What is the evidence that sound traveldd ( -r4(clryvs as a wave?

What is the evidence that k1/izb zyeq+1gx+w eqat ueumh;24+; sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a sthpj 6+ac mmc:6ring 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). Explc+:cmpahm6 j 6ain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from a4px f.7nzq v7 ty,mqm9x e*q+xir into water, do you expect the frequency or wavelengtm,x 7+yxv*fxq4zn 9 mq.epqt7h to change?

What evidence can you give that the speed of sound in air does not tc:fv+bj0;;mjrt (sug13j k8o h- u oedepend significantly oo8u ; ;(robj3j+etch0t m1ug:ks-vj fn frequency?

The voice of a person who has inhaled helium sounds veugd en 3cbtfgsmb5 -. ();hez* j)jq.try high-pitched. Why?

How will the air temperaturej tbc6/-j3kd8l ;ch-nxd1qbt in a room affect the pitch of organ pipes?

Explain how a tube might be used7 6+v 4gkgqwmq as a filter to reduce the amplitude of sounds in various frequencyq+wgk7gmv 46q ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced clolnxny-b9 8to; ser together as you move up the fingerboar9o8;l tn-xyb nd toward the bridge?

A noisy truck approaches you from behind a building. Initiallyj.e g,h6 /rbadvks7p) you hear it but cannot see it. When it emerges and you do see it, its sound is suddehv ,jgr)akeps7 .d/6bnly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in spacepljws8f qd 9)7/s /qpj,” whereas beats can be said to be due to “interferencqjppsfs d9j q7)8l//w e in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p3yxnmm g smr/lx:d: *j.2qfw)oints D and C (where destructivenmm .rx/s m:gx3y:2jlqdw*)f and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas:ba d n 6,dv1;ruhb;ys 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 noiserddvy: babus;, 1 n6h;. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as e8+ iqrhp8 04 cz4eyngc 71zifa superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Ezr8gi qcyp4z4en f h18ei+ 07cxplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the qhzrk9;.l*pgob*wq gyn; o.gz d/ 09jsame direction, with thjl.p;w0 gd zok*o.qh /;*9zyg rg9nbqe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a persf :h6a4 1kxpjnon at rest with respect to the source? Is the wa46nh:p j1xfa kvelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swinga*mz p:60qbm v. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Ez*6mm ap0:vb qxplain your reasoning.

  A hiker determines the length of a lake by listening for the echo omn pqhaq .agi7 ,-ge2kd tgi4:u. moyem44p+(f 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 a.mpkp igq mmd42.ogi 4t:,+a- hu7qgyne 4(elake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just beloz1o oip )9fjbn4r,f3hw the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.pjo4b)r3n 1,fhz9 oi f5 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 iy-fz9yc1qjcu.;a7 0vz/e pbnn 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 sk4wg m.eh u m1uqq2t56chool of tuna on a foggy day. Without warning, an engine backfire occurs on m tq . wegh6uqm2k1u45another 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. Thegif/vd10- kpj splash it makes when striking the water below is heard 3.5 s later. How high is thepdk i1v -/j0fg cliff?    m

  A person, with his ear to the ground, sees a huge stone se/hq t7o7h7g6ohi *bktrike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.7 ohki/6 be h*h7gotq7$\approx$    $ \times10^{2 }$m

  Calculate the percent error made overa 9 rc0ou,1ltf:b4jcp one mile of distance by the “5-second rule” for estimating the distance from a lightninflr0aoc t1p :,cu9j b4g strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a k7hb,z r2fgb* 1ps1zvsound 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 tkz-z/3v n , alhjb95rintensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce hil*7mtgej ++ ,(ri(plnxua)g 54uuia sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint(x uhpute ujr(mgn,+ *)75ii+4lgial : Add intensities, not dB’s.]    dB

  A person standing a certain distance f2 h2pdjpdr7dn - 0d8iprom 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 eng0d 2i87-jrpdp hdpn2 dine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ramkx,bgs1 w7b,)a 9tq.nx iq) r)cwqr:tio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of q) ngbr:mq7))aqcxx, rk ,bws.iw91tthe 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 6zew bmi *7rkslu5 o/0tp h8rux/x k;ww1cv 44conversation. Use Table 12–2. Assume the sound spreads roughly unp/w5wu sxhvbl*ux;kzime0k r1c46r8t w74o/ iformly 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 704yb+bei +5pcm uuhueardrum 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 modest amplifiprli7nx9(q 6g3) azcx er B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to eacl7 (n 396xircxa qp)zgh 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 met)t6ne fm8)zaxag+kh 3 er registered 130 dB when placed 2.8 m in front of a loudspeaker tme6zg) +n38aaf h k)xon 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 die a(dt4+gq r e (0ncrexybueer401w)8fference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levr( e40(wr041e )ut+e8 axe ebdcgqynrels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factorbt,t /xg:e.h m will the intensity increase? Increase by a fact/h. m ,te:gxbtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacx e. k*q1q f+vq hsm4ip8r9+rpement amplitudes, but one has twice the frequenq9fe pxh.+p1imk8 s*qr +4vq rcy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresrnk,tq7qu lar 026bq; ponds to a displacemena;,70 ukb2qlnr6 qtrq t amplitude 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-Hzaet-c07t q ph q-zq0c8 tone that has a 50-dB soun cqc0a 0-ttq7-pz8qh ed level? (See Fig. 12–6.)    dB

What are the lowest and highest;5*buyaf 7y,0zlp h le.zrdd6 frequencies that an ear can detect when the sound level is 30 dB? (Se5 hy dl6pezf0a *ry.,7b;ulzde Fig. 12–6.)

  Your auditory system can accommong-r6 k ha4sq.:a1v,b;iy wapg6h*omlmp: /ndate a huge range of sound levels. What is the ratio of highest to lowest intensity atsr:npv16 a.g;* /ohm a64bamhlw,kgq-np i:y
(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 *bl;mkcdo8 k5 -i*zslof 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension musms lc -*k 5idk8;bz*olt the string be placed?    N

  An organ pipe is 112 cm long. What alum*h.figf8j 92ab) k re the fundamental and first three audible overto) a9*ji8mguf2 hb kfl.nes if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the ta g w3z c bup)ym)ky:*38as,z18 hy4a8sbfmcsop of an empty soda bottle that is 18 cm deeza:wgbm8au8bs 3hafc1 y 4 k*psymy c83)), zsp, 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 oq d*f2q ;(;mx9hxyqzcgnh5 m *rgan with open-tube pipes spanning the range of human ; ;xc qg2( * hymdzx9*qqhmn5fhearing (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 harmo:y au ux2qp43 orvm(3l-r-mflnic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origi-ufl3aqlo2 : -3mupxy r(v rm4nal length?   Hz

  An unfingered guitar string is 0.73 m lsoo;d(* 5farlong and is tuned to play E above middle C (330 Hz).s5d rfo( lo*;a
(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 lehe 6fmeup+ht35j )ab*q -oe3j ngth of an open organ pipe that emits middle C (262 Hz) when the 3m6 -ftbhhje+ea uejo53p)q * 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 a3c7b3ycir+w, t+8 hlp iblu4et 20 $^{\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 hole be taqz 8 k,u qcy gfx;(gx b2/h9:wum*xi2hat mus:98x acu,muyiq g/2 qx2b*(gxkw; fzht 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 y(y+ntm n6wq4sjtc9; resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this;nyq 4 +9ct ntsymw(j6 is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both endf tkb)0;;4r wgs1ac dvs. It resonates at two successive harmonics of frequencies 275 Hz and rw b)04as;vfd gc1;tk 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 yah:y)fh4y)1gsz ,be $^{\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 prf)4t zjo jfsf57y9 +jv )ccm-eesent within the audible range for a 2.14-m-long organ pipe at5j4fo e tcfvms )7cz-yj9j)f+ 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apprsusxj)7qgt:xfqkozrz-r : 1y+: (u+qoximately 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)z jrqzt1k(f qx: u7ysrqx g:)su:+ +-o 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? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when try*le *dsob5 6s, v)wbrping to adjust two strings, one of which is sounding ) w5o*blser,* pbvs 6d440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C pgw;z bd l1 ftj3y)24a(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 operaiknu,s ;+6uu(5onk b qtes 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 the un5 6o k+u;uiq(bnk,sy are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wily nwf+5wgu4, th a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the viywlfug+wn45, brational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tud bgwbmy7+ apkf--zce 19zv0.ned to 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 played together? [Hint: R- 7-d9g.yb0zc w ev+kmfap1z becall Eq. 11–13.]    Hz

  How many beats will be heard if two identica (n9qtrn *wu7:iss+zn l flutes each try to play middle C (26s zn:9w*q (st7u +rnin2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning vm2 3n 19xamcvforks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequenc1v mvxamc2n9 3ies 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 f: 9(v cgijuux0rom one speaker and 3.50 m from the other0 :gucj xvi9u(.
(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 areo+ :fas*i4xxpy3g -t9zxa1zs supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one p+sx zx-*gx4s 9i3faa:z1o ytis 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 air. Ho1hakxd,h) vo6ufc d:q+)qq,h w many beats per second will be heard? (Assumaoqc:,1 d kqvu)6xqh)+ fhh d,e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaq,laom18w;-p9l zctig z(rj3 ms /z(fin fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if youmm-ag ij1fz z3 /(p;rt8,wol9q(l szc move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect p.ie1 5bbs yv s;psy6-if a fire engine whose siren emits 6s5 ivbppy-1.;b yes sat 1550 Hz moves 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 tcw6diwrz. t 1yfm -2agq 30lb:oward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sa 6:fq0m1cr3yziw b2gwa -l.tdme? 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 hf9 ms/x2i7mgthe same single frequency horn. When one is at rest and thx29 m 7mh/sgfie 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 receimc,sjjt7b j v31d3hdx/3x7 teves them returned from an object moving v hx3 mbts 3ex/jt3jddc7 j7,1directly 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 5v d79l5pi tx3d m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does th9d vtixd57p3 le bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pla(wr fb2 t;(ao.n3 fngn:db) (spbqma /yed 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 frequencdr fp. bbtnw3a sf ;)(2(gq:n/m(bnoa y was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves tkftp6u*s8.f :)lrbdn o 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 8fut s:* f. pdlkr)6bnlarge leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wasxk 2c u0q-sz*ves 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. When tximx;1k )blg, he wind velocity is 12 m/s from the nor1),bmk l; gixxth, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if r8aoj0o l6 z fp/hn/jk+* (bxfits 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 sp b:c;6itz lva4eed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s moalz:i;v6 tb 4ction?    $^{\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 atmospherlkay0 / y:+x(ed q4ahve of a planet where the speed of sound is only abh(k y+ vdyxa/qae:l04out 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 shock wave ang8j rh eqopb,:a41a dz w4vf),vle it produces a)vwda bhp:r 4,qj4 ,8fzo 1ev
(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 -in:g;ac:az7*zahhqq3e 8 ni $/theta$ 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 exa 0(4ou;+ohdsn ks mtg+ctly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 k(4; d+ sh+utgonos m0km. 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-Hz sound pulses downwarm3+*mpj hu*vcu -pwvjs,iz(s v7 g6(k zyo)( nd from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desi3 )* j(vv,u nsmohy6pm j- vzi*k 7uwzgc(sp(+gned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octadin(ftfmtc )4(hi 5m6ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists o nf+/v0-w yw4odn;k/u4t iao df many plastic pipes of various lengths, which are open on both ends. a;vwo t/n fnd/y0wd kuio+-4 4
(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 personc-hr v q9 hrgo:ot4t8gp 4e0k.1dhjw8h8z/l h makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such gl gt4cw hh08 .qrhj8p1r9zho-o/8 : hv4dtke mosquitoes?    dB

  What is the resultant sound s;bkwr34t l(fiq us. 4level when an 82-dB sound and an 87-dB sound are heard simultaneousqsl.4 u4r3tf; k(siw bly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 .9oc +nsaptl 7e3j(/: vsmv v2rzi 4ncdB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direc7mc p+vn4/3o2vv :asn sr9 . izjc(etltions?    W

  A stereo amplifier is rate9 7)qvcr(pbpa,f7 y tdd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power oucf(7q9p atvp,)yrb7d tput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wearaugu(dd( ;3*divg 1ca protective devices over their ears. Assume that the sound level of a jet airplane engine, at a diada ( c13uvdg;i*dg(ustance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicat*yxrjxh( 373wq uuv e;ions 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 :civebzoqe,8s7 7 ea32v8ocsis tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wit) uxb5xg bvt-vi /v2c4h a fundamental frequency of 440 Hz and a mcvv)u4- bb5xg/txiv 2ass 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 vl5bcas8g1q c0 ibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again ats58bc lg cq10a 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string orm3xm6l:s9fi u1w: zn f mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should iul6wr9:xm1 3zs:nfmbe 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 ohy*2(n9l0 y-- qwjhq j.zca wtbserved 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 coming from two soupplg afc7;rd;g0xp)p ; nm +-xrces. 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.xma-fp;ndpl )0c; xg7 +;gppr34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on t/ keynys8d 4(y6s(q pb 6f6grvhe stationary train hears a 36y((sdsfbg4y 6q/6yevkn8 r p.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approahhxqw2d2 eppj 7o /+sh0)hp1oches you is 538 Hz. After it passes you, its frequence/xos0qwo p12hh)j 7h d2p+hp y is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate theo.cmbi7kze8 t6q r1z ) speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goeiz z 786)rmoe1cbkq.ts by on the straightaway. How fast is it going?    m/s

  Two open organ pipesn(w.,f lyhmbd81c o +i, sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 mylbw+mcdo fn8,.i (h1 long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pasgnmd; qx+m1 (st 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 (1(s+m;mx gqdn c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aort wb7if62jpgng* d2w.x a is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wa72. gww id 2pnjgb*xf6ves 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/c0ba0uy *uafr- 6h;e ss while the moth 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 detected by the 06 ech*uyba0a fsu;r-bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as -ja+.hmj l+0duw wdqh5c5t u, 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 chirp returns before the next chirptw0d+qml5-c ah +.u ,judjh5 w is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to senhp.y 1 oylcf ix*0,b(*yb.sqad 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 rxas,q( ..1byyfc*h yilb p0*oesonating. 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 presence oeu t:r4f8x5wtka- b,c f 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 funet b54-r8ukxcw ,fat: damental 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, slezli k65r6x-d+zqor o 9nder aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rr6-dz5q6rz9i +klox o od 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 thokj2t4y7 k9d ue human ear at a frequency of about 1ok 9jkd47t 2yu000 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 gr2;iq3dst up efhnw5 .5ound hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu;5e.5qf2p d tui hw3nsde?    $ \times10^{4 }$ m

  The wake of a speedbo,hyyx.5gmli f.d*k q 0)l;ecoat 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