What is the evidence that9z/7qmkql* w d le:xb;mj)h:z sound travels as a wave?

What is the evidence that sound is a form h-meu 5j+dnekl*h 6/x z*o yz1t(s;qu of energy?

Children sometimes play with a homemade “telephone” bjb6bw7o fi 90yy attaching a string to the bottoms of two paper cups. When the 0ijwfob9 6 yb7string 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 the other.

When a sound wave passes from air into water, do you expect r6s-vwy5yad( *,o ohu the frequency or waveleah(,u5 yy6sdw* o-vo rngth to change?

What evidence can you give that the speed of s5z,p /tdq f6abound in air does not depend significantly on frequa6f,5b dp/qtz ency?

The voice of a person w7m istcv;9vxze3)j)cfw.m p 9ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pnmg 4( ,m -iv+ht,qiwaipes?

Explain how a tube might be used*q;pzb kq-lm9h skt*a65 8mnr as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)l pmb rk;-ah*q658stz *nk9mq

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you w ug*zi;v-)7 4g*qt wic**1jjjeo acdmove up the fingerboard j*g-wda gc*vq4ui1 ;t jcez7j*)iw *otoward the bridge?

A noisy truck approaches .xp sv j c.3 +mm lqs/s5vvbzidl7y837you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter d myb 8 css7z..vvmviqjs5p/lxl337 +” — 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 “interf 5f x3x/rejau)erence in space,” whereas beats can be said to be df 5rxeu3j)xa/ue to “interference in time.” Explain.

In Fig. 12–16, if the frequwi,-gb4 tag (1y; tqkd/nv ky;ency of the speakers were lowered, would the points D and C (where destructive and cons g/iwk,1 a;4t-(k;btqg ydnvytructive interference occur) move farther apart or closer together?

Traditional methods of b)u9 uf;bil:z-/mowgprotecting the hearing of people who work in areas with very hibg9 )- iw/ zboum:f;ulgh noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a skuv4g ,0wnfbbjahn)3pb;y1 jy 9.l)6 jfif q1 uperposition of twoy.nv ; bfqk bhy6b194g,j fp3w1 l))ua0f jjni 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 shk (u4hy+ )4jcbol7+ecm 6efbp ift if the source and observer move in the same direction, bpul+64h(k7jb e y)c ofcm4+ewith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the szwiu0hg,ph w.l:06d y1s )v fgc;(jf sound heard by a person at rest with respect to the source? Is the waveleng ss0guf;,wgc zylhhj. dfp016: v )wi(th or velocity changed?

Figure 12–32 shows various positions of a child in jo3.iwj(rin 9motion 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(3i r.n jow9ji whistle? Explain your reasoning.

  A hiker determines theg84k43gpyl6bee hw z 4 length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hea lgg64ek 4bzh4e3p8y wrs 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 909zugmk h//nv i 4e es*;po/vw+azfmhears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep 99v/h *z/ w0omn; aveiu+fe4ksp/mzg is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20gwr::o7d wnnam ,9w (b $^{\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 drif *yx ;nyjn,ug )q5jffss:f iis 5g++a+ting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boa,: gs jsq5f)yifu+g+;*snxjy n+ia f5t 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 spd x,tz95cs( cp1,hu iilash it makes when striking the water bec zc9tx,sih,1i5 (dpu low is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hug1+to8ha j26b0jdvqbee stone strike the concrete pavement. A moment later two sounds 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? bjt6b0e2 avd+q 1j8oh See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one miiixe3,vq9ht t8/cxl * 7 jije8le of distance by the “5-second rule” for estimating the distanctjh89jeqi7 c/v l3 e8 xt,x*iie from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensityt*agmgx : va44 zk;g;k of a sound 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 intensitpj 3j*jhsfi,1ky;hz0 y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simulta7 hf2fj+;j xlh:up,qc neously at a certaihf 2jc : +l,jufp7x;qhn place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distan c*q-,:7b gq-b+ sg,prq p+-kcftengnce from an airplane with four equally noisy jet 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 in :p,q-- cgnqtggs -* q,cfb7+nkp+bretensities, not dB’s.]    dB

  A cassette player is said to have a signal03;4cu /hhyfxh ;qr km-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the m hhucr y;03q/4 h;kxfsignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frf bfq6x3xh+ s)om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere ce+)xx fsh3f6 qbntered 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 areav us(hu.+ )ies:hi *eb 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 b*.rm+ d tko/lz88ay:y :ve :rh;tbgq the 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 from a loudspeaker/+a;btqorhy *d ez 8t::y vr: mkg.bl8 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 dBla *hwg(it+ . .,ldtwa when placed 2.8 m in front of a loudspel. .t h+*(atw,ldi wagaker 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 in9arywfo / w7 n+kr*cc( sound level of 2.0 dB. What is the ratio of the a9c w+rwr/fa7nc(oy*k mplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorudd dv6cjs q;d(f,:p9 will the intensity increase? Increase69p :qsd,c;( jvdf ddu by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaco5qvx 84w8gq:sm bz;dement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?8x o8q:5wsz4v;bdq mg   

  What would be the sound level (in dB) of a sound wave in air that cog wy vw/43beji,w n++4mi-x lrrresponds to a displacement amplitude of vibrating air molecule4lem+3rw,biwg- iv /y4+nxwj s of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound le/vbv:n:,snp xvel to seem as loud as a 100-Hz tone that has,nvnp v s/:b:x a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when thees:er .g2od)rb0(a(/s xntzk sound level is:a .x0nro/ks s(d2g( ete)zrb 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangk gcsrf*.1 1gw0kyjw+e of sound levels. What is the ratio of highes+scwkgfwk y* g0.11rj t 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 fuwjs-y t p, ,-lw(dbjw;ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placew- ,lwwjd ,-tbjy;p( sd?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audib e7 uk27 xc plc8oqnow1v/lft4,;y9uhle overtones if tt;7fv o ,wn2u9 41lq 7ck8hypxloue /che 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 ok m0d4 kg5/mgyou expect from blowing across the top of an empty soda bottle that is 18 cmm gk5dk0/4ogm 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 theut+y vqj4pg,9./o o i*zlzi d2 range of human hearinv4jz +,9 .izuyd2gqpl/ *ito og (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmondk tiy f0t8 3(+9zbh- t(hersd*r pz;r/jh*p vic. What will be its fundamental frequency if it is fingered at a length of onlyy z9( tr-8th *vti3 b /frhp ksjdd;p(e*z+hr0 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle;*xlr2 psi1cg 1z enj* Cj esl 1xg ;pi2cz*1r*n (330 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 lengqdu1 2uw.)ba nth of an open organ pipe that emits middle C (262 Hz) when the temperature )qu2.d1n aubw 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 20qto3w 4yz+*iz $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutec9p o(cq5 +m0n*qeivd in Example 12–10 should the hole be that must be n5eoic*p( v+m c9qq d0uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,.fnf 1zrz,dwqb 6hy, 05h z;cx but not at any other freqyzbf6c0wdnx.1fr ;h z5 ,,hzquencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at t pi/b.o66 cyeiw ns0u)wo successive harmonics of frequencies 275 Hz and 330 Hz.6cbuy.iw) eo /n0s6pi 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 j5( rgv6sb 0dr,q5v)je u lw)y$^{\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 withi; ljs9,(/rdthq cmw q-*s;vu vn the audible range for a 2.14-m-long organ pipe r9(vhtmlwsq ud* ;j -cv s,q/;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 open to the ou otjt6:cwekp1-58yx utside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. wt c1pjytuo8ke5x-6: 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 uxcq( ; 4xqaa h14-tty;)xey pof which is sounding 440 Hz. How far off in frequencacu xe;ty(q qtha4x ;4 xp)1y-y is the other string? ±    Hz

  What is the beat frequency ifo) tbqb2*9,auvh8 hsrb1o2 h g 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*4/cp9o v21mux 65g xhzx*m k2nou4ncg0tont kHz, while another (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, estimcgn vztnh4 * u mg* mto 0cxnou21xox/2954p6kate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz mmaahrm22x.y-6p4pyt x0-flw 55p t mtuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the str5mt6 x-pmwp 0a24f2ah y5mlym-t p. rxing? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenshi5xo i+q 1mk9ion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq95h1x ii+kmo q. 11–13.]    Hz

  How many beats will be heardwu0hjxfsa dyf4, . 8doq;/cv* -j:ifl if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.0* jjddx-0foyl cw.8/;iffhusq 4v:a, $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequ.k6 s,j4yzmjc ency of 441 Hz; when A and B aremk., c4 jsjyz6 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 sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker spzm+/5mswf +im y2e( vje1tlq3krhs5: .6jzand 3.50 m from the otherr5(2s sm1jpfji6k3: mvyhqesz zt.5 e+ mlw/+ .
(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 suppo-l95biigi-l j sed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are plal-il 9 jibgi-5yed 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 wavelengthsoueuzs* dk wz3v7gu5w+ru0 nx:e4k41 2.64 m and 2.76 m in air. How many beats per second w14:ru*wwounx3uk ze+ 5 04sz7v gkuedill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren5 2 6g5vcboyxn is 1550 Hz when at rest. What frequency do you detecto5y 6cv5g2xbn if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sim*uzx sb0i 1mcoi la6-t) 1c-+ gcl:thren emits at 1550 Hz moves at a speed of 32 m/st+ )1h m xa1-cboccg:z-l*u6m0tisli
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward z5 q o1hm0tvps:b l5j.9ji5yoyou at 15 m/s versus you moving toward it at 15 m/s z5jhotlb. : spviy5 om5q91 j0Are 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. W :blov9 xv esa*6jsf;9hen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? ;v 9bx*9vo :sejsfla6 Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0o s7.jlyf039) nftquc kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequency?fjq tno. y97u)l0scf 3    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed xa44wlhh/,*aea v8 wiof 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. Whatw4x l*/i eh4v aw,8aah frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentufm-ma) nm+q8 (dd;n ts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railwnnafqu;( +) t8ddm-m may 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-m r.(ugnz)9mmdt*z; fg d1pn ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1df; mtn)u9 zr(p*mdn-z1 ggm .540 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 frequenwdivvu9j l;3of p/1x;cy $2.25 \times10^{ 6}$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 soucb4ud jg-re6mk5 p56 vnd of frequency 570 Hz. When the wind velocity is 12 m/v bgmu5564p6 krjcde-s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at z5wisg4u 3uc.dr 4/s/sxql )v (oy m1m20 $^{\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) +2ha cec ;mfpj,ra7c 312k+(ewcurrh What is the angle the shock wavcerah f;m k2,u3rj(2+cce h+ 7rpac1we makes 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 ofee-1d0 iev7w c a planet where the speed of sound is only about 35ev-7dweci 01 e m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shockbpz pcn9h;. (eyefb36 wave angle it y 3hcpz .n be6pf(e;9bproduces
(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 b3bv14p(mxj u2 w oz1d$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pla p(ui c3x7pqr+to,hg* ne exactly 1.5 km above the ground flying faster than the s 3pugx+rtq*oc,(pih7 peed 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 20,000-Hhibm::+ uf,t.j rxjaeo ,vj/h:(x :6 p1gpemhz sound pulses downward from the bottom of the boat, and then1bj(:.eh,,:t:xh/ hi p6j:mf+e rgop vmjxu a 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 mrk0eik3ly1c gf yex91z f55 2in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display nww/vn gw8d u3e/m2 (bcalled a sewer pipe symphony. It consists of many plastic pipes of variodb3e ( um8wwgvw/2nn/us lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound closnj;cl s4 rda(*e to the threshold of human hearing (sr a;jd(4* cln0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level w7k (z/-teeke,zv/xo f3ka h;when an 82-dB sound and an 87-dB sound are heard3ef twe,akoe-z k//xh(z7;vk simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i4yxv1ki bjj9 ;s 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiate1y4bvj 9 i;xjks equally in all directions?    W

  A stereo amplifier is ratedmfj r4 ,l(jxq+ at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the m +jlf4,jxr q(power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear pro6q,2x,jojq q vtective 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 oq,vj6 qxj 2,qthe 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 gaintp k,psje )qkry4f ; +7/hj:kk, $\beta$ 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 /er1rngsq lern.x q/0 g*/ke: tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a vi ler8/lf4efh4zm + i6xolin is 32 cm long between fixed points with a fundamental frequency of 440e frx flzl44e6i hm/+8 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibr,6y -fjkw-sbhation above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop,jswbyk f-6 -h 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is opeq3, r ltiepj/4n 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 harmonreqp/li ,4 t3jic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop audg (c7 cjnk8c4s)5b ($\frac{1}{2}\lambda$) 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 comingde :n u.jk 7lvowfa:,im/(4zq from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequenc7.:m 4uq o awf:(,vkl jen/izdy of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is uz)j+b vqidd;*ds q632u :ky wstationary. The conductor on the stationary train hearsd;qvsd:i+q 2*6wj) kyb3ud uz a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you 9ia ;nkvr ((yjis 538 Hz. After it passes you, itsy kn(aj;ri 9v( 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 *s/yj;;lr lf)x i5xdsspeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full5ss jxxyll;/rf* d)i; octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherq 3wm vv;8thn,, produce a beat frequency of 11 Hz. The shorter one is n8, hv;vt3qwm2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pz.jmb b6l m. fc;d/s+east a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of /zjl;.b+cemf s6d.m b212 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 flow in the aorta is8zif2 )irnah )z68m*lk-fjts normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and rk )hf*azi8n fl- t z62risj)8meflected 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 moth is flying toward the z0mn5ckh9r7 xhev: s2/g 7yv g o0gow(fgc)8b bat at speed 5 m/s The bat emits a soun/(h y5 7o0k)ocwcsf8hg nr0 927:gegvgbxm zvd 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 26uru1rjsy 1nsound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by tu 1rsnj62yu1rhe bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once ustbj dq1i-tf (4f/fc -x:q rr1ked 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 blow dqcr4tx( 1-qft:kjfrfi1b-/n 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 pre7axd9x uig 9t)sence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. atxxg9d)iu9 7 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 demonstra v 2ylbc0bf9 5logp8(.lv hxv/tion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the othv0b./ pgv2ybc(h v l 9l58lfoxer 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 theix/ tuj8ph* .h human ear at a frequency of abohhi.j xu/ p*t8ut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach /ix;0vk; -+mbt(zeaz xwsim+ 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the p- 0e; w+ xmb(;+it/z sikxzvamlane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb)/ )st0herijkb)jqsoz3m, t.oat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h