What is the evidence that soun9 m6*.b .jsi vtkjcs:qd travels as a wave?

What is the evidenceme7up m(j1u1j that sound is a form of energy?

Children sometimes pla g(, xmpah :vgwmgkq-d04;e 8xy with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speapme0w8q;, g:xgx-h(kavmgd 4ks 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 into water, do you expec d/t)af8i kuk9t the frequency or wavelen) id 9ktafku/8gth to change?

What evidence can you give that th vki.3tfq3- bq 8lf;)ewlgf7uui o(o6e speed of sound in air does not depend signiffwo7 gibe-3u (.vult6ko iq;3f)q8 lf icantly on frequency?

The voice of a person who has x om- bm,eyi(2inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ p/vho6kro* 1r4b9 j ytvipes?

Explain how a tube might be used as a filter to reduce the ampua fh)(jl- 6 stvys,c*litude of sounds in varilss*jau6-(t), fc vyhous frequency ranges. (An example is a car muffler.)

Why are the frets on(0r56p, py ssgayfdu( a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?,fys a5u ( s(6ppr0ydg

A noisy truck approaches you from behind a build2nm3r )a xqe/zing. Initially you hear it but cannot see it. When it emerges and you do see it, )x32r eza nmq/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 “intww6/ g 4aempk 244psozerference in space,” whereas beats can be said to be due to “a g ewkpo42m6zsp44 /winterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lo 8 h bm63tifyk;*2ismhwered, would the points D and C (where destructive and constructive interference occur) mi;s tm 6f23kyb8 mhih*ove farther apart or closer together?

Traditional methods of protecting the hearing of peowv3cz ,w+ )q;ek+qfcuple 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 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 le k,cwqf ;ceuz+ +)v3qwvels reaching the ears?

Consider the two waves 4 fl8if 07ozxfshown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two comxf870o4 lfifz ponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move il;p 9a.-lgd tyn the same direction, with the9 g;apl-ldy.t same velocity? Explain.

If a wind is blowing tllarm1e)f eyn)i;n,9sux ) ., will this alter the frequency of the sound heard by a person at rest wit )r;9i1 )ln,yxntfe). emsu alh respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ohk)wkg/ 9lpnh+b(z xs u)uc.: n a swing. A monitor is blowing a whistle in front of the chi .g:+u9(sl/)kz) u kwhnbxc phld 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 of hh1eg(gc u/+xs7mqeyr5 y/y+r er shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s 5 e1qy(gy+cmrx+r / h 7yge/usafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. 0oc0/f lgk e8agfl6)k He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 mg gok6ca0) lefkl80f//s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelen0*ql s6b ig)mjl 9u5g(n.ryedgths 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 dk0yefuk9y uh-r+ea0ue82qj 8ay. Without warning, an engine backfire occurs on another boat 1.0 km away (Figee92y-fh ue0ky uk8a+u q 0r8j. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it make0 nra6b( i)mors when striking the water below is heard 3.5 morrab)n (i60 s later. How high is the cliff?    m

  A person, with his eari c.la y sfv7))(f +3muygk7tw to 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 did tiyw+fa mtsuv k)f3 lc(.)7 7yghe impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one megbnwx d7(u5: fo: 7) tzqjj(cile of distance by the “5-second rule” for e ot77(n wq)c zje5(jxf:ubdg:stimating 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 pain level of 120 dB?6uas, bx6oub;ms p 2a,    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 so*pni pw3al*m 2y ce.u:und whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d6jm 6rftky/ d/B when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hiyj6/k6/rfmt d nt: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four v dd oz(hzdyf1ei9mg( 7di1;0equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the y7f;iiz m1(zg d od9h(0d1edvcaptain 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 dB, whereas for4 7 .vfcauuiz3ps8do4t x;ed : a CD player it is 95 dB. What is the ratio of intensit ositcf34vupd e87;daxz4u.:ies of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power l(m,/kanvceg-q70rv j y.gc- output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth.7v r jn-qy,elg k/cagmvc-(.0 $\approx$    $ \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 a:ddl 7wd q br-5wo8v8qrea 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 l(tu4eb.bqdnx (d.zim2v)2 e250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level .d budltq2n4xm2i( e e(b)vz. 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 rwy dmb+nk:wj4) c pkn591gs u;egistered 130 dB when placed 2.8 m in front of a loudspe g4cjnsbpn;w:19u d5 mkky)+waker 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 difference in sound level ofxcd ftf5 -zub8u c6f64 2.0 dB. What is the ratio of the amplitudes of two sounds whose le zufbcd5c 48uf6ft-x6vels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound//lm ricm)kv 26v/sxi wave is tripled, (a) by what factor will the intensity increa /v)i26mi/clkrvm/ x sse? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenrc7 fa y.x8m )rmwe*: 9j*cmwct amplitudes, but one has twice the frequency)9 m: cc7rc*yj8.rw e*fammwx of the other. What is the ratio of their intensities?   

  What would be the soundq sx1 5 eju;35fezkvez rjx471 level (in dB) of a sound wave in air that corresponds to a dise4uj1qs1fx;r ekv75xz j3z e5placement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound :nx1d*es; m9(v vrz ablevel to seem as loud as a 100-Hz tone that has a 50-dB sdsv ezva r*;n(:mb 1x9ound level? (See Fig. 12–6.)    dB

What are the lowest and higb+w6 yegv5,v.6zgop dhest frequencies that an ear can detect when the sound level is 30 dB? (See Fi b wo5gypgvv.z, +d6e6g. 12–6.)

  Your auditory system can accommodate a huge range of sound levu 4c+n v k jl7-pvy9rj2n:do.fels. What is the ratio of highest ofupr j7ckv:nvn+l. 4-2d yj9 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 4 vk57r0l6a9fg t3,z cts/cs gn40 Hz. The length of the vibra 76szt59r kg,lcst3 naf0gc/v ting portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm ed6ky- r**sif long. What are the fundamental and first three audible overtone eys6ir-k*f* ds 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 u k mc25 lz47djhwl 5l2;ofy)iblowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube?2i 4uflmzk75johwlcd ) ;25ly    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-tubg9eg +ws( 86in ovegi-e pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r9g(sgnow 68e ve i-g+iequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frechxl;6+rj/ ;t8 fudb kquency 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 ori8/ 6 h rltd;j+ufb;xkcginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle Ct vmtw3( y7ejr-0mw ,c (33,wrt0 m7 emy(w3cjtv- 0 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 emits middle C ( h ydg49c3 u9c,pk8kej262 Hz) when the temperatudph3yj9, c 8kuk94gecre 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 2u,h6/z6 efz8 yhs9k rfagl18x0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiec8zqbo-x9 dv* kdlxj 7dbd 0*+re of the flute in Example 12–10 should the hole be that must be uncovered to play D a dd7-zqdlo j b **d08rxkv9+bxbove 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 resona s0gyg-9oby,( w w3hcr gzbh -kn4dyv6mob888te at 264 Hz, 440 Hz, and 616 Hz, but not at any othe8bwy b-g0 gc6sdyow,4yk8b8hvg - (r9zh m3onr frequencies 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 mjzo e l g2nkm2f,qku5 )lov+54 long is open at both ends. It resonates at two successive harjl5ongqloke ku2)4vz, +f25 mmonics 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 l 3u;bn7ynij 5$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for ad u9/4ywdf5 qmg*(lem 2.14-m-long organ pipe at 20gm (9l/* ye5d fm4duwq $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It iwf0u:6d7/wzd2 dcp h lpb b-m9s open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your ans 62updwm cbwh fl zd:b/-d9p70wer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, on1 ()bbiq/b)bwp,+)ak ynnp gqe of which is sounding 440 Hz. How far off in frequency is the other 1ki,n )qngpb+q)/w)pa yb bb( string? ±    Hz

  What is the beat frequency if middle C (;lic0h+h jt45 auq vote0 :z:e262 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 anotwe.z o e(tanb/qiy(ko 1.o.k :her (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating1k (kw.y.en:ebiztoo. o /qa( frequency of brand X.    kHz

  A guitar string produces5ybuuo15; v4ok tg qq:2s5urc 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hq4urb tcouovug5:5yk1 2sq ;5z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned c+g (m .6uxl55bpuiomto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard 5c+5x.io bumuglp (6mwhen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eachak*f xj5iqz/9 try to play middle C (262 Hz), but one is at 5.0°C and the other at qj/x9*f 5zika25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4 0os n8 6gzf*r*0mrx9tv3xm cs41 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 frequencio vtx368 mxr cmsng9s*fr00z *es 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 z 1wd,5qur*rb 2u 6xcc0 tb5owspeaker and 3.50 m from thed65t 2*wwqcrz u10,b xub c5or 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 6eq*mx7xr3 vavvm s7+osed 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 xrmvmq6s73vaev x+*7 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m xty /0u vso2y1g2x2 bvouh 28lin air. How many beats per second will be heard? (Assume T = 2 x2 01y b/uvx82s2ho2vot yglu0 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when aty2d/ sz rmo2 * m.kztq+oy*ib( rest. What +z2/m*k yiq2 .od(sy*btz ormfrequency 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 detect ig/o x3 p8nr:qlf a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s /:r83 gqolpn x
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20q :xj8g(ybd3v00-Hz source is moving toward you at 15 m/s versus you movingvxby 3d: jgq(8 toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is;d1oq*qpud:4r yv9 ro fb m6v95ojc.f at rest and the other iy4cuo v;v*bjm5p drf 16 9fdo9.rq:qos moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them retm+qx+l:at quisa03f 8urned from an object moving directly away frot u03ia:sq8+am +xq lfm it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed )sp1jn/m-uhv;sjb sed2t1o/ of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequenc to-jmu21jepdn// b1ss ) v;shy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, mo+5 yj6tefdlkl97t3 a tuba was played on a moving flat train car at a frequency of 75 Hz, and a sece6d3ltof m75l yjkt+9ond 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 mb esa4 3lv7ghhv.m 76veasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be vsm4 7h.6l vh7g3bvea1540 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 ultrasonic wav,ns7+ezp s; fves 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 570x;l (f erl:1co Hz. When the wind velocity is 12 m/s from the north, what free xlcf;:rol 1(quency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if it *jr1p+z1dk;ojhd9jgs 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 atk1r 6qt9(si*xh:wzr k Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction* rt9h6 z:xiwk1(ksq r 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 atmoss w:tvi-ibp +6l +na lc*u(s2vphere of a planet where the speed of sound is only about +wu(til6p*v:sabin 2 -+vlsc 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/* pqd : v,15qmhvhtyw;s strikes the ocean. Determine the shock wave angle it producesv*tpq5yq:h1,wm v d;h
(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 gyy4j-76yix ztv5o1a-j bs: e$/theta$ 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 sbr4a7 9u4mqv km above the ground flying faster than the9r 4buqs 4av7m speed of sound. By the time you hear the 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 slr t-exdi.( kk(/.eam+lr rv(ends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is desilxav-+k( im(ke/l( rr.r ed .tgned to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible 8qf0 ;azm;x+cgui f7prange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe swkae i;njm)w2e z a739ymphony. It consists of many plastic pipes of various lenw;aw9n7ja i3mke 2)zegths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresholdpx0 kvv(u +5act of+v7 of human hearing (0 dB). What will be the sound level of 1000 such mosquitoev7fp+vx5k+o 0v( autcs?    dB

  What is the resultant sound level when an 82-dB bij;cq :(:n:n3f ,)nat qfk nvsound and an 87-dB sound are heard si(vn:bft3if q: ,a nnj;cqn :k)multaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10+u 5y)fl(s mvv5 dB. What is the acoustic powerfsly+m )v( v5u 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 oug8rtbjb1 +de-eb.4zw -tgn;ltput drops by 10 dB bbwjeg.gd bz-rtt148-; le+n at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typiodra cmu8d2 8*+hhs ,ucally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radiuoh h, audc82+r8 sd*ums 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 communicatiur 5*3u wd1bftrxu 2(x3d:h*we2y uhxons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tunes67)s gnppd 1fd to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between2uno10kj 37pr+ tyovk-rz8bc fixed points with a fundamental frequency of 440 Hz and akvt oyr u +k81p72 3rojb-z0nc 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 vib; zt6hctm-ki *ration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the zk6ch*t mt-i ;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 igd7g2k0lvk7+5s o+el tt iq1 hs open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in thektq+ekdg svi l7hlgt2+ 71o05 tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate uj imb+jm ;i**04jodmas 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-p yu*mbl87u7jclab*3 1e(lgpHz 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 tl*p 7 83c(7ubpg*jll yab1em uhan the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is sv1 bn9+iuutfw(u .+ ritationary. The conductor on the station u++n(1u.r bwfviitu 9ary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approacpy z 8oj,ugt26j/9jduhes you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? g 2j 89yd j,puu6jz/ot   m/s

  At a race track, youi pq/tzocj4 ptiri(tk50 2 6t9 can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octa ( pj54p/oktzii20tit69q ct rve (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of zh+h m q4c-6jh21y rat11 Hz. The shorter one is 2.40 m longmy ha4rh jz+q-h1 62ct. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastowg4wyslco /l/-cc7 p-r 5tx- 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 (c/-4s-c7 xplgw o -wy5trco l/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 him, at C?

  If the velocity of blood flow in ) q3c vf+52w -fmtpbgothe aorta is normally about 0.32 m/s what beat freque wbmov2cfpf-t5+gq3 )ncy 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 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 is8kx m7qafm:* q 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 wav8 *m7ak qxqmf:e reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.2owsn72c : fvk The pulses are approximately 70.0 ms apart, and each is abou2v:f7w2sc ko nt 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 signl+gtd3w9e :vi3c cv4 nals 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 4vc 9 :gw vt3iecld3n+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 as an open tube.

  Room acoustics for stereo listenin6 mdc(3s*, ej hfcjq;cg can be compromised by the presence of standing waves, which can cause c h qjc,cfmde*;( s63jacoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing ue :vsc:6 a1e2 jiea)nrods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90iu6 2 1eca san)j:eve:-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 h iu3kv c75ong5uman ear at a frequency of about 10oi5cn5vk 3g 7u00 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. A/ tvj3lp-gm k4n observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhea/ jtgmlp-3vk 4d. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1k1lw.am *eh()m ehr *w5 $^{\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