What is the evidence that sound travels as a ni(rt wb3i, 9xwave?

What is the evidence tho,co osy b4 sdy5c(qp(9:k m*hat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a)8p 0zat 0hkl-upf f0a pg5yy0 string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heartp00y-f8hz05) yagu alp0fp kd at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into watez s*.hs 7ejtekfgxn qx;5.w+wek+;)6ula( ku r, do you expect the frequency or wav .qluk;z.k+s hg6k+xxwts af 5* ;e)enwuje7(elength to change?

What evidence can you give that the speed of sound in air does not depend signy, i1hv3b26ze9c) rro n7 yyzlificantl ylbeo yvh2icy)9n, 1rz r6z73y on frequency?

The voice of a person who has inhaled helium sounds very h :s7t.d 8i+qgzd 6sxkyigh-pitched. Why?

How will the air temperature in a room affect thgsv 807dg*up 4;fwo fhe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce t 8s. ;g1nn qplzf*ub3nhe amplitude of sounds in various frequency ranges. (An example is a car mufflezg ln;us p1*8qnnb3 .fr.)

Why are the frets on a guitar (Fig. 12–30) jqw its6fpxc;z v5xuo*)qb0*xkf8 (8 spaced closer together as you move up the fingerboard toward the brix*b ciw;qx6 v 5 jpox0(sqf8*)ft8z ukdge?

A noisy truck approaches you from bechgsjendn7 re+pt 4430*kf0zhind 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 high-frequency noise. Explain. [Hint: See S0z7eh0 j3*+fk4dn cntes prg4ection 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacx ;cy3o x2roz t4o19jr38dnbrc, t,hye,” whereas beats can be said to be due t2od;3yn,8or troxzy9xjcbh 4 3r1,c to “interference in time.” Explain.

In Fig. 12–16, if the frequency 6ou ouu8*h/y7m xump7zdoz96 of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or clos8 xoz9uou6*z hm dupyo7u 6/m7er together?

Traditional methods of protec. vrc3z-7 sffs+qhi2 jting the hearing of people who work in areas with very high noise levels have consistesh7fi s3+f. jr qz-v2cd 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 ears?

Consider the two waves shown in Fig. 12–31. Each wave i(g 76a4ct6cjr k kt; jfp1yp,can be thought of as a superposcapf746pk,t1 kcg; 6 jr(jtiy ition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in tb n +0p udemg3cte(c31he same direction, with the same veeuc+ e3d10t(gb3n mp clocity? Explain.

If a wind is blowing, wirh0e vtce5 f/2ll this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavehrv25tef 0 e/clength or velocity changed?

Figure 12–32 shows various positions of a child in motion o,) 6.c vpj9gybwml 5pba5xei4(wf.yrrw 2 .it n 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 f bbppty4 xv. ,lmf9(cjw)ir6a 5.5wrgwe2y .ior the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shouj.iawsl,cp.0ye hrk-yw 3 -0 cfo;6b at reflky f .sji .00-a 3eh ap,crblw6y-;owcected by a cliff at the far 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 waterline. He 34p ch8kzf.9fsy9mr:e p8 e6eiyza )yhears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the oceany hzzaep9 4rsepikc )8ye9y3m8:f. 6f 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 wavelengths in air at 2vyf: igl smi3(fup4j-a /oe.80 $^{\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 ;zww3huc73hh 5 8qg::kn uhzfon a foggy day. Without warning, an engineufhz3hc:7k5 h:8w3hgu zn q ;w 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 splash it makes q66ivg63 j owfwhen striking the water below is heard 3.5 f3g666qo vwijs later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge s:lc5sa )2o:qp s4lv crtone strike the concrete pavement. A moment later two souns4c :2v ll5qps ):acrods are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-secodbh0.ayvs0: dnd rule” for estimating the distance from a lightning strike if the tempera0.vb h 0yd:dsature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levk 5qrtt0 j2:bdel 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 intensitysrj/pjc8c8cd h 1 3eg/ is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously h yci my:7jf i;jxt844at a certain place, what will be the sound itmy :ix487f4jhcy j; level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jeliluw -,jpochw 8g5bg(1g. *st 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 intensitie.jih,5ggulws-clw (1*op 8g bs, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58v-790wmd;nq.ydj 1gwox tf4j dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise f9 w md1xv-y 4j.t0fwogjndq7;or each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fropxvan5* ;f rv6h m5ze:sp:2te m a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ;mtvavxn:s : 26pp5 *ehfer5zcentered 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 eef.kvk -ac6yypn44u 4 1x+c kcardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B is i2 p*awju 7qrgl89vu,chy8s 1rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 mij uc718p qru l g9ah*yv28ws, from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of da,-9p( ys p rxik oqk(g6n1y9a loudspeaker on the s(p91 i6k-d s,r(yn pk9q ogxaytage.
(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 typicallyc9x3 +x3exbh yb :lwc- detect a difference in sound level of 2.0 dB. What is the ratio of tlx-hxcx:3yb+e9 bwc 3 he amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a bzlri k )7mv/ :p7;jxyy7rhr*sound wave is tripled, (a) by what factor will the intensity increase? Increaskp*7)h ;xr7lryji/v:7 byzmr e 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 thez(6a pj*vcu7t frequency of the other. What (upac jtz76*vis the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that;asb6cf/w2z 6.adge) jwks 0k k(nh 6a corresponds to a displacement amplitude of vibrating air molecules of 0.13 mmkk6sz(f6wd26.0 wb gh ;aj/ksac) e an at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a qumm9. +n;kg r100-Hz tone that hamu;g9q +.rnmks a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when theb:7o unule( 6t sound level is 30 dB? (Seouu:n(bl6 et 7e Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whaxsd2sj5 c r2m9t is the ratio of highe rxsjms22 5dc9st 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 violsdfebf( rp3: )ub/bg 0in has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. ff)grs( e:/d3pb 0bbuUnder what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and c3/jvqq+o 56deeq3g w first three audible over3qc+odewe5 q36qg /vjtones 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 frequenz edzuhof8( *te 6pa1.:d xsm0cy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assummsahfept 8: du (.e6ozz0dx1 *ed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube :2p,vwy8gvb5lx.cqp6h uk)upipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes ku:g)upplx .w,q2c h5vb8y6 vrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz adv t3u*uipg 3:s its third harmonic. What will be its fundamental frequency if it is fingered at a lep:diugv u*3t3ngth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lonw* uo/cl6q vf gsnb+(*g and is tuned to play E above middle C (330*+b/s (ogqfnlwc * 6vu Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length r;pljk-+/ryn/hah,jfe- 9ta of an open organ pipe that emits middle C (262 Hz) when the temperature is 21 hk-arr ,tay/hjlj/-n 9p ;e +f$^{\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 2bc xm9eey1mr) 1gb/9l0 $^{\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 holcyb+z+s o/uwv p ;0l*nmdw8j;e be that must be uncovered to play Dld8o;pjsvy */m cu0 zn ++w;wb 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, and 616 Hz, but not at ( 9rqv56bqli u cluwx mkk.;;3any other frequencies in between. (a) Show why th;59k6wu;q(.3i llm rqxv cukbis 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 open1kwzq ;6k)y gz at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 zzgk k61q w;y)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 + )evn 1b5bjlp$^{\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 prkfcrk0o- nv4 8esent within the audible range for a 2.14-m-long organ piper4f0 -8vkn kco at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lonchmw6;lxyqf5) ;txj1g. It is open to the outside and is closed at the other end by the eardrum. Estimate the fr ; 6 ;)cf5tw1yjmxlhxqequencies (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 sm ,n.lqwb5w4 o when trying to adjust two strings, one of which is sounding4 mbo,w5lw qn. 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if m,xhfdk(5np/3+ bx yqy iddle 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 kHz, while anotl-jphg3j4c dfx0(o q 0 jh)dk;qmf:1ther (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency od tk(3400;)gjj f fdp-:c mqoq hj1lhxf brand X.    kHz

  A guitar string produces 4 beats/s when sounuu f ),8 5,trj2zy tlel72svpfded with a 350-Hz tuning fork and 9 beats/s when sounusjvz8t5f7t e,pl,r2l2)uf yded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Thehwks 3( izt-x; tension in one string is then decreased by 2.0%. What will be the beat frequency he;s h-k w3xizt(ard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try e h5cqp4*)1s)yy9v txc7bj02zba zte to play middle C (262 Hz), but one is at 5.0°C and thp 09q c jves4z)c*12azbx7bt5 yhye t)e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fo)8godcpvywv; 2i7cxp; f,o f8rk 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 C7f8xgvivw c8f)y;pdp;,coo2 are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m aparyd ,f/ig0z,n6:az uwqt. A person stands 3.00 m from one speaker and 3.50 m from th gd 0wq:a6 uz,yif,/nze 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 pip 4j 6*a9t5 yu b0oadhjhx-:ztano tuner hears t0*ut4d 5y:b9hxoz h a6jp -jathree beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   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 w* .kmxjhc7si :avelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assh7xmsi:c k.* jume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque1m6n+vbfpn5occitmj -9ox ;/ncy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 5fcoon9 1x ;i+-vnpm 6 b/tmjc30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fr ihq56yl+ o;vp34xri lequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 lx hi 4iyq;3v5 r+po6lm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movin) mxr(gi n49wbfn -yo3g toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freqxfn49or 3ywgb)- (minuencies 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 ps/*lfa: v/qbwith 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 freqa/pq:b* v/fl suency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 5km354k3a8jcmir nro2z5 4bds0.0 kHz and receives them returned from an object moving directozd r28 a5k4kjs3bmcr3 45nmily away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall cn9d g0cn6;cpat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat c60n9g; dncpc hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a movi4w5pu f8;;z6 l+vt ysrzwjb+r ng flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while aty 4;s b; +tjz8rr+zvp65uwfl w rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to xu:2f0z5l.n + v qnzhomeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound inxuhnv0:nz 5z.fqo2+l 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 usi1ji,y(ss tqcsng/z41ng ultrasonic 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 velocit dvedl;3 7vj2py is 12 m/s from the north, what frequency will observers hear who are located, dd j7vv e23;lpat 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 o21n.h scq.rxz 6x 5l9nih d)rsn land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (u:ci c 9 jg2epz7hw, vze1-8mfa) What is the angle the shock wave makes withm:e7c izwp-1e92 h,8fczj uvg 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 thd,t 35x:v bdh90ph7fgn(k8 a gkg:f cdin atmosphere of a planet where the speed of sound is only about 35 m 8h(cg5:tb 3 fv,xkd:n7 akfhdgd09gp/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.0 y,oliy;xc92sfny+ c 0ca;ee Determine the shock wave angle it producc x;lyeaone+c0 0f,2y9y; csies
(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 ka.y(qyx ;z ;o(1txawvvj93;f idk uq6 qo97o $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ov ymqly386 n:1m(3r bpbqluv9g erhead and see a plane 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.by lqy6g39:18bnp( rqm3m lv u0 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 soudbv nc9ms5fn rz- z8i /u/dne3/ly4q*nd pulses downward from 5/ zfrd -9ul*nd senb34/qnvm cz8/iythe 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 hrn16phjj)bl,x6ya2qb gn15 the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum hasgz zoaie90)c;ml;dyno kqn2+j q.9t 9 a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whk2 ni qjcn.;a9ylztm9g)eo90;zd q+oich 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 axst + x:xkz t71+a2sulkn f9r:pejs/- sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitsstj:r/uzxtf l7x k ak1s+n-p2 x+: 9eoes?    dB

  What is the resultant sound level when an 82-dB sound and anlr6jl40hft d.w tufj/*px1 2 z 87-dB sound are heard6/ dxlhtfjfl.0 4pj*u1t zw 2r simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placzeej7 lx/ kv6vi;k7v0ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all jze6ekvl x/vv 7 0ki7;directions?    W

  A stereo amplifier is rated at 150 W oumxl tb,9ch/r6 ycf3w ,a;o r:utput at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wxc9 u,; wr/3b,myfc6 orhl: athat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wearf(-: vuhdzf-c protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine? -d-u chz(ff:v   W

  In audio and communications systems, the ga 1mnvocu .c7elez ue 2 wd7hnjal12a *a:-b*0xin, $\beta$ 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 tkf:ap: q (jec1e k5*dzo 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 between fixe52z)0 ;sshgv 8vpznm y0sr2xffgi79cd points with a fundamental frequency of 440 Hz and a mass per unit length 70g )r0z ys2h92zi5mn fvspx 8cg v;sfof $6.1 \times10^{-4 }$ 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 tube filled witr1;gr7 az l 0gw)5htabh 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 level is 0gzr5a1 7lwr;hgba t0).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 neaklhf6t) oqw/)ij(- xcdc l*t: r 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 the tube? )6 *lxktw jo:- dhc(cl ti/q)f   $ \times10^{ 2}$ N

A highway overpass was observed to re:l711qsq fg goh,uj:jsonate 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-H:.uau,e1o idjz range coming from two sources. The sound is loudest at points equ1je i ua,.odu:idistant 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 train is stationary. The conductor:blq-k(yq(j 6 c)n uos on the stationary train hears a 3.0-Hz beat frequency when the other trlbsuoqc(6q:)kny (j-ain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle a8xen:h6w+q *q igrw1 v-vd;has it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the traiq 6rhvvn x hwa8q*iwg-+ed ;1:n moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening ir(1zl6l- kogto the difference in pitch of the engine noise between approaching and receding cars. Suppose the soundl1r lzk-o 6gi( 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 of o 0, a 1w7a;3puj*zu4uydiqtd11 Hz. The shorter one is 2.40 m long. How long isp7,ddu az0ti; 1 uoq*43juywa the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a i8 9katx.)foo0tjj 7kstationary 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 fk09 ix8tjk ot7 o.j)afrom 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 normallt;fah.r9f c 1(ks5h yhy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasounfh9k15t(ahf.rc; s hyd waves 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 speedpmrkza s4 3mem1(j; h: 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 e zsp1jm4 (k m:r3mha;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 sound pulses as it approaches a moth. They;u fa,ri0l lh 8q:gogte)o94 pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far:o r; fq0 9li,th48le gouag)y 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 signals from one Alpiwf.ys p j58, dyljrn15ne 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 flat) horn. What iss5 n,8d.jyf1ljyprw 5 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 cseq zh7 -q/m.+fcx 8d) (6mqi rrn+ i0i9hfxhvan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the (em. -h mr6vzc +hixfs8fqdx9q+ q7ii r)nh/0 fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”7emg;l j1ryt) involves a long, slender aluminum rod held in the y er)j;1 7mglthand 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 emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fre;ao;ki h)y d6dquency of about 1000 Hz iad;) o6;dyhk 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 2fl6d0eot-fs v:x o(p :.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the planeol-(d0 e f::fsxoptv 6’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat b87zvj97 n+n xzu5jnusx;06q f9vv hqis 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