What is the evidence , oo0oo*0x- ttx x; rgef-;e2uxhg:od that sound travels as a wave?

What is the evidence that sound is a forxucq8ku8gu ox9.z s((m of energy?

Children sometimes play with a homemade “telephone” by attaching a1hko8y::)rnvlze z g / string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. l kz)g 8zre:ohn/v1y: 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air inigw6ggtf6 /w1to water, do you expect the frequency or wavelength to1gwi f6w 6t/gg change?

What evidence can you give that the speed of sound in air d 9e4t;bw1gpbbr vt,( uw(i ;wcoes not depend significantly w bgr,tw14pv(b;it(;cuwb 9eon frequency?

The voice of a person who has inhaled heli3hn8 nu1qz(7ipno5vgj5kqn7e2 )p8d yd m 2k pum sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pis;b2e p4(1wu 8or czeapes?

Explain how a tube might be used as a filter to reduce th f+n0or;wqq1 ye amplitude of sounds in various frequency rang o n+f01y;rqwqes. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as youx+ozs8o .: avu move up the fingerboard tozoax8u+o :.sv ward the bridge?

A noisy truck approaches you from behind-;tuav 5*yr sn, k sxlquu*67z a building. Initially you hear it but cannot see it. When it emerges anyqu;,al5ns*x -7v*rz k uust6d you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen5x 5 n1wiyjklo/y+j tlj 8m-4yce in space,” whereas beats can be said to be due to “inte -j815+wykynij45joxy tm l/lrference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p2 vkfu 1b tvbg.ml dz*/-m4x1xoints D and C (where destrucm/ugbxvxm-4k11 z *2b.dlftv tive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hevfu0 z o0:rkm5aring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detezuf 0k vrmo50:cts 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 i hw * :i*qei+l)bytpp0bd/0ycan be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are thb0ylp/h )i p*q+b0d :tiye*i we two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obs rt/fku20r -(bu/cwuwerver move in the same direction, with thuu2 (urr/w/0c bkwft -e same velocity? Explain.

If a wind is blowing, will thisn( nb)a8tf8-z i4oqb u alter the frequency of the sound heard by a person at rest with nz8bout 8 )na-f4(qbirespect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child z.j r92;dgrlpin motion on a swing. A monitor is blowinrdl .9rjgz;2pg a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo f / x nerrr0tjnc;r2.*b(a(dn of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shoutin .c;n dtn* 0nfjrex(rr r/b(2ag. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the eci1:fneqm 73v 2xpq 2 o4k)j--k *twmwkwto7rdho of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speee4q 7rxk1p-3 o7jq* t f-d)omktw2nvmi w: 2kwd 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 20 -l.kg vhltslyw87--m $^{\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 abokye w:g;j n.,e sr:k:,a8kneove a school of tuna on a foggy day. Without warning, an engine backfir:jk,yrs. gna w8 nkeo;k ::ee,e 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 clifa,i cp mik- ,9;k:zcp7rcw;yi f. The splash it makes when striking the water below is heard 3.5 s later. How high is the cl wi9p;myi;7 c,aip:,z- cckkriff?    m

  A person, with his ear to the qk2y. y7;*mb divchdo76: crnground, sees a huge stone strike the concrete pavement. A moment .hkq6 7*i7rd; mcy2vcd:yn ob 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.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-sec9c o9 bqkobf.u5su k jv; vv*moj.+:w;ond rule” for estimating the distanw9v ob; ;jo5o. 9vbv+kuc* us.j :kfmqce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of pd ((q) rt jhw(so8)ira sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sn 4wijiir bn 2d(k+f*1ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95. gdzc1 re2kv, dB when fired simultaneously at a certain place, what will be the z2ek. d,cv1grsound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance fro(-b;op zpj uf4m an airplane with four equally noisy jet engines is experiencing a sounp- f;z j4ou(bpd level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBe7 t gte(j/n-m;tf d/g, whereas for a CD player 7-de(m/g jt/fengtt ;it is 95 dB. What is the ratio 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 speakinnkkh ie h8*-gss, ;6:ctwxc8e g in normal conversation. Use Table 12–2. Assume the sound spreads rough, :ek6e;xh- ckn8s hcgwis8t*ly 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 +cse ohw0, o* 3 -wpot:uv:bmfan eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier kprs 7- owgj9n* /4kpdA is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound levelkspgw7p-d/ oj*4r 9nk in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regd ipxqkok,lq4 *3/r +mistered 130 dB when placed 2.8 m in front of a xk *lp+q,/iq3rm kdo4 loudspeaker 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 dktq 0,vuqfzs9 (r6c:v etect a difference in sound level of 2.0 dB. What is the rati s6fqc, q09vrz(u:vtko 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 tbmtf+ - bl55en2:s on03lheu aripled, (a) by what factor will the intensity increase? Increafs +0b lub3e n52o ahe5m-ntl:se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqleh 3zl8 5v -j-kzrfh,ual displacement amplitudes, but one has twice the frequency of vkfrhll5z j -e, 83zh-the other. What is the ratio of their intensities?   

  What would be the sound l5kr4/9 syo meo1j2jlvevel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz y9e5/j24o vmko1 srlj?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-a-9d7b7tmpxobk3 a/jy 0l 7bvHz tone that has a 50-dB sound level? (See t 977y k0-a3bvmbpa/jlx d7b oFig. 12–6.)    dB

What are the lowest and highest frequencies that an ear canavh9mc hv5p.e9 h;l :y5p0c6g 7xockw detect when the sound level i hc p0oeyk ;vph6hw9xg .m7 v:l595accs 30 dB? (See Fig. 12–6.)

  Your auditory system canc yt9thc;upn1l94jv/ 3z; jiu accommodate a huge range of sound levels. What is the rat/ ; 3vujhu4 j1 9tncz9tpcy;liio of 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.nxoa 5wd6x* wwg+(e 0f The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what te+gewn*d( o x6x5w0wfa nsion must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible ory3-+ jl wdl0a hrutfx0qq6/ u-2 ejr0vertones il rerxfju+ l0tqq/0-ua0d- rwh236yjf 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 :c,+fe:kzr li5nly h;top of an empty soda bottle that is 18 cm deeprci,+:;5hzylfl enk:, 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 qtk kdac-+10c8 :q thrwith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ran1dk:-+r80tqqcah ktc ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frss)e1wg9 k*)vg oqd3 o1xqjm5 equency of 540 Hz as its third harmonic. What will be its fundamen1mqxwd 9*g)ko)se oq5s j1g3v tal frequency 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 tu9esm4yzc +s q4ned to play E above middle C (330 Hz).ss+4y ezc9 q4m
(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 p:qm-xdn 2/ssgipe that emits middle C (262 Hz) when thens -2: dxg/qsm 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 atrw)uja5cb/hnc6j 2k tti9 5t. 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpii2 m88 ih2sfuuece of the flute in Example 12–10 should the hole be that must i2 8hm8u suif2be 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, :v3 o(g)e+zndvnn jg(440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thisgvnndzjv:( ( 3oneg +) 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 ) g;v)ust8fwvm long is open at both ends. It resonates at two successive harmonics of frequenciess wuvt);fg8v) 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 19bl jglrrdr0 l9;6gm$^{\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 tb+pss k(c5 k ke,0koo)z( jdv4he audible range for a 2.14-m-long organ pipe at 2cke)z( pkkvo5,sbd0( ko +4js0 $^{\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 tjdzl; ex8db.+n; kc1ehe 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;l8+xcj d .de;z 1enbk 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 etw bb7jy74k m) lop84every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is tk )y7wlp7jbm 8e t4b4ohe other string? ±    Hz

  What is the beat frequency ifpkxta25b5 c1p middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates atd+yx k enc0; p))zh-ji an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 50e0;ixn )kyh-z+jd p )c00 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/sq/ b2hdo9rcr+ym k9+ t when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hr 2ob +9trycqd/h+m9kz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fr2 u5 d a38ujvpkzpc *ddk;x)j5equency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strv puczd *jk2)5pjd 8xd3 5aku;ings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to plxm zfq-,9rwt 3ay middle C (262 Hz), but one is at 5.0°C and the other at 25.tf-wx,q3 z mr90 $^{\circ} $ C?    beats/sec

  You have three tuning fork em .h0gsh)n bcl7u-:ds, 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 i b).dc0 se g-7nmh:lhus 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 n1dd9ccx hg 2ychgm j g 2:f*v5:b;zi;m from one speaker and 3.50 m from the other. ; cv5mgdhi9gx:b*g1 :;cjh yd2cfnz2
(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 vagu afy-0lbuki:07g4ibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together.4ag0b l a-:uyg7uk 0fi (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 waveo8a 1i2 c.ngcrlengths 2.64 m and 2.76 m in air. How many beats perac. 2cg n1o8ri second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain firjazxliya(jm lq,f * -7z 0i+5ke engine’s siren is 1550 Hz when at rest. What frequency do you detect if, fzxzji(a *ak-m+ iy50llq7 j you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire ezn g2yaq+i e6)ic uqhqt;81+ongine whose siren emits at 1550 Hz moves at aq86 )ict+n zhg e;oq1yi2+qua speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency i7cb*/xr9d g pgf a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the * xb7rcdg g/9ptwo frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single f nnwzdl)39y-irequency horn. When one is at rest and the other l )3niwzn9d- yis 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 ultrasbfc*(h9 hw-/c6 oy uwsonic sound waves at 50.0 kHz and receives them returned from an object moving directlsw 9u*c hh-c6(o/byw fy away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thcw mgdt*wm ,kenv x-1yzy.u:+ . dgm17e bat emits an ultra*gw mwzc1 eny+ ,-xtdu7:k.dy1vm.mgsonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pl*m.+kn. *edllnob d (hayed on a moving flat train car an* kn.emlbhld (+do.*t a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spe;r (gwgculis6p3n+s0ica1 6 eeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue6ar1w pu sgcec i(36g+;lins 0 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 from the sound source?   Hz

  The Doppler effect using ulwx/e9jct(jv-0hr. b ytrasonic 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 of frequency 570 Hz. When the wind veh.y/bjqr 8lt8 hmc)4*srpw/yg*g/s elocity is 12 m/s from the north, wy w8.g/trc8rlh*gsqje4y*m/s )/ph b hat 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 7 3zza/ 9z8c.yz njdmjif 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 utqh p-kk23ry4:n5 se 5yean,tbbudh5h,9v2 (a) What is the angle the shock wave makes with the direction of the airplane’s motion? q5heb5kb9 v: p3a, k ueths2du r45hy- n,2ynt   $^{\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 of sound s4ys wd:) 2nh3n ahra/is onlywshd2 3ra h/ y4sn:)an 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 p2)iin 1lyc3 mw:8sn)ig sqm5ocean. Determine the shock wave angle s) :wn315)li8c2syng mpq mii it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle l ys udnzouu,:94:8o f$/theta$ 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 grounze9 zq6,o ht)aey9 l)dd flying faster than the speed of sound. By the time you hear the sonic boom, the)q9d z6l hey,a)9zot e 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-Hz sound pulsh,pm q(ug77 wzi/cm:ies downward fromi/qzc7gmw p:ih, m (u7 the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are th9n2urd):jo gfere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphon5,v7bx2d foo mapm 2x4xq5bn 3y. It consists of many plastic pipes of various lengths, which are n 3m,bdabm2x5qfo75o2x4 xvp 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 personyw95yl ilzm1tf e/ .v0 makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitlw159 mlf.ty y/0iv ezoes?    dB

  What is the resultant k u8er8-bgg 1rsound level when an 82-dB sound and an 87-dB sound are heard simultaneou r g1e8-rbugk8sly?    dB

  The sound level 12.0 m from a loudspeaker, .xx2es sl1sb-)h-( xidle;v0 xv ec4j placed in the open, is 105 dB. What is the acoustic powebl (xvj x ie hev2 xssd-l.s4-x1e;c0)r output (W) 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 dron2o0 56zcs s8f isg5v(w1lkv+q up7nups by 10 dB at 15 kHz. What is the power output+8z (fq vpk2ou6uv0ilw5n1sc7g n 5 ss in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their g0+p03xq - jn1hsbu5xuajw9 aears. 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 th a0xwjb0jn+g53u1s9- aph qxue power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gb3/w4ivu/ hfc3wf akx 57 cms6ain, $\beta$ 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 frequentsc/snxv cz,y4 :a1t+mkq.m3de 4 /kicy 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 p mkwe v0w3t:gz0;bqo:,zlt :toints with a fundamental frequency of 440 Hz and a mass per unit length ,zt03 g;bm:k:vetqo0w wtl: z 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 invkj+o* ( r71, u uwexog*yl6rcto vibration 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 abov+ (1*gr6r e ,uko*vcuxoyljw 7e the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar sip79)jb pih, tv 1o(w+hcfx1 deym.sp me,89ztring of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the strof)bz (e 89set7m1 c iy+id9,1hx p,.hmpw vpjing if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reqv5 ;qvv5h ux2v., bmtsonate 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 ,.rm)w jsm2 tmq1t .qktwo sources. The sound is loudest atmtq rj2kqs 1wt)m .m., points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. jmzfj u 9 mqls*z6/8b7One train is stationary. The conductor on the stationary train hears a 3.0-Hz beatmfz 67ujqls /*9b8mj z frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistl rp/7:v5iig 4haao8 rdwk0u .re as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constau7/i85a 0:o4rhvria grk dw.p nt velocity)?    m/s

  At a race track, you can estimate the speed of cars just m4d +qgdztd2 -m*p5 vvby listening to the difference in pitch of the engine noise between approaching and receding cars. Supposem -v5 qt*g2m4zpd +ddv 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, sound.6vvh; ;.p1b cvi lzd)m:p xpsing together, produce a beat frequency of 11 Hz. The shorter onp; 1vvds.p;pc:v).bx l hm z6ie is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppositm3o;:wu28x 9qroy mgjd g(mi2e ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, aoqim8md 22 ;mojwur(9:g3g xyt B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.i00+ l:kkjb, z 9xgfoeoa6vcb r:x98 y32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the r9i :xog:ya ev0 9cok8, bx0jl zr+kbf6ed 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 mot1 4:an aw1:di vhsrh5wh at speed 6.5 m/s 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 bat after that wave reflects off the moth5 : wh:n1 d1wrahs4vai?    kHz

  A bat emits a series ofyz dwa,nd4i8x*g;l 7i t9at cjp1n,:r high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apar7zi*a;nw4rn,:8g dly aj9x,p idct1t t, 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 chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ongizct/ ose* ,gy)5g. le 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.) Model ass 5)gt,ilog .z/c*eyg an open tube.

  Room acoustics for stereo listening can be compromised by yol7 t*l s gvh8g9t5 ;8aez,xst fxg*q) ey0,kthe 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, andh09ftt 8,a g*y l5s8xgzsx;etvyoe l7)q*,gk 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,”vk +lefe8jq2)kf . /vi ktd50i8u5gkfq d-ku3 involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With /- 3 8l5v).f8i2kkuke fqf50dvitk+ uqj kgdea little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold ikwkxwe ud2*p en-7)9of hearing for the human ear at a frequency of about 1000idk u wp n-2ex*kew)97 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 sonicu)wb, u3;ik gmfa t6elf5tx(7 boom 1.5 min aft)i ft376bu5f,( m e;t lwxukager the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatc gl-yh6jod );+ nveo8hb4w/a 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