 3(mhugui.iktmn el6-1q 33xend and also 75 cm long. How much tension should be 3g qtmule3 mi63 1hu .nkxa(i-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*q o( d95yqigbb(1lgj6zlpl, to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourc ccf9 .z4gz;ndes. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency isgz4c.z 9dc;fn, 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 whist hmbs)zh 2tr+e;rv6 s,les. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approac2vhhbtr)s ;,6e+mrs zhes. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it q j*pp. f*8rwgpassegjq8 .fw**r pps you, its frequency 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 listeniitq2 k1iezb2/u 42lwvs4fw4d3,o d tfng to the difference in pitch of the4 du2iq v/fw 4ote21ib 2k f4tsw,z3dl engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequen9jm 4o 6mtzj3e6kr4 6 wr+uaqtcy of 11 Hz. The shorter one is 2.40 m lo 6tm6au43 jzemqtk9or4r+ jw6ng. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pasw+be5 z7fpcqy 99j h1pt 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+1 9e9hzw yb qpcp7f5j 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 b 3;ykqn3nycb*f( a1o*vuj6cm lood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavek fy jm*c c1y3(*abn; u6vno3qs were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s wo0lb- aospqb4;5 i:4radk7x shile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave ofi bpsaxq:4d alo7r-s 40 b5;ok 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 8+ru yxl4x2 vkof high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abou4l2kyr uxx+v 8t 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 once used to send signhntz-s+j6 4aa03 dysmals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. 60msda 4-t 3a zjn+syhWhen 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 listening can be compromised by the presenc 4 vji)sbf2a8yaqpi+- e 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. Calculate the fundamental fr)q i-a4v pjy +f8sbia2equencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” invotlh:6i *q kyvt .3j+( ajspx5xlves 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 “sing,” or vt5ijsq6pl(+ *x.j3yht:x akemit 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 f9rtx (a ef bruimk(:a1oqw70:or the human ear at a frequency of about ki(: r0aamx1qwtru:7(e9o bf1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observyv c*4yl 0hz+aer on the ground hears the sonic boom 1.5 min after the plane passes directly ov4chl0z+av* y yerhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat hanpjw yl9c, d.d+1 f0is 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