What is the evidence that sound travels as a /did3tcb)s z 1wave?

What is the evidence that sound is a form-anqphsu /0a2 of energy?

Children sometimes play with amjuml (rg..wl) 7i u;y6*wuxk homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the so6..(urjx m *guw7ikuml; w)yl und wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freq;z nvhf.szm29h cz1-tx/cjk/u/zg g2 uency or wavelength to zt/h2.zv9-m k ngczf/jxz gu;hc1s/2 change?

What evidence can you give that the speeds7vqasog )aov n2z0 j o6i--j8 of sound in air does not depend significantly ono 6i nv 7oojz2-g8as0a -qsvj) frequency?

The voice of a person who has inhaled he jzf9kp6n za s+b lw384ip5e1clium sounds very high-pitched. Why?

How will the air temperature in a room affect the qbw7hitoyt7q6 17 wwg/v 0i;lpitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of g,js n4(. adxgsounds in various frequency ranges. (An example is a car gndga. sj( ,4xmuffler.)

Why are the frets onyw: 1 c7zupah9 a guitar (Fig. 12–30) spaced closer together as you move up the finger:c9uy pwz ah71board toward the bridge?

A noisy truck approaches you from behind a building. Initially you heay6 a,jdsr10obybgdi- p4cwp5-v va5.c3x )s er it but cannot see by1y v0g.ai4j -w3s b,aec5 )sor- vp56 pcdxdit. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferekvz3wn u:,h 7i/9a zlynce in space,” whereas beats can be said to be due to “interference in tail9: 3uykn z,wv7h/zime.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wft9ffuj2c/ z1vebug5v4 8 bs- ould the points D and C (whergtbfe2fuzb1 v8-5 /jfuc4sv 9e destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work intbme9ml3 +rybn0/mcm w4 26ti areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise red tm+i 9tblrmwc6n m/ym324eb0uce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave tm/b*sd nbn5gml7fe;*6; 3 pimlnv b)can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of llpmn3*t7nbd)b ;v sm 6;/ i5nfg*bemthe waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obser9/0qzo46dcy legvh l 3ver move in the same direction, with the same velocityoc qh l3z/vg96e l04dy? Explain.

If a wind is blowing, will this alt16fo9. bkmfc cwzm5/eer the frequency of the sound heard by a person at rest with respect to the source? Is the wbz6/ e 1fk.mof59mcwcavelength or velocity changed?

Figure 12–32 shows various po0o (r r8nstb v:d*4jztyc- z: r4ho;orsitions of a child in motion on a swing. 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? 0 yb:t*v(j :orho8dr r;ns- 4z4 rotczExplain your reasoning.

  A hiker determines the length of a lake by listening for the echo of heri9he-kvyaiv/;)pw9*8 k;im do b bh1x shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimatevkoxi ;1-emyi b9*9; ha ik)v8p/h bdw the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the wl2w0rtms7b5side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at thi5r0sb t2w7 mlws 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 i*4vopj kf a.wrhbr8 b ./)wh1nn 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 f.lgx(i3 d;jsjust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–333dx.il gf s;(j). 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 60ez0 +b)n3 isvgqb23*mbcjmi .2u:dwh z qlysplash it makes when striking the water belz:q +jv2wbd2q*3l0)m zgm .iyenhcbus bi3 6 0ow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear :xb/l0w6 k qgkelc 2v l3z-f1nqws3f6 8i t7svto the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away : fc1sqvz /lll e w-3v6f26bx3 ktsq0ikgn87wdid the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent eqs vtz3a :gv l+8mjd6xc8bwjrp3s37 + rror made over one mile of distance by the “5-second rule” fqsv:pz3+8 63dwr7s8tjg m+c bx 3al vjor estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paij.pu-n5t/ ze tn 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 level8fn;nw-fu b:1+mcg iaro/fj2 of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 *9o.lin mwqb2 dB when fired simultaneously at a certain place, what will be the sound level if only on2l ow*n9ibq.me is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a csm)gb);air g *ertain distance from an airplane with four equally noisy jet engines is experiencing a soundrsa)gm b;g)i* 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 rubk4jaf:q pb-7pne 9:atio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of inten fj::qkn 7 ep-bbuap94sities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powerznh +micf;u6kgl-l) )0;offj output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound oi;uhfg z)fjl- k)+nm6 l f;c0spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area i n7zn8on(jy /lh +(x3dwr .gvybn t1*ds $5 \times10^{ -5} m^2$ (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 amplifiym4yo y3q h xw:)wy(.3bgve d6 x;dmk5er B is rated at v y6 4qdm3.yw xhx)be m gdyw5k3:y(o;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 each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 k8kscw /w;,xem in front of a loudspeaker on the stagcs8wx,ew/ kk; e.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. What is9 djnfjtbd/*+ the ratio of the amplitudes of two so ndbjdf /j+9t*unds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a)wqtl,qba:4c / by what factor will the intensity increas,wqb lq:ac t4/e? Increase 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 th+0m 07q rbx.apub*iv re frequency of the other. What is thxv u0br0am.i 7bp* q+re ratio of their intensities?   

  What would be the sound level (in dBozb(6f t/qyqbvy5 b*0x4 2y wn) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mmx2fzbby oy0* bn4/ q6qty(wv5 at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as +k(fs) :ny -pwru+ cwdca9 k-ta 100-Hz tone that has a 50-dB sound level? (See Figr+fn: c(k-wuy9k-)wpsc +d at. 12–6.)    dB

What are the lowest and highest freqfa;n, 4emnp+ ouencies that an ear can detect when the sound level is 30 dB? (See Fig. 1,am4o; nfepn+ 2–6.)

  Your auditory system can accommodate a huge range of sound levels. What i42 ob lshmn: uq;n-if:s the ratio of highest to loouqlhs f n2:4ib:-mn;west 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 -g1yje 0pdu/zd*u3re5 b6f vj/fg ur-the vibrating portion is 32 cm, and it has a mf-u-/j v f*u3 rpz0rbd61juee5gyg/d ass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three anp kwoi9te:.7q,d 4 veudible overtones if :t,epen dqk7iv49w.othe 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 woulauv-e6;99 roswg k,;p 6lxg jqd you expect from blowing across the top of an empty soda bottle tvw6lapx jog ,r;es-q 9gk;u96hat is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build ok(b)- o0ysk fjbg5nxv3c9v8tr vw/ mex0b9/ a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? 3evx 0r x9wt k//nvb -cf g5)9o8vbyobk s(0mj$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string ic+*s trbw1jt)s )ie. (a* s8-hwqvwg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fing r.(ii twjss)-be+c8awhq g1 st*v* )wered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl l(d: e3/swqzse C (s:eszdql /3w( 330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emit, t0coeiho0) +i.z cyj:es jz+s middle C (262 Hz) when the tempe:zy ojs+c+,h eoz.0 icejt)0irature 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 o tmj1,h,r;kw5 jnn2 g$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of themwm;sbnhex*3c (:(c w flute in Example 12–10 should the hole be that must be uncovered to play D abov hmwm(ex w sbn;cc3:(*e middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 t945iuw bbw*prj7hb,ybh6 3c Hz, but not at any other frequencie,b ic*57hwtr69up4b b j3wyh bs in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m lz i)9y3 x+edrkyofi(4 5ae hrsg+: 8eqong is open at both ends. It resonates at two successive ha3g9x)yfe5e8 +qe(ydak sir r+ih4:ozrmonics of frequencies 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 d+j5*,prvxi; hz0i3e i.xj fk xh8c9a$^{\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 witp tnly r *vgj,07unlyn)e0(a* hin the audible range for a 2.14-m-long organ pipyyt*eu j lgnpnnv,0a(r 7)* l0e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal isjg uka aj+5 0.v4fahn+ 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 st40h5n ka.v u +fjagja+anding 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 bea/m: q +xei72iu r3hsmtt every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off iehix:msr32u/7 t qi+ mn frequency is the other string? ±    Hz

  What is the beat frequ*sf1 mpd d**2 *sauvuxency if 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 o*uht(m,r)98ueh mx mr perates 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 freqummh,r e*uxr)u(m8 9h tency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wrbn+poce gn20si,ea l8,u5.dith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency c us0l+.r8ng,eed2 iao,np5 b of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequencynq y -:(:qyhwk, 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: Recall Eq. k (::qyqn-hyw 11–13.]    Hz

  How many beats will be heard if two identical flutc ci bxgd025q;20m ni5rj+efqes each try to play middle C (262 Hz), but one is d5 2xq;+eb50jicn2cq0 mgfir at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 5uaxjtdhsa74j 7xycl; ct; 5:j ++fapHz; 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.5japj:47ax7jtcc+ ut; hdf;yx5+ a ls What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one s4agbjpi+wy+ 7 peaker and 3.50 m fromyia4 ++wjbgp7 the 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 supp qx(o(q,jnt+ axp 0qc0*2 uwzbosed 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 is vibrating at 132 xoqat +2c 0uwjnbzq*x0q(,p( 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 wavele cm7d3/ 25bj wkha azxni/2zt0ngths 2.64 m and 2.76 m in air. How many beats per second t cbzziha32jk/70n/m2wx 5 ad will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certai */gd-x4h4kvqaj1ddaa oh n0 2n fire engine’s siren is 1550 Hz when at rest. What 0aa1ovh4*dx 4k/ j-h q2ad ngdfrequency 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 you deteqlu6e( v/ lmn(ct if a fire engine whose siren emits at 1550 Hz moves at a speed oq6v((mnell/ u f 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq24d yi .xhgrq3yvuk-. uency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are t-2x.q3ygh.4vurki d yhe two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one isyyf(sznzg .h0no0 1u/c-m q.r at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz.g/nfho0z qc.zyy snu-(r .m 01 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 receivc17fcv 5i zjg0es them returned from an object moving directly away fro17gv cfjc 0iz5m it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b fu mla8j g8j:0 hr2,pxgu c,4d,fp8xfat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqp p g,xmf2 r0,u:h,uj8a 8fgxlf8cjd4uency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler e:slpn6; -ni uwxperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car apsn ; lp6-inu:wproached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to m96b)fok cc;6a- rj6f d6p rrobeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg a-6dbc) rbr66j6aopf9cr ok; frteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency e.m doute.45b $2.25 \times10^{ 6}$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 sou+aud k cwz9qo,6gf2/ knd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located+aokzf/ qck92g ,6wu d, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its sp.l coabzb171 leed 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 (8o h: tvak8ww)iav +6vghf1z speed of sound is 310 m/s (a) What is the angle the sho6 ah at1)zhf8vg( +vik8wwov:ck wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where thr fj:7km(.b qdto(y q1r q4n-te speed of sound is only abymd.1fr7(4tqq(otj qknb: r- out 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. Determ4iz8 e/f evv,mine the shock wave angle itzfv4/v emi 8,e 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 1ztjsow*u1n m) 5old-q w /bk0$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead aa8w.7o tasqrw bs+9(y nd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear tw7tsr .wb(aq+9os a8yhe sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses xnad831f / be5zsh ;pbdownward from 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 (isexb81znah ;5d pbf/3n fresh water)?    s

  Approximately how many oxo tpl3:(ra0 sctaves 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 ccpeb;(zx st09tmw -rnxq d(- .onsists of many plastic pipes of variou e-qt0(wr mzxnb(;-9.cpds txs 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 closeaud z:v/p+ sy* to the threshold of human hearingsvuyd:p/ az+ * (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when itow *qi 8n8jq079l(qy xb4bnan 82-dB sound and an 87-dB sound are heard simultane nq9 iqbj n08yl*ti(wob4qx78ously?    dB

  The sound level 12.0 m from a lou u kd4 q4vmjy gu/f)0 8guruj72h6nat4dspeaker, placed in the open, is 105 dB. What is the acoustic power o8 tu) k fygn0j du6q244ur4u7/gjh avmutput (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 o-zpe jkvjx1w) :+ kg/ 6xflbk*utput drops by 10 dB at 15 kHz. What is the power output in watts at 15 vewlj +k/k 6xg-:kj1pbz x)f*kHz?    dB

  Workers around jet aircraft typically wear protective devices overe3 ,wvxa* c1nf4cka .21nqohj their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, fkqhx 4c 1*v oacjw23e.1,nna 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 communicall; /7 ne az97kblf5 ax-zu0 -ph+mubktions 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 a9fsc.e :j1 3yjjtjf l fg18+sis 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 violgql/ny ))f( ib)k (g6ak.msvfin is 32 cm long between fixed points with a fundamental frequiymf6k(av gb .sqn kl)/g( f))ency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abow9 ax k6dp2mjfm(*w 1nve 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 9nka xfm1dpwm (j2*6 wresonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at o0(h(mk ni9r7+,vsk suybxwa 7at(nx,ne end and also 75 cm long. How muckv70ynwhmnusk+9 x,a(tirb ,(7 xs (ah tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full8i 7+ jeyjmtb3 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 tx75nzuseet) ,ygwoz32, la*two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the uewly)t5x t,3 zona *e7,zs2gfrequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stavuuh*af 5i6u +tionary. The conductor on the stationary train hears a 3.0-Hz beat frequehu 65av i*fu+uncy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle )+6ragk+2f zfhgkn v 0as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was+f6v 0nakrkg hf2zg+) the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the s/) . 8 m5xnf,zhetayyapeed of cars just by listening to the difference in pitch of the engine noise between approaching and rzmyta ax)f8he,y.5 n/eceding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce mb- h+.ckx xj5a beat frequency of 11 Hz. The shox k+.j-mhcx b5rter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car asp d4lf(k5zgd fy) .cx+ it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they.y xdgl 5k (d4czf+f)p have passed him, at C?

  If the velocity of bldgb gxb+y(t m6tcw,)3ood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel) txb3by,cdgw m6g(t+ with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at s *zp eiagw-dbh 30v/uh ,/d y;4pdipj-peed 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 frequ/dii pv0d;,dzy4 u-p3ah*w /hj-bg peency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequ .xpa:-q+soorhi7n7yzk. lj2c 1 bb,uency sound pulses 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 fr7 olarni:1b q,sj-.zx+ yk.ucp bo7h2om one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wa xa:o6gpdli ::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.dxipl:6o:ag: 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 compromisedyl;3zl6bv:q *k8/y mew7ooet by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Co/ml k ;vz8:ytb 7loe*3yqe6wonsider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendem85obx :h (n9e b.vbbqyh 6kv*r aluminum rod held ik5x.68(ebymb bhhvn9 vb :* qon the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 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 the hupdp1mopt e y9xl)hi5 0 i3p *7njbi6b5man ear at a frequency of about 1000*ioiyd) t1j 5 95phpi mbppxl6enb307 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 hearex7w/w/w t,x ds the sonic boom 1.5 min after the plane passes directly ,x/w7w/d e twxoverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 4vzdr ucu r40d+-rpa -$^{\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