What is the evidence that sound travels as a wavorseb h4cu z. uz*:d-9 4*ekdde?

What is the evidence that sound is a form of ener.xyl:rlnuvwu . gjr(j8g)m/ * gy?

Children sometimes play with a homemade “telephone” by attaching a string to theg.lw4p)-ob zs bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the oth szw 4b-ol)p.ger 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 w/qcic. lmzp:;ater, do you expect the frequency or wavelengthp :lmcqi. zc/; to change?

What evidence can you give that the speed of sound in air does not depend j+mx *kk/p-i*-c cf/u sd4i kabli: 6fsignificantly on frequency?i pim +ba dsxj-ku4-/:k/i*fc c *f6kl

The voice of a person who has inhaled heliu y7fng,6e( votm sounds very high-pitched. Why?

How will the air temperature in a room affect the 69q 4gxckpk zq7ysj mj,f;n+q5 q5 dr+pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitln f pd6+auiwy l80x mh+mm(y44ij9l-ude of sounds in various frequency ranges. (An example is a car muf m+ n4mij(0 l myx69f48yphulwia+ld-fler.)

Why are the frets on a guitar (Fig. 12–30) spacedsze() .wi s8nhqgc1,y closer together as you move up the fingerboard towae. s,nw)ys zg8ci(hq1rd the bridge?

A noisy truck approaches you frojri pnuf8jh9 uo1/ : +6k8p0f:vkswrw m behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sup jj0w/wu9r8+u f 1k6 8kip fh:ovr:snddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said e*/uyr9 wqyulo ai6-jvb0ef4 ul+u)-e1sv f1 to be due to “interference in space,” whereas beats can be said to be due to “interfereflwue )v raly*b-1+-vusi6e qju4 fe90 o/uy1nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers wewhl; ypy//;g;vdbow0re lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer topv lowyb;gd/; wh0 ;/ygether?

Traditional methods of protecting the hearing of people who work in areas withquz 2q 4jzff/7 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 reducz2uf qq/zf7j4e the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supnrw mnnd1n.+md/ 5cp( erposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), arndd. r/nmp( 51 wnn+cme the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thlv5 3shq7o.q mxtlm4i6o-tl +e same direction, with thtqq-l3 +s46lo7t. m lx 5ohmive same velocity? Explain.

If a wind is blowing, will this alter ab;vqn+djs 1xf h+ jp n8b sm+dgy(5:-the frequency of the sound heard by a person at rest with respe8s1d -s; fj p +nnx5jaymq+vdg( +bh:bct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a cxghk, p 54j:4*f5fw j8cdtk lfhild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which pospk8 ,4lx 5j*ghfdfkf :4cwtj5ition, 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 l27w - ml1bdlk1mik7tiistening for the echo of her shout reflected by a cliff at the far end of the lake. She hmk 7b d k71llii1mw-2tears 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. ydmb- 9gfw. vk m/, -whatow:0He hears 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 not vary significantlyhwvo0t m w9g--mdbaky/ w. ,:f with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air elic z3m y0j2gyp,5m 6at 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 o rn ey1clh/0 u3xf4 (eprcxx7.f tuna on a foggy day. Without warning, a73nl41u0xepr (hx cyc.f /erxn 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,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when + -dwo*jfz ;yx x+(xc: mem)yostriking the water belwf)yeomxyoz+:+x- d x* ;mj(cow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to th5s9)u)0h;gr +qhenc 6c,ghieff6 cyqe 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 th0icn6ferh)gg,q )c 56;+ f9uhec qyh se other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ov p0f 7v+ce.loa.3i5nwjeb /qi er one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temowq/5eial0 ep3fni7v+. cjb .perature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a 4lo;o krsru2k x 4;t:msound 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 j9me zccc,+x 4sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firo5l/r6uk4 a ksed simultaneously at a certain place, what will be the soun ul5o/k4kras 6d level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from1nr49 (gtkyij 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 i9k4y j(g1nti rntensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 5r v, a4rtbwj118 dB, whereas for a CD player it is 95 dB. What is the ratio 4tr1j1,bv rwa of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converswp.kov) 9 i2)p k4scya9psfy-d9j e)cation. Use Table 12–2. Assume the sound spreads roughly i 29sk)s)).pya cw9d- cjppvkefo94y 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 whoseup)l/.hev7c tq z(k e1 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*lca9q 8ca*3eta uha0 9bpd)jja 1v,f rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wj0**8daelhcup at,vqa ) 9f319 cjabaould expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB+zcx20c z l.md4hh +qm when placed 2.8 m in front of a loudspea+4hzdmx. z chcq+20lmker 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 difft .4*+uu lpjwperence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by thw*+4p.ut pj ulis amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) ayc2u6z wwesg u8u7 :p6n ,cr+by what factor will the intensity increase? Incre pn yc ua2e7ruwc+uzw6 s6:g8,ase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice k fhxgb *+*yvq5s10yk ab4vx+the frequency of the other. What is the ratio of their intensities?14kb0a *xx5k +*+fqvv bsgyhy   

  What would be the sound level (in dB) of a sound wave in air that25rfq f/;sz k )a,kpum corresponds to a displacement ampz um;k f2sq,fr/a)k5plitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone tha+ahmw(y dkui zh43 x8g yuzp 7t:)gt(7t has a 50-dg8 um udwg()+px4z yk (t:iz7htay73h B sound level? (See Fig. 12–6.)    dB

What are the lowest and highest freq(6l t fs4vbys)uencies that an ear can detect when the sound level is 30 dB? (l t4bs(ys )vf6See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the rrx8.:hx4jsb ;k(pg f patio o8r ; .pg:f xj4bpx(kshf highest 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 440 Hz. The length of thufci5 qz(p9w/f(ajg 6t56cope vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the t/ppicz u5wa6 g o fj6c(qf9(5string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and fi27y eei/s mb-jrst three audible overtones ifj ee-7m2s/ib y 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 y2 fhax: ef;-t co*yfs0ou expect from blowing across the top of an empty soda bottle that is x; -fcfet h *0ayo:f2s18 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 org.gnuv*u z .bj1an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what wub*u g.. zjvn1ould 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 harmonic. Whavmop(na c+di/6:e ii ( e6r3yit will be its fundamental frequ/ce6r ipo(iy e+ 63ndv(a:iimency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunedivyqr:k7 o;v .8h-k-dl u sz7u to play E above middle C (330 Hz). 7su uk7zr --:vqvy.dlkih8 o ;
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wh+nl6 0sb-mftqdegb1/ en the temperaturtm+q/g bsb - 0ef6ldn1e 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 20 m hb0og7 x*g a3b(v6vt$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the h aues0za i4 :vflab6/4 p7+nkgole be that muna7 +f4 a4:e0g/6uvkzsibp alst 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 *emh hxw xs,oi-7 4yby.v/q:v 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pi syxxy.mqv*:wih/4e,bv-o h 7pe. ----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 yk4lgnho32 8 bends. It resonates at two successive harmonics of frequencieog3n4h82l b yks 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 4z af th-rah2nia56y9$^{\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 aud93ddk40iqfw l ible range for a 2.14-m-long organ pipe at i9l3fkq w4dd020 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal islj2nmk6 n2h;q; ,uobz approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6?;;22nq ,kzjo6umnb lh $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to wxnv4wd-0. bb adjust two strings, one of which is sounding 440 Hz. How fbdw.xv bn4-0 war off in frequency is the other string? ±    Hz

  What is the beat frequency i liz-5o phy1(+jq2h3ct9b pfdf 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 operbhx vl: 31rg kw5gd47jfq 7hl.ates at 23.5 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, estimate the operating frequenqlhrg1lw 7v .h4 k3bgj7:5d fxcy of brand X.    kHz

  A guitar string produces 4 beats/s whe y7fq7zfrwc. 6n sounded with a 350-Hz tuning fork and 9 beats/s when souf.zq77cfr w y6nded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension t)q)xc3g) qj1 rb+w sns1ozn8in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hins s)b znr3cg18xjq1) qw+ ton)t: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play hm3gc30 f.ccx1e7s s jmiddle C (262 Hz), but one is at 5.0°me.s73fg 3 ccsh01jx cC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of y3o(w7 iqm4l 4kuak47f obb5a441 Hz; when A and B are sounded tok5oa743oq7kb 4wb4 fiy ua(mlgether, 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 sta 1p had: zac1r+d*r4wonds 3.00 m from one speaker and 3.50 m from acrzd o1h*a 1p:+wr4 dthe other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a uoss lw:;tq; f. 0oa.-h2bglupiano tuner hears three beats every 2.0 s when theo0 :lh.2oabug;s; tfq uwsl.- y are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelen8lleea* t,b5rue:.vs gths 2.64 m and 2.76 m in air. How many beats per second will b evs.e*r,eaubl8l: t5 e 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 when at rez8r5r3owk h f4st. What frequencyk485wrzorf3 h do you detect 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 i2jlz5mp(zl; you detect if a fire engine whose siren emits at 1550 Hz moves atizzj( 5m;2ll p 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 toward you ua5 qh4vc- -k* fwet9sqkfcsv+8-u 9mat 15 m/vs k hm94 *c5tkcqwv uf-9faqe+-8s-us 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 withh -jnrn+ta*yk:d5o i -om2a+sbdy6 2q the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the drrq+hmny :-5d2s-ia2okd*jn6b+ oyat iver 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 th.zqv7 wspfg cvu4 g8w2+3ka3 jem return2v 4+7pjgwqcz g a3uks.vf8w3ed 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 spee4 q5i9- m*: zi2 lyzzejq cqqwxa/-0lrd of 5 m/s As it flies, the bat emits an ultrasonic sound wali 4q92xzcqi0 /l:q*-wyzj ezr5q-m 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 moving flat t6hwd emma 6.vl3/ys 3fh i1y3prain car at a frequency of 75 Hz, and a s ./yvmwsyfh33h1 plia66d3m eecond identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow lb:p7 suc 0c :w;g4lrpspeeds. 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:l7luc4g0br; pcs pw : directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o3(yw.ebk n0+1cp d c geof3f)ef 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 5:x: gy gm.ni;eqz)ke 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rgyzk 5) e:geiqn:x;m. est,
(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 lany+*r c imsy)2 :.lfjmyd 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 3ozti u0; sm8pi5k+l 1;u+z+e vr .jalz10 m/s (a) What is the angle the shock wave makes with theiu +;lzejlzirv8;+5p. a + 0omt sz1uk direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed 1b6xx;/;hn,gjnkqn 7 nvrk x: of sound is only an;jn, :q 6rkx7b;nhngv 1xkx/bout 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 ocean. Determine the sy zxtg- dbe *-0;qhyej(l:4pr( k 7usthock wave angle it produce0*((bx th kz quj yl7esd-tgpy: ;-er4s
(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 egcl ifur:5)/j3;lj n $/theta$ 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 17ja ewv2s; 2ql.5 km above the ground flying faster than the speed of sound. By the time you hear the se22s7lv wja ;qonic 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 dewc);y7j4l timvice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth f tlm7; 4)ywcijor 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 human audiblw6jwm*3uy7d)qa v(i db i2rg 6e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disprjm1(ppb u 3g7lay called a sewer pipe symphony. It consists of many pm(pbur71 g pj3lastic pipes of various 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 close to the threshold ofjkbz5g3 8h8nc r vv7; fkb/i*l human hearing (0 dB). What wkl7;jkhv3izf *bn8/ 5grcvb8 ill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundmd6 nm.q(gwk6p/ gf ,bt6b/ vf1 opr7:sg+qvc are heard simultank7sfo/grm cqfgmv d p6 (vb+p/tng1b.q:w6, 6eously?    dB

  The sound level 12.0 m dbn5xm +x5a1/ f0gvhcfrom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) bx+5 5 adm1v0fn/xchg of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropssqai:ai+c: d tv ,xn/(j2c zp4 bia ts,c4xvpq(d+: n j2zac i:/y 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivy51 pqoa8l6x.q 9bpdl e devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a j bl89ox. lyqp516adp qet airplane engine?    W

  In audio and communicate) -esa7scs hu5vb0 mf0;(t1 2n vnivqions 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 tunan- x6tlj0fa52gmqb0 k;8 a(vve yoe3ed 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 cm long between fixir671w 5gxcfk ed points with a fundamental frequency of 440 Hz and a mass per i1r 7 xcg6w5fkunit 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 tube fi:xsss i ub51o5lled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. Ws5b:s1xi 5so uhat is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that cksl9hs.(u 5 zis open at one end and also 75 cm long. How much tension should be in the string if it is to produce re5slkhcsz . 9(usonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observedt* tct9gnr a1;wv:7o 4) c*gebrcb( bo to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range x,pbxr-qr .90vl y)wf coming from two sources. The sound is loudest at points equidistant from the two source9 xf0q)xr.y plwrb -v,s. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statiui76hj e0ds /xd,x oq,onary. The conductor on the stationary train hears a 3.0-Hz beat frequencyh x0idexq,ds/oj 7 u,6 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 is 538 H+fo ;gsz/k3bw z. After it passes you, its fr g3szokb /w;f+equency 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 cars just by liste bo 8e6(ipagv/ning to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of ab /8pe6i ova(g 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 toge5a:7y, rfgjka s +5urzther, produce a beat frequency of 11 Hz. The s u ,rjfyk57azag+5:r shorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car a4loi3 irof1t6 s 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, (torifi4o 613lb) 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 y15xnn ddpg a k.f7/rpw-8 ;aain the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MH5;1 r nw8xak py.af- /nadp7gdz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth- u 4;v6m-w.jcz th4p4vhu d dvw2j-w.jae3xz is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detem 3a;w-4z 6 puvjd-jjhwz v.-x4 w .42duhcvetcted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pqru6+l vlsdzu/64n b0 ulses 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 the bat so that the echo from one chiul0 svn qd64z/urbl+6rp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa3;)m(u 8 lmosonwm4ig s 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 this horn, and which overtone is close to F sharp? (See Table 12–3.) Mods on34wulm (migm);o 8el as an open tube.

  Room acoustics for stereo liskzi +bx84;pf wtening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m higwfxiz p;8b+k 4h. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long,yk hvit,6q 8xc-b ms xxac5f4o,d 4e:, 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 sound6xtv4ko ,d:eq,4hbci , fsx -c8maxy5 . 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 ths d pwrayo1q*rms5.*6 reshold of hearing for the human ear at a frequency of about 10*qws6 a ypmr.d1*ro5s 00 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 observer on the ground hears the son 9y (ks 1 hih**q+ydlq/hise/mic boom 1.5 min after the plane passes directly overy kqd1 li*i/s*(hmyh9s /h+qehead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 potn-xj r+bs6 7-5orgfvx1 p -$^{\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