What is the evidence that sound travels as a wave8 -va:x-anuos?

What is the evidence 5ks2s/lcge rcp63 mc81vb t(uthat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a strinmcxke yj.hhlfu -(be a9o242 y57mt4d g to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be he-y4h(o k2db f jt7xc.me29uhl4a5ymeard 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 yoq8u1 u3ax i o2irxog*img67yq:,(ezf u expect the frequency or wavel,x2zmuqqxi 38f* ur iea(g1iog o:y 67ength to change?

What evidence can you give that the speed of sound in air does not dnj:ecqdfv1 ,)l i/b3zepend significantly on frezjnfi,:b)3vc/1 qldequency?

The voice of a person who has in98oyt/4tba21; omfdiju9k f wk0jg7h haled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organss-jk6f (8ju u pipes?

Explain how a tube might be used as a filter to reduce tl0fp hr(a cfkrj938(thi: (wuhe amplitude of sounds in various frequency ranges. (An example is a car(3 r c 9athwh ulf0jkf(pi(:8r muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together l -myb:.h sly,as you move up the fingerboard toward the brid.lyys:m bh,- lge?

A noisy truck approaches you)u+ byf g.+qlb 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” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15l by)b.q+ugf+ on diffraction.]

Standing waves can be said 7q ease 4edav48g*higyaey58-u (b0 xto be due to “interference in space,” whereas beats can be said to be due to 7(x-8qg4a 4b*se gyy0ueee8avidh a5“interference in time.” Explain.

In Fig. 12–16, if the fre*voxjjg; 1hp; 0uov hb ./hej+quency of the speakers were lowered, would the points D and C (where destrh; j1xev+;p*j ou .ob vjh0/hguctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in ar;y 15abnb5gruyjv i 33eas 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 coulr3u1g ya y5b i5bnv3j;d adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–-x t-apnb: ap7mq2, mtucc 35z31. Each wave can be thought of as a superposition of two soundqm 5t7 bcacpt-m u2a,:px n3z- waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directitm4 xt12st b.ngroc 2:on, with the sam1ts:r mbttc2x.g2no 4 e velocity? Explain.

If a wind is blowing, will thi91f(d ; avv2ri th8foas alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or vvar9fv21f ;ha i8td( oelocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. kbyemd* a)2v9A 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 frequ9dk)av2ebm * yency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the uba;bz wk356t9 *s4zdwv cn7i fh3a j/6oi+n yecho 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 lengthwozc+ h5avszuni nb;/ytd33jw i9ab6 *7fk 64 of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below th tqln. kgh9 *6jtu/ *j2ah2qjpe waterline. He hears the echo /ht.9plk 26 h*2ju qqn*agjj tof 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 not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 4o15cptz 9 dfpj.z.eg sf/ en-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 ag8 efgd+2lv/1l)vr s qbove a school of tuna on a foggy day. Without warning, an engine backfire occurs on ls flgvvq e2)8+g/r1d another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff.pm ofed.x6/b 8 The splash it makes when striking the water below is heard 3.5 s later. How high is the clpf o8de6x m.b/iff?    m

  A person, with his e iq*yj3u+6bm dz e*.ef bqle/x6l bfc w470o*uar to the ground, sees a huge 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 concretq d+oe7qc/4.*i*0bu6*bufwl mfy3 e x6ljbeze, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile n9kef. ry uue; 14y+sq v3dqw8of distance by the “5-second rule” for estimating the distance from a y 4qe 39nqw;dku8e.+u1r vyfslightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s 8kd+z hw+bv2tiy(. tgf nzux05 )6canound 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 intensityj/ i( renqb zt(ixu)/,b0+ oxv is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a shxh *i ct0k2lp+ae.d :ound level of 95 dB when fired simultaneously at a certain place, what will be c .ati:d+l0pe2 h k*hxthe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from anxp 2m x(c4);qg7txcruo8 p3bn 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 ag2qb7)x pxtc8;( m4r3oun cxpll but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to g,p*qb,gcgb .7ti7zr 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 noise for each dep,.tgi b g gzr,bcq77*vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal c.*rp+8ff xbzf onversation. Use Table 12–2. Assume the sound spreadsf. x8rfp fz*+b 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 w wvsfchx96(2,rj q:p)r hdrlc/xze4 .hose 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 modest1n+ki0loha a7 os4kviy5h o(31(jqi q amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a pooj4i y1a10(l kv kn 7(oho3q+5 aiqhsiint 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 placedato*c7h n,; sb 2.8 m in front of a loudspeaker on the *nhaos7cb ,t ;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 75kg1s ym .gd)bvsge9p :qcdr(*uhb1in sound level of 2.0 dB. What is tprey5(97bsg*)1mqd :1cv sh bdgg uk.he ratio of the amplitudes 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 fact pj, djlihvr*4j;r+n 0or will the intensity increase? Increap+j;il4*nv,jr hj r0d se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equdx8z:wzj5+b 5rngd ie l u+o,ze87x+oal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their+ ex78bz5 x+wuzg:zi,jodl n dr+ e8o5 intensities?   

  What would be the sound level (inh18uj8 cojz0kkw 8vx 9 dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating a0k cohz 188xvwkjju98 ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to see(c3e9 y dpbks0m as loud as a 100-Hz tone that h(p cybes 9k3d0as a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can 2s 4p)u -azowxfipt1qcs5c 7:pm:v6l detect when the sound level is 30 dB? (See Fp)s1cmaslix :t-2: w4o5p6 cu7 fzvpqig. 12–6.)

  Your auditory system can accommodate a hulwa , .v(vm i9u2zt8ojltm6 (l1asb(cge range of sound levels. What is the ratio of highest baomza,1 .wt9v t(micj82 sllv l(u (6to 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 fundamen7slp89 d bch.fqom6 y8tal 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 86fdq8mly9 cso p .bh7the string be placed?    N

  An organ pipe is 112 1iwhbkxyk3 ; un7naxe3p,;3 jcm long. What are the fundamental and first three audible ove3kke3xj7;x uypa ; inn,3w1 bhrtones 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 fr)- mddoj i+e,9e hyn/tequency would you expect from blowing across the top of an empty soda bote ,/yi+ot h-me)djnd 9tle 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 3tkrfhwe g(f5i1.p (othe range of human hp if(to3( . 5hwf1rkegearing (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 harmonicft6hpe+f m /0becy-rhxms4k vn j(nu6* c)6l8. What will be its fundamental frequency if it is fingerelb4 -hs +*)et6v6y(ne0uf6jckpnmh/ 8fmxc rd at a length of only 60% of its original length?   Hz

  An unfingered guitar string is nh4rx0o o.lfd0b yi89yyini q5rm2/p1x+m)h 0.73 m long and is tuned to play E above middle C (330 Hz)0lyx40 i yq5/ndf)rpo.b9r onhxy8mhm2i+i1 .
(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 (-z3 714fk7;fxv ek zv(tvv b(qwkggf6262 Hz) when w-37f4qk1f7v; ezgz k( (tvfbv gkv 6xthe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune rd.4 ) luzrt b7qpk*j c.kj:5aat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece yw1)(obc4evk/ ze2y wof the flute in Example 12–10 should the hole be thaky(wy42e)1e wzv o/cb t must 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 resonate at 264 Hz, 440 Hz, and 616 Hz, but o39q tme eyt;xp 6itag43/ne+ not at any other x9na 4oemtp/3yeqt+3i t eg;6 frequencies 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 1q7yd; er8h;m i.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. Wymh dq8e;;r7i hat 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 nx .r/obv8w 3rg+3vja$^{\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 2.14-m-long org6x4ie4sc w /3s oi,volan pipe aox4wii3/le 4sv6 oc,st 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 outside arh mzt m gm);,/-k;qnwnd 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 gr-,m;; m)wqm/thrz kgnaph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat everu31yqbpb +g0d y 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. Ho 1+gb b3yq0dpuw far off in frequency is the other string? ±    Hz

  What is the beat frequency if mid8vmn ltaz2diu4i -*c6dle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) opa9*bi p a33mnlerates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrillaaim3 lbp 9n3* 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 tu9)a j rdo /9rr)fg1lnkning fork and 9 beats/s when sounded with a 355-Hz tuning fork.9/r 1joln dakg rr9f)) What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned toss/9ht k8s g8)8vjh5cnd 2s0cogdwy1 the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are pla0s82td1j sk5) c 9gsv/sgncd8wohy 8hyed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each trymyp1rvpo p62mn:g p7, to play middle C (262 Hvp62p: yr1pm,gpm7 o nz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency offwtj3hj6o 73x 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 frequ hwoj3 3ftx76jencies 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 3.00pqhwc3f.c/ l8e+nc, b m from one speaker and 3.50 m from l+fc8 ,wcbh pq3/n. ecthe 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 ath80 e- q(dhips7az2 vn 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrvh0z2dq (n-7 iae 8shpating 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 2.642,v +bolor2omy h2gr4 m and 2.76 m in air. How many beats per second will be hr l2ho2 o,b4v2r +myogeard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f wo/:vv-na;a pire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a sppov: /; -vanaweed 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 wh lhabd. dp 3h9yp umkn3c)usd,(4* b/dose siren emits at 1550 Hz moves at a speed of*/bhu(4d)3 . d lb kcumsdadhn,p 3py9 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 toward you at y4hag0 ;th+6tbnn/wr-vife : 15 m/s versus you moving toward it at 1fat/w04 +nhy;h-6:b n gt rive5 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 sawvs;j m,xi10h me single frequency horn. When one is at rest hj0sw,;1vix m 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them re9xqitajm 1*x8turned x 8t91qmxaij*from an object moving directly 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 t1b9qt8c. v z6guc- 9n.amp;aset kt/m/s As it flies, the bat emits an ultrasonic sound w8kz-agt m 9na1btv.tteq;c /cspu 69.ave 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 was played on a 8r(x-xw;qf ctmoving 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. x8 -(ctf;xqwrWhat beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to u /2xik r.497zde dez)rrnfr-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 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away fxi-d rzze4kf 7ud. )r2/r9 nerrom the sound source?   Hz

  The Doppler effect using ul c72m:jge8;lbgy6sfb-mm aj2trasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound ltl:t(ji t(x.of frequency 570 Hz. When the wind velocity is 12 lj((.t:ilttx m/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 lawl0- ffys kkmr88 m49tnd 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) What i +wfz(n7hcz,ts the angle the shock wave makes with twz7,+ hc znt(fhe 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 the7ubr z0pj1bf j u,1f(mnlpf194z*vlq speed of sound is ojpr1f, u1b*jnfzbfp (llu 09zv 4 mq71nly about 35 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 ,11f3hk* zj ix kf)graocean. Determine the shock wave angle it pr3gx )ka1hf,j 1r*fzikoduces
(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 1e:bcyr jt7 u1f ie4us9/i;ze$/theta$ 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 the ,;dagta u. 8j3txacjk1(ah2 f ground flying faster than the speed of sound. By the time you hear the sonic bc u.j,3;8t1 f at2kd gaa(jaxhoom, 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-Hzc pl+/wemnk pmq9 g,,w9ycrbv 2278bk sound pulses downward from the bottom of the boat, and then detects echoes. If bv pcwpm ,e8qy/9w gr2kkl,mbn7+9c2the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in ),3yeu ) 2ri vn dnr/nqfjlx(6the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dish, c hvis0bj .o8g(g1ioq,2 umplay called a sewer pipe symphony. It consists of many plastic pipes of variou2v0goo, hi.hmq,sc(gu j i8b1s 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 ;r um *,)yj7qxkd4uyc m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?ymk,;4 r q yc)7jd*uux    dB

  What is the resultant sound level w: p,)zh+q . i yqrrgfdo/7 5w2zw1cvephen an 82-dB sound and an 87-dB sound are heard simultp,7odw: 1yr.fpghqw ce +)/z2vrq 5 zianeously?    dB

  The sound level 12.0 m from a loudspeaje: d yg/6,on ed1twdt+vrf.:ker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionsdtnofj 1vder6.y:gwt e /, d:+?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outputaa2bd ;8pmi8q8 c smk8 drops by 10 dB at 15 kHz. What is the powe82pi8d ksbc8mm; aqa 8r output in watts at 15 kHz?    dB

  Workers around jet aircraft t8hil.rb:qd;jm d9l p9 8a;m+gg ,m njeypically wear 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.8d nlarg; 8;9 mjd gh+.e9qmm:lipbj, 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 gain, hzlx /h-q(4yn$\beta$ 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 frequenc*hxeyz1c :2u v2nowk9qyp9rk b 7 5+piy 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 vim1y/(ot,k/yk,ymm8 km.hc w m olin is 32 cm long between fixed points with a fundamental frequency o8ok why1 tckmy/my(/mmm,,k.f 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 open tubelmru4 s+evziyyc/ 8sh) w/1: y 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 t yu1hz/l+e4sw: r vi/s)8ycm yhe 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 2xuu nr0g o p)dp65 m ;badn4xbc--gr/usca3;8 .10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string -rnn;50gp pd/a) 4x c ab8sc6uur ;o3xbmug -dif 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 resonate as onxf2e)* y - z ev /xg-u 8bhmk+w3/t5uygsa1eqke full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two so;+ (cm7hnchxsurces. 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 i (7h s;hmnc+xcs the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor obgjm0pni; 4r * toz20xn the stationary train hears a 3.0-Hz beat frequency when theirgtb*zp2 4n mj0ox0; other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After ipavk 1kd83m-et passes you, it1amkkv d8p-e3 s frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of ta;n9xw*u*b cnx5 9gd cars just by listening to the difference in pitch of the engine noise between app d xnbwc9tu5 ;*9nxag*roaching 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 frequj4gx;dciv, 0vgyv i10ency of 11 Hz. The shorter one is 2.40 m loiv x4j,0cdvy g i0;v1gng. How long is the other?    m

Two loudspeakers are at opposi(f/ k//uanxen te 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 tafn k/nux //(ehe speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is no kbsk3th ,/ox)rmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow t)k/ho ,bk3xsand 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 m7roe) t ppk/tcgd93m3 oth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequegc /epor9t3pm7k t d3)ncy 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+1ugwwmpj r.8rh(w 2y27( k 1.tqlks4y fsrxx moth. The pulses are approximately 70.0 ms apart, and each is awr.lw8g(muy xfhr2 wpkj1 7x 2.(sqt4sry1k+bout 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. 12gmma;;kqm)/q d ,v hl*–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less hv/ *mlmqaq d,; ;m)kgsusceptible 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 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 prese a5*m)w;wqxsz;:e(w vfias p7 nce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room)a5;mpx 7q a:w(wvewifs* sz ;.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lon-l z9;o8uh)ua esi8lv w5id7jc bh1 b,g, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 97cdis5j ;ob bvih -8 az, l)ul98uehw10-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 humam c1 zg)qzq/vpa 4b;y7n ear at a frequency of about 1000 Hz ba/ g7qcz1qpzy m )v4;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 oovs* 12s,tx if-.vqzjbserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s a1j 2v *xqvi- of.ts,zsltitude?    $ \times10^{4 }$ m

  The wake of a speedbo0r irl8pfb f3 +z*joyyk/9d1pp tkj61at 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