What is the evidence ths4uv lls*bul,(;r dr7 at sound travels as a wave?

What is the evidence that sound is a dj)t/f*+pzq y form of energy?

Children sometimes pla e i8mhlfoanq xs,j/*8 jn65r8y with a homemade “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 (F88 mqx5, e*8sln6 j/jnfoairhig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expr1w gbjl)p51/9a qmlfect the frequency or wavelength to chang bfmlqa 1)rpl/ 1g5wj9e?

What evidence can you give that the speed of sound 2le o25rnhszs da (0c/in air does not depend significantslo22ed (z/shcar05 nly on frequency?

The voice of a person who has inhaled helium sb gt 2jigqvip9+z*q (9ounds very high-pitched. Why?

How will the air temperature ix/+a nhyg70nz,uj *dln a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amp4qy+u(ch qip io0v7 mod03k7plitude of sounds in various frequen 4iv pid7koqyh3 00 +o(mpu7qccy ranges. (An example is a car muffler.)

Why are the frets on a guitar (i:)yj0per kd)/ yu0m,z s y)gyFig. 12–30) spaced closer together as you move up the fingerboard tosyy/rzm ) g y: kp0j0e)ud)y,iward the bridge?

A noisy truck approaches you from behind a building. In 4wc, 3 upf6uajev42dnitially you hear it but cannot see it. When it emerges anc4w 2nu64pfeaj, 3 dvud you do see it, its sound is suddenly “brighter” — 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 “inte ,hph :txr6l dzks7.n0rference in space,” whereas beats can be said to be due t,sk76:d 0 r phtnlzxh.o “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,5t2yh22tkja s would the points D and C (wher2tj5hs2k2t y ae destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ufa . 5+eta-spi:jvc7 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 electroni e.:cpj t75f-ai vu+sacally, 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. Eac i 6du:/komom1h wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whichu6d1 :k/mioom 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 .o)40zg1unmoee 2ham44yk jfthe same direction, wie0n m f)a 4o4z o2umk.g41hyjeth the same velocity? Explain.

If a wind is blowing, will this alter7 .ft:ruzjb4 dw0rvy; the frequency of the sound heard by a perstr.wr j0 u; vzb4:fyd7on at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion1yi8owf tm/6 /kkb qr: on a swing. A monitor is blowing a whi/m6o: qty kwf k/r81bistle 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 your reasoning.

  A hiker determines the length of a lake by listenin.frs9 t)gsr y5g for the echo of her shout reflected by a cliff at the far end of thet rr9sg)5f .sy 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 j j:u2+*ffz1aah,jr,zz nos/ym.5m zaust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean .m/ ,: zyah, of+a1 zjfsj5urz*mnza2at 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:iz9mv gbd68y 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 drift2 k 5jx+xnv-tp0d- (d22kwsjaw0opi ting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the b 2xpkjk5dj in+-t( 2 pww0soaxtv0 d2-ackfire 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 when striking thha*tge l:c:ix.sdb ( 1e water below is heard 3.5 s later. How high is the cliff hs:(gexai1b *.:ldt c?    m

  A person, with his ear to the ground, sees a huge stone strike the concret e (t z2e)zqgwu6j *-q5ovv)jde pavement. A moment later two sounds are heardd 5 6v2 jtuj-gzqv(zqoe)e*)w 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 mad7 fghr0ax1sy(h*g lpahgs/ ; ;e over one mile of distance by the “5-second rule” s;r/hgagy 1h*g( lax;p fh0s7for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun4a1s-luqgy7xn3 l5 fnd 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 /7u; +oa gnr1rkfadfd+ts 2 f6t9em4 ta sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultanevi rp4gq4+d jd5:5 -nwijvc4yzimu2 0ously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intuc vg y+iv0:4jw pjd4 ni 5q2mz-ir5d4ensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally/,h(uy2 ib ubvdf g;fs9;p bt( noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level w bi 2fd(vt; ,;hu/ byfpu9gbs(ould this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said t;1kj+s *jsa l7 qf9zfdo have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background ;+jslk 1s djf*af7z9qnoise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a pe7 g)z98 hcm4h1 r-slauhn otv-rson speaking in normal conversation. Use Table 12–2. Assu ual c9m7hh1no)- 84gztrv -shme 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 i*7oeg *e xuao 9hu5xj)s $5 \times10^{ -5} m^2$ (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 4ch a;nf4i at4 4mrq(vmore modest amplifier B is rated at 40 W. (a) Esh ;4c44fn atqvri4(amtimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.qee.qyca)q(;icgh * l 8kz 93k8 m in front of a loudspeak8e;.a *(ckcq9ql geh iqyz 3k)er on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2im 2r )mp b7bfvu05b bf hir;t+*.eaf/.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See 0)v72b muirhff mb i 5f*b+p er/a;.tbSection 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intnbmbb9;4 mi qg0)d va 0+i6l7 sd3ypdsensity increasev09 +lg)i34smd 7 y;b0b6ambdnspi qd? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudu/kx z -- bn7/,x xut.zfrru;ees, but one has twice the frequency/k uuf,/xxrze z.-tb 7r-;xun of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tha- wpqz;db zssp +1r6 t7m0)tzwt corresponds to a displacement amplitude of vibratingb1 z6- tmpswd;w+s zq70p rt)z air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what so) m 7qre 7ywdg24dossa6uh 6f0und level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.mdgq s6sh)0oya7r 2d74 e6fu w 12–6.)    dB

What are the lowest and highest frequencies that avkspa)+ wa 3e;:pssml3yz ot- -3m*rln ear can detect when the sound level is 30 dB? kl- l eop3yvsm*+)rt z;:- 3sspawma3 (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thfhtf7khu(zp:1j-r +5gp j+ ywe ratio of highest to lowest int5j gy 7fp 1p (kz-ju+tr:f+whhensity 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 freqgdps 1i7/)hup uency of 440 Hz. The length of the vibrating portion is 32 cm, and it hpdih u1ps g/)7as a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamnt19waks3xk js4w c8(l 70ty eental and first three audible overto(jtxls8aw70 n 1ewy4k9 ck3stnes 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 frequency would you expect from blowing across the top of s2 kgq*y3ch3qan empty soda bottle h32g*qqkc3 sythat is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the rang uxhl:+nyj.te dl((*z e of human hearing (20 Hz to 20 kHz), whlx z( .te+:d uyjnl*(hat 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 54 i w)c-7 zud)yt b,,khk+u6bvk0 Hz as its third harmonic. What will be)7ckt)+w6hkb- y ki,z,uduvb its fundamental frequency if it 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 to play E above midd.gyo: vwr ;8w(nikllt/7pwj:le C (330 Hz). (oyl r k7/t:w j wlg;in8p:vw.
(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 (262 Hz) whq: xi-+gn+bfkxi90o k en the temperature is gobiq9x i+k-n:kf0x+ 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 atcn3*:9dd9b g4 yr*vwebz.5 vqj:s nbj 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the ug 4ifbmes* 0cuv5wqfa /1a13flute in Example 12–10 should the hole be that must be uncovered temc fiqs/0f w bavau*5431u1go play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hzt9v4 eu 4cr- 0f/aymrtqco(n j2tg4k- , 440 Hz, and 616 Hz, but not at any other frequencies inv2ytc0g- /e f4t-9mtq(4rnj4ku ro ca 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 qdk l5rws:7mbj g;8/n ni9r4 vlong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz5jinqwr r v4d/kml s7gbn:8; 9 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 p -bb;vu y3+xun bl tg07 rr34-1mfndqk;yc0c$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a )eu4-h jiny1l2.14-m-long organ pipe at 20 njuei) 1 -4lyh$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cwu zho*jhc1a: 11 bj628ghbpem long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standig16 :bhcjb1z18e2 wjo *hh uapng 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 9zsw03o d p,bmtwo strings, one of which is sounding 440 Hz. How far off in frequency is the other string? ± w9mo d,p03zs b   Hz

  What is the beat frequency if middle C (262 +ux 2xj9a)* bpc fg p33tuwkr6Hz) 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 another (brand X) operates s5yzu+hu cug8:j dk95at 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 s: c 5ugu zyk85djh+9uplayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork a;xfcefc( 6 /svnd 9 beats/s when sounded with a 355-Hz tuning fork. What is the fe6; x fcvs/(cvibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one sfncp(3 s;sofco/s+(j ,lqb.h j*n.y string is then decreased by 2.0%. so3 *, +sqs bys.((lnjf fp/o;jc.hncWhat 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 identicaloswk g1;-r+obwn-i.ygq7.ntao 0s 7m flutes each try to play middle C (262 Hz),.bwt;-nmy. sqg r1oisw7 7- knoo0g+a but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning; v727ztb d9rg xp* bf-npfddnrj-.r( forks, A, B, and C. Fork 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 are the possible frequencies of A and C? What beat frequencies are possible when A and C are sougdr.zpj7pn db-d2( -n b* rxr79vfft;nded 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 .)e*pl3ybs jj stands 3.00 m from one speaker and 3.50 m from theeyj*. )spl3jb 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;sb j5( tt*egfwx5u e8 at 132 Hz, but a piano tuner hears three 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 ?jxt5wte 5f;gb u*(8es   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 2.6p *c:78enusqo vjhwmmy 808z )y*sl.b4 m and 2.76 m in air. How many beats per second will be heard? (*0q78vpmso8uch nj)l:s* zmy .8 y webAssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire eno 8fzwquw*1)vu0 m5 tpgine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of u)qmv1pz 5uf* t8ww o030 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if4ycykgd82z /s+x3iefg z5k7f a fire engine whose siren emits at 1550 Hz moves at a speeddzs7ikfy3 x5zfe48yc/ g g2+k of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movi(;enj1f d a e,sogdv/o3-ynj2ng toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they cl gf,j3s/jaonv e o1nd2e-;dy(ose? $f'_{source\,movine}$    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. When one is a3 r3v*zds9la rsz()3w y aebeyo* )lv6t rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit?bs9)r eol *a63zva(w)r lve3sy *ydz3 Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.01a w,5 kb .( (awavycanh2df:t kHz and receives them returned from an object moving directly away from it at 25 m w 1hc(na,.ya:wa bkfdt2v a(5/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emit 46s vcesgh f/r2hl,i2s an ultrasonic sound wave wit22f rh 4, hicssvgel/6h frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedmk2j0g9,tsp)9da 2*kjtfx zwg6 j -nje (-aym on a moving flat traingp*9g-xjjttmm2jn,)z a kde fj- s0ky29aw(6 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 speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasoaa,or cx n u pt;jy9)3*oo4r5cund waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue ) p;ayoo jruno*xcat49rc35,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 lt ;hwu.of86 r5ph si9 sm8n*mof 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 frequepp5-xob wl+9cncy 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at c-+pp 59lox bwrest,
(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 ihzwdt y23hsx 2-5 i,tk.m9khon 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 (a) 2 xcalwn iw872(3qmboWhat is the angle the shock wave wb 7mcx(8q 2i3lo2 wanmakes 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 spe5 cezn 7dvfhiy53w08m.8mwa led of sound is only about 357y fe8mh.5 zcdwa80nwv il53 m 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 osoow3 k:o)1* vd8l ckmcean. Determine the shock wave angle it ks k*:cv)lo 1dwm 3o8oproduces
(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 7ty6wb4 szxy;$/theta$ 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 zjpqn lo:ar+ 6.6a+dwc6jp* lm*tg.jexactly 1.5 km above the ground flying p jm .qjrl+:p.6nd+c 6zl *oa6jagtw*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. 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 2skq0jv7 )b5 (iz+ix jo0,000-Hz sound pulses 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 qji (xj+zio0b7)5kvsis the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range*j/u,h0oa/cye,a9wwo1zad, t la hf-99msbo? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of m+ ,ku2 ujx /nskys;vz+rv/ ey-any plastic pipes of various lengths, which are open on both ends. +e v; sy,syk-jvr nu/z2k+u/x
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sou-*1 n4bkwto2dn 1 qgepj8wi,f nd close to the threshold of human hearing (0 dB). What will be the sound levetgn4i-f *jon,d1wp 1w8 be2qk l of 1000 such mosquitoes?    dB

  What is the resultantf-ksaox v7tzt5 odkf :.bs/ l)c.)s3u sound level when an 82-dB sound and an 87-dB sound are hea73x :k.ask5ctobtzvu /fl s)fo.)s -drd simultaneously?    dB

  The sound level 12.0 m fr9uror*l7g ml7kzi9(x om a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally inmx(77r lz* r kigl9uo9 all directions?    W

  A stereo amplifier is rated at 150 W outy5ao* 7gc*p)a czbv +mv1 lahzky;*o*put at 1000 Hz. The power output drops by 10 dBo*y z7b*z*o;1lk+hm c ag)a c*5vpayv at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typica1xmd 9unwx.1 s8/hpb ally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a di9a b11/8psuw dnx.mxhstance 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 communicath*oo5*iat *kx./bfga(htn)y s *of3 cions 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 is tuned to a frequ i,in 9oq(3frjency 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 (p5ijt u3une6*t .xy xvste2* is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length ofiu3yx(5jt eu2 .x vp s*6tt*en $6.1 \times10^{-4 }$ 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 vibrati8+ :pzycbcu:-2aooqj on 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 level is 0.125 m and again at 0.395 m. What is the frequency of the tuni - occ+ o2zuqajbp:8:yng fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at og) r4*uge(*)xpnqif kne 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 hg)f**nq4upg)(eikx r armonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate asbo/ hfuke0;c;n 8k0 hq 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 tob i(+ll3g+:pg)xbz t8 fp r3pone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frepg3gzrbfl+ +l to ipx8)pb3(: quency 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. y2 jylj:k)ic; The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is;ykyicl)2 jj: the speed of the moving train?   m/s

  The frequency of a steam train whistlelyz 8tykra7 ql2 :nl96 as it approaches you is 538 Hz. After it passes you, its frequenayz2 ltlk rlnyq9 678:cy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can lp .dhw p)8z; x*duu(westimate the speed of cars just by listening to the difference in pitch of the engine noisz *pxwuw;d ld)p.8hu (e 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 frequency of 11 Hz. Thlbp 1b(n0jas j 3oyw,,e shorter oneb(1, ljb ps30nay ,woj is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppositell6 jtki+7f 0f ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequenf l0fl +6i7jktcies 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, (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 fllj o:ufy9)s3 )k0emf vow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dir9 )l o:ey03u)jfmvksfected 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 while the;/ q/hoi1dni-exag s4civh99b 2l1bp moth is flying toward the bat at speed 5 m9 oa9 2i-/gpcl1/iqhed;b 1b 4 svxinh/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 reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. j z;v4sj tz(5fThe pulses are approximately 70.0 ms apar4(jzs j z;5ftvt, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was6-uv)4o ;x tp5rvtwxq 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 flat) horn. What is the funo uw r6vx-v5tqx)t4p; damental 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 ca)v0xh tsnvnb 5+;(pkan be compromised by the presence of standing waves, whsv(n5at) +pb0nhk ;vxich 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods z:bu cs(g/v;-wx9bf4p s1w cw,” involves a long, slender aluminum rod held in the hand near the rod’s u v sws w-b4cx f(1wgbc:;zp/9midpoint. 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 fren2;-zsnftoo) um174b wzofp( quency of about 1000 Hzs4)oo; ntufz-b7omw2 (1fzpn 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 observer on the ground hears the sonicw ul 6mi;fphk+ -d.vywtvl* 87 boom 1.5 min after the plane passes directly overhead. What ww +vy ;m-7 *lfv.hp ul86dtkiis the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat io q.6n nw/2aake lp00os 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