What is the evidence x1;89czg9 m80ri x(hmlar rw uthat sound travels as a wave?

What is the evidence that sound is i6gy1 -h3;vx z/rhsgta form of energy?

Children sometimes play with a homemade otx uf*h9yr 5wlb:z61“telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sou1 ht*lz y5:xrwu6bof 9nd wave travels from one cup to the other.

When a sound wave passes from -ut+ )r heg,feair into water, do you expect the frequency or wavelength to fhgrte-)ue,+change?

What evidence can you give that the speed of sound in air does not de-uca4+klfrwwx0hq 5nd 9), 8za o x5mbpend significantly on fr, xzlwac4kwd5-f9oh ) 8a mqbn u5r0x+equency?

The voice of a person who has inhaled i *+82c,ett2x t fx82b0pxkqpm7relnhelium sounds very high-pitched. Why?

How will the air temperature in a room af4yqp:h o8t*e2fxnz c,le48 wbfect the pitch of organ pipes?

Explain how a tube mighk b*0 t0:e)us*c+qvfox.7fnzd f(jl ut be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflerls:f+uq0 kx*un( dcboe7 f0.ftz j)* v.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move zpg/bhdo 3)s0.5l hguup the fingerboard towardd5 l)h ozsu 3/g.pbgh0 the bridge?

A noisy truck approaches y4i1p)thh9 yo iou from behind a building. Initially you hear it but cannot see it. When it emerges and y)9h4h ty1iiopou 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 duegnt:qoa d,6a7nxp;b9lo 4je/ to “interference in space,” whereas beats can be said to be due to “in jxnt6n goopa/ q l7bd,e9;4a:terference in time.” Explain.

In Fig. 12–16, if the frequency of the speaker y7t+-/otii.o- 1wcyh;kdklr s were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or -l irthi; o.+tk1 ycoy-w/7dkcloser together?

Traditional methods of protecting the heart3hm 9p8k*vg;qn j9iwd3sem(ing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduk h;vtj93 3ni8*9 m pqde(swmgce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be fg).zjlp.a g8 thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. gj8 )a lg..fzpIn 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 t uj7h,2szesecez7 0 g.he source and observer move in the same direction, with the same velocity? Expla0 sej7 z72cg.zhe, uesin.

If a wind is blowing, will this alter the frequency of the sound heardz+j 8(ctpo,qp by a person at rest with respect to the source? Is t8,+jz(qcppo the wavelength or velocity changed?

Figure 12–32 shows various positio.aniped/8fn6r f4 / xz 1qwz)pns of a child in motion on a swing. A monitor is inzn / /ppe 4xzra1q.8ff6)dwblowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listeg )ksg7ijc/ sk4 -c2itning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lck-4tck gs/) s 72jgiiake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He heawommm n4(-znd*a 9cc- rs the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does nonwcmmma z9( cod4-n *-t vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengbo4rc(tb(m1lj04 h lj ths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. Wiwtr hcf)44il(thout warning, an engine 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, 4w)frh(il 4ct   s (b) by the fishermen?    s

  A stone is dropped from t8n8: ai4uhvvw,+phiq f s*l.xhe top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clwh*v+p:ax n.48il u,sihq 8fviff?    m

  A person, with his ear to the ground, sees a huge stone strike thm) h;rn m( uptsq4k(1he 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 a4hqm k(p1husn)tr m( ;re 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 ofqthc 0,xin1qhio3w 07ixc, h9 distance by the “5-second rule” for estimating the dista10h,xnixhwhcq qi9i3o,0 7 ct nce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at th,cz9to u*.hr 1peb8o me 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 levely kn :9.6z6qi. kxthxk of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prov+ho x82sifb5 duce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities,x5ov +2hsf8ib not dB’s.]    dB

  A person standing a cert uyk2 rx;fdmelh87u20ain distance from an airplane with four equally noisy jet engines is experiencing a sound level borderinf2;xru08e u mhy27kld g on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereasvqbs. 0 bo v+9kt7uy insy6(h*szp:w0 for a CD player it is 95 dB. What is the ratio of intensities of the signal and t(: wz+s7oyby9*q sn.ivhks t6 pbvu 00he background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakkykwa63 :t9naqe )rwja,1e0v ing in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the m6 rw 9avkj,ae: qe tn)0way31kouth. $\approx$    $ \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 ao,7n)evpx*s rc/h .xnn eardrum 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 modvq(vh(z)umqhd i9 (e2 est amplifier B is rated at 40 W. (a) Estimate the sound level (m)( z(h vqhd2qu9eiv 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 dh6 nxv *5dfsam0 lfn04 su uh(p(q,/ojB meter registered 130 dB when placed 2.8 m in front of a lf s0 jmuunopf/xls 0 *5v,4(dh6aqhn(oudspeaker 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 2.0 dB. Wh7e5p5m px:v: w (2hhqpx/bc wkat is the ratio of the amplitudes of two sounds whose levels differ chq5x x5m:v2w:hp/e kwpb7 (p by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,yi yk lgql0o8l5bn8y-fr-h5hsqz3s+ 2 k2,a b (a) by what factor will the intensity increase? oz5b22-ykqk0+lny8brq3l8ig5 , h ysh la-sf Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, butyw3j15 6eh5qh ,jb pow one has twice the frequency of the other. What is the ratio of the w6,hjhq y5ob3w1ejp5ir intensities?   

  What would be the so p4x ;r **rv,:9hn5s m)nly*hhlahbrdund level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moleculelh) hyb,5x*d 9 r*4nnavr:sm* phhl;r s of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to iu0( +kxefgc0 om1b6aseem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6ue 0bc+fm 1a(i 0ok6xg.)    dB

What are the lowest and highest frequencies that an ear -kg2+z9(ig kl9k*whtcn9mgl can detect when the sound level is 30 dB? (See Fig. 12–6.) ink gchw tz- l gk(l29gk+9*m9

  Your auditory system can accommodate a huge 3eg4,ie*sxl5 n0ou/e-ixi+pt9d nc hrange of sound levels. What is the ratio of ,*9nhe40 i +/d5l ueixi-s ngxt 3pceohighest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 447g g vm5moz+/o0 Hz. The length of the vibrating portion is 32 cm, and it has a mass voz+mog7 5m/gof 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. W. l.km2x pf.en rm39pre4z8w chat are the fundamental and first three audible onr.w 92 p8cpxml.k 34mferz.e vertones 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 frome q7a) ilx)uf9z 75yze blowing across the top of an empty soda bottle5laq)79fx e7 )uizyze that 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 range pqvk-3 sjbalvy ozr15/o ,.2 9bqu+mtof humlqo-rv3p9uq k2vs5+ jamz 1,.b byo/ tan hearing (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 frequency07h)k oq5olzx of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengx ozl7oh05)k qth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above m:x)yu3gy i(cqiddle C (3uc 3:ygixy) (q30 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 of an open organ pipe that emits middle C (262( 51e+ ;hyeistjk bb6b Hz) when the temperature is 21hbe;e5( 1sb tjbi+6yk $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20 mgdh cf0uvu3x2q /vp/6p -8dy$^{\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–bsot;qf1f9 r4 ph ;;iw9xdh 2.zc o(hr10 should the hole be that w4r.rs f;9hop cbtq1x 29;oidhz(f;hmust be uncovered 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 res)(lbltdmu w150hwith r 88va5onate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betweeawh h8lrl5 (w)v5m0bt8t d u1in. (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 .d0d 0owgdvg 9pho- ,h1mxsk 4long is open at both ends. It resonates at two successive harmonics of fows4dgh1k mvx0p .,- hd9og d0requencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 izlur* szp 9c81oe7yo+- zi7a$^{\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 ig c w) q9,vuzk0c-sx6uav 8e4range for a 2.14-m-long organ pipe at9x )k-0 8qc4 6w,zvegs vuuica 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 toc i g-y(y,jty/l ozj:: the outside 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 Fyg /:z,jiy-j lt(:coy ig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s whrk6n 711ug .yvpm /dk(w en-hv 0bh;inen trying to adjust two strings, one of which is sounding 440 Hz. How faw.v h1 pe gdvnuhk i/-y(mb6nk01;nr7r off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) andzp /nlre jr8 (,vwt y8h7ne7j6 $C^＃$ (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 qv3 tw9(+u8f axcqto).5 kHz, while another (brand X) operates at an unknown frev+fo8q3 w)cqt9xu( t aquency. 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 of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning 4abn j5tdpp* +msu7o+fork and 9 beats/s when sounded with a5spnbo7m4utaj + +*dp 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fredp /muq*mj(qln84 qcpf - 4z,tli0x3qquency, 294 Hz. The tension in one string is then zcnumxp dm qpl4- 30ijf84,(q*/tqlqdecreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each trur63 zgzwejzo+ 3g95 cy to play middle C (262 Hz), but one is at 5.0°C and the other at r 6g9cz zog+e3zw 3u5j25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B tq z qjs9446y n) s9ldtmkwz/(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 b /jd9l)m9ys(46tqtqkz4nw z seat 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 m(xoj0 *3mk vsn3eyv.pmf 9 /gspeaker and 3.50 m from the vg n 3*eymo. (9j vmx3/k0sfmpother.
(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 zxm yjakoyi, lyl/5,8 l -6t:bbe vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one isyo m8 zx,lli ykj-ba:6/l ty,5 vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in g4nj p qvdaz7 9.c)+jsair. How many beats per gdnjq)savj 4z+ pc9 7.second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whegzrmy tmti0 pi0 1onl2/a22i1 n at rest. What frequency do you detma20i0i1zo1tgn t ryl2pm/i 2 ect 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 frequfl shay;3j ny4)2 na (zok*9cwency do you detect if a fire engine whose siren emits at 1550 Hz movesc ao lzy)ahswnk39yn4 *f j2;( at a speed 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 moving towas-+)rx1x - kw6oj.j9vxxopzl rd you at 15 m)rw.p j o+6k 9-xxl zo1vs-jxx/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn./jdgxvp* bz2, q:t* vx When one is at rest and 2 / xqxv *zp:,tvbgdj*the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultra cvl 9hw2qumr/kqhce;u +4(8e sonic sound waves at 50.0 kHz and receives them returned from an object moving c euml/8uweq+k ch(qv 94 ;rh2directly away from it at 25 m/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 qfta.s1/ cmt a4or3(xemits an ultras1mxt tra csf.( /a4q3oonic sound wave with 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 wklbk 3gi ,nm+ o;s7ux9 1wxwsjh.m7 (bas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at ;s ,o7k+u1lgk (jbwn.3 hbmxxs m w97ia speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppogw, f3glbrw5lxbhp 34nr4yac83 -:x xse the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the-53wcahwb:brx8yp fr 4xx,3n3g 4llg 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 wave 9w3sj0 wnmd7bs 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. Wh5ag utllk , (nm15yfx/en the wind velocity is 12 m/s from the north, what frequency will observers hear who arumg/x a(,nl5 f t51ylke 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 20ibhukuu to*ia) yek)l,+r;69 $^{\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 z6b +q9ni+gr smj60xvsound is 310 m/s (a) What is the angle 6zvj+6q9 gbr nxsi0+m the shock wave 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 5q0 y)j(l + fb6dp4wrssoeff )the thin atmosphere of a planet where the speed of sound is only about 35s)4+()l js5owy 6q drbfp0f ef 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 t 5 + irjvlpal041ukh0dhe shock wave angle 4vdli0+kh1p ra5l u0jit produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle n2h zrjxo0(f (/ numncsh 0c,9$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above thevh( g)n bw,ls u a9df3j/v47qk ground flying faster than the speed of sound. By the time,/qn)g ajw3l7 buvf s4hk(d v9 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 aj:sy+,/ ps.cfa 9 7 m ui/:zd:rkmxnpc sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for.c/uya m: kpxn:zi9 c7p,s/rdj mf+: s 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 the humano0s32pfsfuwjf8t )ldj7 5 (ii audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It c;sqq diaf /nwye*2 4+monsists of many plastic pipes of various lengths, w;fad/q+ywqms e *2n i4hich 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 close to the cqr(c vqjeke+::p,y ,threshold of human hearing (0 dB). What will be the sound lec jp,r:(+k,qy ecvq:evel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87k0 nfztk 4p jf;a2(k5s-dB sound are heard simnkkafz25s( kftj ;0p4ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, luw(ca.t0ve7 4iu )eyplaced in the open, is 105 dB. What is the acoustic power yvi0u a()e.uel4w7ct output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W oda;fv o44. awiutput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is aa; o4d4i vfw.the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically thd6y ;hv5s3t.9b c ehwear 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 us. tt;69vhye3 5hb hcdnprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiod,(/-c1 rf ;n :cxjavntgb4erns 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 tunedu01( pv ,7.mfisghmyd z;i- fu to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 c3mbcz13 fx0 aicl2(im,zv.fz-zu od2 m long between fixed points with a fundamental frequenc2x, (vam3oc0izdfi2b1 zf zl3 z.-mucy of 440 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 vibration above a vertical o-g4jcfk7z, jopen tube filled with water (Fig. 12–3f ,4kgo cjj7z-5). 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 tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that iq5 .d32c kev7cfhj5d ks open at one end and also 75 cm 53kchd j2.df kce7v5qlong. 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?    $ \times10^{ 2}$ N

A highway overpass was observed to resmgt0)5)vfv j . r0cfkgonate 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 tuhyrg)6 uppyi c*m rbq-+3p,:one 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 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 ofi+)m6b qpcg *-,:rypy3huurp the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stukx/a( yr h1f7r3dj2 tationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed offj t /ku1xr h(dy2a73r the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is vhhneh+xww ))rpw1g o5f apb:x; 14/fa24lnp 538 Hz. After it passes you, its frequency is m wewa:5nf xpo;)lap4rh4h2gf/1)n1wxv+ b hp easured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by +tp,d9lcfi; mvuxhbr r0( 0 3clistening to the difference in pitch of the enm 9c 0hx +f0bupr,drvl;it 3c(gine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1euv4 o*p)n)-gyy w/ o9t secp91 Hz. The shorter one is 2.40 m long. How y/9neu*4 o)ep y-ptv 9)soc gwlong is the other?    m

Two loudspeakers are at opw *wsg;yhs:) 1 +wnkewposite 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 frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after+kh w:;ss)1n*yg wwew they have passed him, at C?

  If the velocity of blood )bf6,8ps h:wsx ) jmmmflow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cellsm:s8x fw pmh6bs)jm,)? 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 towarqaz f1w g0eg4/d the bat at speed 5 m/s The bat emits e 4/agg1fqzw0 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 yi w46ixl()oa48av u ffrequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 m ux4l yiofw)4(i8av6 as 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” (Fig0 qf j8vc6n+cc. 12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of tj+n0qv cf c86chis 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 duh2t/w j40hwh3i(me06 v0suwyw/q opresence of standing waves, which can cause acoustic uvj0 o/3wuehy4hw i0w /shwtd(02qm6 “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, calledpatjnl+1 8 yp( “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, ayp(p+l tj81n 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 m yr-1 4 gcqitr,5aut2the human ear at a frequency of abomt,r14q c52ya- gri tuut 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 2.0. An o:zeev(kva 2y7p 2*zw gbserver on the ground hears the sonic boom 1.5 min after th2epv(*zg zv: wy eka27e plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaqngacb51)t o 7t 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