What is the evidence t8 sksh47ekbh 8d-.l0fyygu-l hat sound travels as a wave?

What is the evidence that sound is a forma +i ;ac0 4uu*xw3 hsn/jfhh1i of energy?

Children sometimes play s1*..: t zothedchbk( with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When ttkdb ch: h1.(zeo .st*he 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 sound wave travels from one cup to the other.

When a sound wave passes from air in1z s y/i3j *j9)dar8saxhpi-:h9 hebpto water, do you expect the frequency or wavele9xzjjpasy)is 9dhi ap3: -eb/h 81 *rhngth to change?

What evidence can you give that the speed of sound in air does not depene4g1 s1t5fnxue m,f4m d significantly on frequency5xgs mt eem1,1uf44 nf?

The voice of a person who has inhaled helium sounds ver9b1tn gb 9vk*vg5pnzqd ,i01 by high-pitched. Why?

How will the air temperature i.na9bbu77 m:h7a wc wsn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitud/haw - ulprey q3(d6n;e of sounds in various frequency ranges. (An example/ ;e3npa hr (6uly-qdw is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spa)m/*mqc v/y c;b0lbbw ced closer together as you move up the fingerboard toward the bridge? l;/*b /)0cbbc mmyvwq

A noisy truck approaches you from behind a building. Initia)4iwn ,6ja f9st orjd55ln y04myq 9yally you hear it but cannot see it. When it emerges and you do see it, its sound is suddn9rw t)04na5 sqi,jo64fyay mj5d9l yenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said tlq/z) b9ywcpf3 h 4gz-o be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explain.z9 p4 c/ z3-whylfgbq)

In Fig. 12–16, if the frequency of the spx ; bt6w:8/hg5djbg17fty v(tbyj5mz eakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or cl/58 g;xbd( bj7:ytvf z6wtt hg1yj5bmoser together?

Traditional methods of protecting the hea)lfo + eqk8y:7dg0agjring of people who work in areas with very high noise levels have consisted mag e0 k8gyjl)7aof:d +qinly 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 reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12/p qj4+sunmkz4yd45 s–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which znj5pu 44ksym d/+sq4 of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observmcvoe d/a8a(q1s6j zut:ev5) er move in the same direction, with the same velocity? Expl a:zajv muce1 (se 65/t)q8dvoain.

If a wind is blowing, will this alter the frequency of the soun1thk q(l/ mds(pm4y x+jyb83 kd heard by a person at rest with respect to the source? Is thhbqy (j8 x+4typ1l(3mkdks m/e wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A m*(zdyjrd6 dc2 onitor 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 whist(*c d2dd6zj yrle? Explain your reasoning.

  A hiker determines the length of a lake by listeningscc-nn h ac0 v:)as:1a for the echo of her shout reflected bansc hnvca:-)c:s 10 ay a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He f7oapu shkd 58o11z.vhears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in1vo5f1h8oupz7kd as. seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelength*;0tpzeus,9n n2 yh9zjz k s:is in 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 school of tuna on a foggy day. +1vzo; 2uaz5 7gs/hjn 2u xo nu:zn:ysWithout warning, a uz+o:27 uzov/5naznynu1h:js;2 sgx n engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The 0, mgw5msgn 8swe /la)splash it makes when striking the water below is hear ),/wmes agmgl8 w5ns0d 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete paap(co/pic1 2i) m gf1gvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1p)c( caf1 g/1i ig2pom.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 divb 7x gdt)j+mf4we+e*stance by the “5-second rule” for estimating the distance from a lighm edx tg74 j+)fb+vwe*tning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sod (moi;t.xr a/und 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 intendrakl) 60 z8m 1cekqa.sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simult)taqju33n 0p haneously at a certain place, what will be thh33 0ujapt)nq e sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally 3 dex u1l17/yhl y2ojsnoisy 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 enginelj yo1h1ys 7l ex2/d3u? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBlz9 8ngna h1wb4e;s(j , whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each lh nes w8z;94a1 jgn(bdevice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in n l.u;ou imtd24ormal conversation. Use Table 12–2. Assume the s.u2 i;tuo4mdl ound spreads 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 eardru.a)m8xerlt ))m t(q ntm 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 1kh57ull85 at6pcye90 zbs eu more modest amplifier B is rated at 40 W. (a) Estimatehkz llc eu655t08bya1 e 7u9ps 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 m in fro ci3;awpk03r gnt of a loudsp a3i0;c3rp gkweaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a differenbhv6tw ++c ho:9tu)ffv:xq 0qce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: S9) chxtvvhu+f w:q60ot +q:fbee Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whaocl w+rf;x lvlza 0h. .d5dg3pd4 q: lgaa-+r.t factor will the intensity increas x cr;opq wa0+aghd.a+3. l:r vfd lzgl.d-54le? 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 the frequ;ezdcfb-t ja 0 x2-yi)ency of the other. What is the ratio of their intensities? d0cbzex-t;i j 2y)-fa   

  What would be the sound level (in dB) of a sound wave in air that correspondsw4jrg 1l rfwq6y6d,32t 7o bcg to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 ,4fcglgwdb ro 7wq2y6t 13 6rjHz?    dB

  A 6000-Hz tone must have what sound levelsgp 2f4 -8cpgw v28kjr to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) v8 pgcwk284 2 fsjgpr-   dB

What are the lowest and higb3dv gwoq+7,j hest frequencies that an ear can detect when the sound level is 30 +q b v37dogjw,dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range 0x pe3)w wra :-yxk ax1cfb,l(4cxcz,jg9 ;hkof sound levels. What is the ratio of highest to la,r k9cfxlw:xb-(4,c waj xc )xe1 kyg0 3hz;powest 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 frequencbcx9n: visnk;mj (9p;y of 440 Hz. The length of the vibrating portion is 32 cm, and it habs n 9xnicmp(;9;:kjvs a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamene 9xv :2 nhq9wkcg0qd9tal and first three audible overtqge099kd9x2vc q:nwh ones 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 a o :(5,fxabdzhwc-v 7icross the top of an empty soda bottle that is 18 cm d(vhxzw da-:7fo ib 5c,eep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of humn42yc4 xzpsa 8 o+cg.aanp8z2aagcy.44cso x n + hearing (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 frequencynw8ho mo+,) 3i oock:-gm0 x8 3kneosk of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originalon0o3x3 kk8 +:s gnm-owciem, ho8 )ok length?   Hz

  An unfingered guitar stpcx csp)7s:o57z 6 outring is 0.73 m long and is tuned to play E above middle C (3307cs oz:op7cp s6u tx5) 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 qlh,eg 3 3mvccvnb : i:c(.f*korgan pipe that emits middle C (262 Hz) when the tem g(fcc3, nl:veqm.ik h:*v3bcperature 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 ael- /s,b7uayc)agh ,;bpj t;z t 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 shou4;q ailze)h9w (es*-ploheg9 ld the hole be that m9;laoi z eg9)-4s * ephlw(ehqust be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 26/ nmuacal;i4di*s.ro tb++e3m0e3b f4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is anfs n i3 0a*mot++b4mcidbu.3a ;l/ere 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 ends. It re/(sjl zc+ :7 hrtb;aqssonates at two successive harmonics of frequencies 275 Hz and 33z/s : cj(;bqrh7la+t s0 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 c1 x(kfi(br j;t/fndu /(ftk)$^{\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 wit l sx6v3jw39j1- jqdxqkjx5 o9hin the audible range for a 2.14-m-long organ pipe at 20 kx l13jq -3dj9j9oj5 qxwxv6s$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside a 8u2ix-8hjarbnd 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 rexa 82-jbhui8r lationship 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 +3zahrtv( ss.8uzkm42.0 s when trying to adjust two strings, one of which is somr8a(.sh ku 3zz+4 vstunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ac.sh:4 v xzx,sgffs v-pj9v2; nd $C^＃$ (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.0im kp9xibr1 another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans wp 9imb.1k0xrihen played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound bqx xjak 7hx;2 5b+;n7(enpbned with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuni( p;n7+nbq;7 hkn5e bb2xjxx ang fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings ar6f*9 acwt uw4osze;.( 5yjh jje tuned 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: Recall Eq. 11–13.] f *y a.sj;(zuojew4t9jc65wh   Hz

  How many beats will be heard if two identc hkgbs xj-g7::fmb* 3ical flutes each try to play middle C (262 Hz), but o:* jm:sb gxhb3- 7kfgcne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. F+v, av xkxn*,h)s:3r6 qavlbis b v*9xork 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 frequencies of A and C? What beat frequenci6vnabvv*s* xlrh)9,:q +v3i,sb kax xes 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 speaker and 3o;fzdf) qyhi:4*m vz sd 4.uw..50 m from the othef. m)zzdqu4:hd*o if s ;v.wy4r.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner he(4 e.09;haxqn jajkrmars three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequencye(0na4 hqa x j9.;rjmk 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. Hom2fpfr3) 1wn coqpboxe ((2o8 w many beats per second will be heard? mnx cp (o8fwq )1(b2ooer2fp 3(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is ou4 f)2qoe 8pj1550 Hz when at rest. Wjqe op)o2 4f8uhat frequency 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 freque/: k g-yc(wr 8d6zkdv, o2tprency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m8k(c tpkg,/ze:vd r -6y 2rdwo/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sr*bg ko3bz,ff)j 8d uksh )36source is moving toward you at 15 m/s versus you moving towa*zogk3s3jd u s), bkf)hr6b8frd it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single swi0)lx5m u0pn:6hvqfrequency horn. When one is at rest and the other is moving u0): miql vx65ws0nhptoward 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 ator;igje 83n9t 50.0 kHz and receives them returned from an objergone t 83;ij9ct moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits abt/dnf + wd-20e x nspba2aw;pho 8y.-app5;s n ultrasonic sound wave with frequencyn-pwoa5s2pdntf;+.a02he/s pp 8bxwday -b; 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flatdso: v .t zfy7e(dgbk1yu4 2 w-lx*: b.lsffu+ 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 w:72zxoe yv-bf1ulsy:wftbddgsf + 4 ku(l. *.as 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-flo+ df-+pfvv1 xow speeds. Suppose the device emits sfv++f d-1xpvoound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ulusk fonz33r a, )a*u(utrasonic 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. Wc.j l;7nk9n elhen the wind velocity is 12 m/s from the north, what frequency will observnjllc9k7.n e;ers 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 its speed atvwec6,4,is ,ub nnw*s 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 31mus/ ru)(hh +zdvm2w+0 m/s (a) What is the angle the shock wave makes wiwrhmh)vu2 u+ z/(s+dm th 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 wl 23oj :xq:fpw7e3qi-wth4x qhere the speed of sound is only about 35 qfxe-:3wploxt 2w4:iq3q7h j 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/sr mor(.s0y/gu strikes the ocean. Determine the shock wave angle it prod/ musryr (g0.ouces
(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 8i(rb ,wlg r3x$/theta$ 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 aek l -/b,hu(,ey6jopz rxjx-3bove the ground flying faster than the speed of sound. By the time you hear the sonic boo,-xr e h(l3x e/z6yojbpu -kj,m, 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 devx*a) 7gyyd ,a2 j8praoice that sends 20,000-Hz sound pulses downward 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 pulsea8pa, a)yy7*xgo2d jrs (in fresh water)?    s

  Approximately how many octaves abe 0z vu01tl5*),zg a*tqqw04nrwau sre 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 cor2l/izk8mf:cl6 7m ) mo-zgc ensists of many plastic pipes of various lengths, which are open on bothc2:m 86-zkf / zi)lcmolmr 7ge ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thz;ahmzmy,s9 ;b f(3;l tq, pzbreshold of human hearing (0 dB). What will be the sound lem3a fys bmhp;9z,z;bl tq(,z;vel of 1000 such mosquitoes?    dB

  What is the resultant sound,ui;ic+mbd+9s- i g ob level when an 82-dB sound and an 87-dB sound are heard simultansco i,gb ;-bd 9i++iumeously?    dB

  The sound level 12.0 m frog( /5ukmtq a1wm a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equa1 ugat5/mk(w qlly in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.1lp 0o4fbg98awy l uj p5 e /6szxb/os:/iity4 The power output drops by 10 dB at 15 kHz. What is the power outputb14 wu s:0ofxyy spo /8/il6tg49ai lj/ez5b p in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective -2b ph+qejfh 6ha1 s)pdevices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would bh+6 he2q1-pjsp fhb)ae the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sk0g bkq0o*9vg ystems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency 1q8u9fxp ;z:p mxzh/.8reg soh71 s3 m5mk (cns$\frac{1}{2}$ 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 ifmeqyqtw2 ;7k4 t/eantl) ) +between fixed points with a fundamental frequency of 440t)/iym4 ntfqa et; +w)7l2eqk Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wig* y0p- 4zawaly-t+mkth water (Fig. 12–35). The water level *ytmyazp ga-kw0l-4 + is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. 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 opens69 ,q nc2ld bb4pji6q at one end and also 75 cm long. How much te,sqb jb64 p 9q6ind2clnsion 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 obs()de9fh q lnl;p-w 6tkzsbk plq-+2)k erved 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 500–1j m v1,tiq:l3a000-Hz range coming from 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 iqltavji3 m,:1 s the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Oski + uw20dra;ne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movin 2awkri;0usd+ g train?   m/s

  The frequency of a steam train whistle asxl4 *(z- othx/y/ szm,)x-hio)gjreg it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How far(otex h)xzzg 4-/ il,-o*gjsmxyh) / st was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate -ox /3qsh+c.phd zf*mthe speed of cars just by listening to the difference in pitch of the engine noizmhd cx pqh*/sf+ -.3ose between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes,y 2s(i* hci9spzz:6yt sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.49z* y(z2:tic6yihp ss0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moven/1 bvc1ps2o1jwl z+i 8 gaag2s 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 have passed his+cz1j2p1g1 nbl8 i/g aav2ow m, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bekt.mxst,e+p m /)lp(s a ho*m7at frequency would you expect if 5.50-MHz ultrasound waves were directed along the .*,/m+lhx)(sksm ot7p m atepflow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying tow6a5d/uqquv2 j za i8 x,ywj3s;ard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the freqz v3 iqq82duws 6auxaj, /;jy5uency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as(k0xuz;j) f+g7o2v; vr dtt ky 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 chirp7(+;ok)fd yz uv0t vjx;g2ktr is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ot9jt)yysc63 h z,0yt1svf5 r cne 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 i6fy0 ysr, y tj)ht9t1v5cscz3s 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 coc d9bgaf,4 oo*mpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m hig,o9 od*c4bfagh. 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,” involna gk4an)tz*ut2 z*,mves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand* 2u zan ,nza4g)tmk*t. 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 human ear at a frequency oipzrg l4.uq5ug*i /y(f about 1000 54gg/ ilqp.uruiz(y* 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-mj * 0dfjcjz8 the ground hears the sonic boom 1.5 mi8fjj-cdz* jm0 n after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbszo- bom:o* 6u i.f.groat 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