What is the evidence that sound travels as a w(,zt.evi;qg wave?

What is the evidence that sound is a for.),5 m4opzo 7p xkyqgi tll05vm of energy?

Children sometimes play uj3 9 aq:d42,2zgdezvd eof,zwith a 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 sovdzjofqdae3 d:924 ug,,z2 z eund 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 exi dk:;3pqt1 a i.i4kbzpect the frequency or wavelengtk tz 14. :p3kaqiidi;bh to change?

What evidence can you give that the speed of sound in air doey p(6y05oe unzs not depend significantly on frp0(6yn uyz oe5equency?

The voice of a person who has inhaled helium sounds very high-pitched. Why? b a.ct;se-5cs

How will the air temperature in a roome9 zcf)0qo:k9l) aqixs5ml 8l affect the pitch of organ pipes?

Explain how a tube might be used as a ff p d3h(jt-t)wilter to reduce the amplitude of sounds in various frequency ranges. (An example is a car m tfht3d jpw)(-uffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togeppg+*a acfr61u*mzh1 :hsr /ether as you move up the fingerboard tom1cap6f*gap1r:+r hs h*z e/uward the bridge?

A noisy truck approaches you from rgbx ft+tgenak */ )h8n+ z;7 b/p4ityj nrg56behind a building. Initially you hear it but cannot see it. 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 1j;n6 8ihnx gtn++a/tk p)4rbytg5efr7g/bz* 1–15 on diffraction.]

Standing waves can b q wv:qt;0h14 jonp8o*m 46ltxroak4osa/ xf1e said to be due to “interference in space,” whereas beats can be said to be due to “interference in ti0a8o;* t1 4n: ooqo1w hqv mjsx4tl/xapkf4 r6me.” Explain.

In Fig. 12–16, if the frequency ocex m+pj2ln(eh he3 2 88w(zzof the speakers were lowered, would the points D and C (where destructive and constructive interference occur) me +o(ljpzzec2w3(x8 8ehn2 m hove farther apart or closer together?

Traditional methods of protecting the hlw2 g ,ee2 dtsp1l 23ovgux*z5earing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a devi2vge ue*d2o2pg l51t sxz3w l,ce 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 c)wknn4 t)n;3w.xrlw 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 component fre cn )4;wtnknl.)r3xwwquencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the z/w1s3fctj6m8 ;gh 1psnxb q/0;ftfmsource and observer move in the same direction, with the same velocity? Expw/ 13bs ;fmf/mt6xnjs;h0gtpz q18fclain.

If a wind is blowing, will this alter the frequency of the sound u e*q-zli *j /ekay6 zn8ds0l(heard by a person at rest with respect to the source? Is the wavelend8*l*ly je /z6aqu n0 -i(skezgth or velocity changed?

Figure 12–32 shows various positions of a n-5e(4gmq 5 .ayyq 23e /g+oopy) wi skceix0ichild in motion on a swing. A monitor is blowing a whistle in front of the child on the gro5qi xio akewm05e q3 +y)4(-g/y.pgyei s2on cund. 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 lake1 bht .::*uro*x(ln y+xg k rx6xpd3ru by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.6r(p3::xu+l xoxkr.yt* b1 dghx* u nr0 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 hears (,5iuc)-e,esh swva x 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 m/s (Table 12–s ,w )ecs,veix-(uh5 a1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airp4k sqxhf/2j8;g6rj,ems ; xc 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 forwai:pym6(,3(,mjd ib fucb1 ggy day. Without warning, an engine backfire occu:m31a6,ifj y,wrd( bpim(bcu rs 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 spla,ta4iix3k3 6lzh *mmp sh it makes when striking the water below is heard 3.5 s later. How high is txa 3h,imi 4z*3mplt k6he cliff?    m

  A person, with his ear to tyc uv.z4v47f ihbn z72he ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one tz u by.4vc 2z74fvinh7ravels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error madec6 r 7,at4awlo over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature isa6, la7 wtro4c (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of w/df+( tl-qo iy*f46qk2hkx 45 wriz j120 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 i 2e5kp mqjuo t7v;w;z6ntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whe83od +7lmu1ddlb (tfkn fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hin+td3d blm8ku 7 1dol(ft: Add intensities, not dB’s.]    dB

  A person standing a certain dis,jn su ro6gs89tance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if o,9ssj8un r6gthe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noist33a) .b-d8h bdpf ulu f11c.zs5umlse ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio oc-f h.d3uu5t8 spm1b.buz) 3 sladf1lf intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of soundz6dqaz/ :-(ry cc8mav-re p z1 from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly oe(/r z -vyzqd6 :pm cr1ca8-zaver 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 arep i8,ud(t,jdzhq7: 2q l ynia.a 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 the3j+9-:yil nafm* wwuv-jb ( fj more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeake+l:aj9 -vbw fj- *(jfuiw3nym r 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 front oxo(1va g ymt5:f a loudspemat ox1gv: 5y(aker 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 differenz 8ayfep4x (h r w:z8/p,:khyzce in sound level of 2.0 dB. What is the ratio y,farpkh4y8zp: e hx/z w:z 8(of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) b/jc*l czc+fa. y what factor will the intensity increase j/ +zafc*cc.l? 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 nil2johfgd0.n sk7 k1m ft 2, t(+;rpythe frequency of the t,s +f o.01hrgdiny 2tk k7f2;jm(p nlother. What is the ratio of their intensities?   

  What would be the sound level;-5ic 2qkgv91*x cvi,. tu xkemt(stb (in dB) of a sound wave in air that corresponds to a diui 9tt k-i;m.ck1xq v sgc*2et5,x (vbsplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as l/elz-xpwtp() oud as a 100-Hz tone that has a 50-dB sound lxt - zpp(we/l)evel? (See Fig. 12–6.)    dB

What are the lowest and h7gulu q))wo2 + s2oftuighest frequencies that an ear can detect when the sound level is 30 dB2us )ot7)uu2q+fwlo g ? (See Fig. 12–6.)

  Your auditory system can accol,-/ lqzk(tvw r6cax )mmodate a huge range of sound levels. What is the ratio kq-t v) xcw,(a6z l/lrof highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 ;rlk :4uf*rrt/i7xe s1s ag9oHz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinroltksi rfs /4arg;*xue791 :g be placed?    N

  An organ pipe is 112 cm long. What are thp1olyx 6s0 ly+e fundamental and first three audible overto0lp1o+ y y6lsxnes 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 frc*kmfd 5m2/loaotb6b7bg ; q,om blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a cltfqgmb7o * k/b,bm;d 2o65c alosed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pi( an *wwf2 y;d+efo:9g 6vufqbpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what woef da f;v :u+wyn 6bw(*o9f2gquld be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has i()2,mqgzwjqb5 .bbd(oo ,nya frequency of 540 Hz as its third harmonic. What will be its fumb(qdg.zw yjn5qo,i )bb, 2 (ondamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tunek-b43q i eytn 8k4ptq(d to play E above middle C4tp-b4ek83k(iq tq yn (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 .h)ajk/yj j9p tq5h5h tn(5qjpipe that emits middle C (262 Hz) when the temperkhjpynjqjhq/9a.t 5j t(5 ) h5ature 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 g kgcy.*o s8d fp3ibg22592gh1opai e20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute vs4cv;zbi- cv0g (tr6 in Example 12–10 should the hole be that must be uncovered to play g04c;( t zs6cbvrvi-vD above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, butqcea)ct80;) c thn ve( not at any other frequencies in between. (a) c)) c;08ecq vane(tht 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 long is ope, jr+ n7jkml.an at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 7nlr ma, jk.+j330 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 +k i f6+sw1a6u*/afmwh9y zne $^{\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 forzs-2gbs vlndu)hv v6 ,h0vz-3 a 2.14-m-long organ pipe at -b v,lvs n)036z- 2vghzvusdh20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approvg3cwhno :4 0xd) z6soximately 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 standing waves in the ear canal. What is the relationshipo4zw6 3hsnc o:)dxvg0 of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying xy fdso cpm+ ,y:2*l0nx5al *fto adjust two strings, one of which is sounding 440m*xlafd *5yx,l2p :o0 nfy +sc Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and(0r0gn0 og mv9j wk5fml:ox t) $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operateslxe-9(a lfyk7t cr8 edn+w+ bycex//) at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill ceyb l/ xd)r/ ewcx+kf 7+- 9(yean8ltwhine 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 f-gj 8fa-mm*aere ;n9when sounded with a 350-Hz tuning fork and 9 beats/s when sounj9-m8g *rae-ff; nm eaded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequen : 99rs/ass8 ;rwlkdejcy, 294 Hz. The tension in one string is then decreased by 2w9r s;sk:8lad9jr e s/.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutex /i8vle sftd )d-xc-n:pr) 9ps each try to play middle C (262 Hz), but on- )dprf/ i)l:st-vc9x8end px e is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin)u /8qd4zgc ;lrelat0lh nxv +8po7:s g forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded snaz 0+8ot4q: g/xr )d lc7vph;l8eul 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. Al/gc ,z +d)aea person stands 3.00 m from one speaker and 3lzd) /a,cgea+.50 m from 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 supposed to be vibrating at 132 Hz, but et /c+js+nmuk0 )lj* wa piano tuner hears three beats every 2.0 sl0s/j+)jc*wte+k mun when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound 1; we;appv6cw of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 16 w;w pcpa;ve$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freque.*+jd1l ry;gqu aceo 2r41ap3 rsf5eency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency d4r1quga1e js e 3adyr+ .5fp*oelr2;c o 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 qu53gj9mxo- o vg8dn* do you detect if a fire engine whose siren emits at*do oj9xqm 8u3 5-vggn 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mo75oroc-2k fzvvq4 x nfuzb9 0;ving toward you at 15 m/s versus you 7okq;5zzv4-r ub0v x2 o9cffn moving 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 equehy , dt ek9.5*xnb4y4ephu2ripped with the same single frequency horn. When one is at rest and the oth e,udbhkpt94 4n52r .xe*hyyeer is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz andxcv(i 0l;jm09s 1xixk receives them returned from an object moving direc(i lxmj0k9;i0xcx vs1 tly 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 ba/s uvz ngk5ks bs-u *.q,2vkd;t emits an ultrasonic sound wave with f*/;ks 5k vq.s d2g- s,nvukzburequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, m1 lhw 6vlh6r:s/ce f 6zlq3 6xh/oq3ra tuba was played on a moving flat train car at a frequency of 75l31lclves rmh6: z6xf/6qr6h ohw3/q Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo3/wz 9 fv.k..mebm-ecpc /bayd-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 iac. fy- ..mbcb3me/ zv 9ew/pks 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 waves of frequenz,qlzu nda ni/2 5*- u+cuzd4lcy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When thelb(l4qqn*jdb4 jb / g4 wind velocity is 12 m/s*4bnl jjb4/q(dgb q l4 from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its)*c0nx/ r n cjhwlsu-z-w5 mh ej*):bq speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310r .plv.:bl*mp ym4v ,m: lo-k jupy*c5 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion? l b.*yl4ul- ,y: mk5r*vvmc:pp. pomj   $^{\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 theti -pq h79cb)p thin atmosphere of a planet where the speed of sound is only about thiq b)c97pp- 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wao663 pg8gw/ xbq fakyfx-s5smfq8f ,( ve angle it produces6 fpfykq8go(xf6wsbq/m, 8ax- 3fg5s
(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 00ufux3pfsk .$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see w()b5p6oj to ra plane exactly 1.5 km above the ground flying faster than the speed of sound. By the timeo)(5j6 p rwbto 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 sends 20,000-Hz sound pulses downward a8 npfkkcnhxt5tq-81ln8 a97from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh wate kl858c pf-9anhnt 71nxq kat8r)?    s

  Approximately how many octaves are t*a+tc)jfl6cx7 fbg*4 bai r4there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It ,6bmarjb1avy46rz f5 consists of many plastic pipes of various lengths, which are openrfrj 45aa,bvzm61 b 6y 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 9 )hd1br xmayvbr:+ e.makes a sound close to the threshold of human hearing (0 dB). What will be the sound levem+d: v xb91yrehba) .rl of 1000 such mosquitoes?    dB

  What is the resultant sound lh.+ 0ehqr7qhs evel when an 82-dB sound and an 87-dB sound are heard siqrs.h h+q 0e7hmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 10v(nk;0y0: 3co:tfl2g) xsimd p df7 vf5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all dos)t::f00 m fn 7ifdgx d;v 3p(cvkl2yirections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thg (8:v:ze pich/: u7jhhg8phne power output drops by 10 dB at 15 kHz. What is the poi veggu/jzhc:(:h8h8nphp : 7wer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wea lz8+ hymhbn*0.+ixig r 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 radius of 2.0 cm. What would be the power intercepted by an 0lb8mniyxh+g iz *.h +unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, t6k0 afv:xjpypln8 mzx 5:;-grhe 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 i 4vsjl9q zg2zr*n6v :vs tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental f ur dr8qwj;/;frequency of 440 Hz and a mass per unit len8ru;j/ f;wqdrgth 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 vertica6( onw)xf(my4s40h.a j gz zxql open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube abov .joyh f(maqs6z0wz x)ng44(xe 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 gccgu (1.* exse is near a tube that is open at one end and also 75 cm long. How much t*ec(1c .eus gxension 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 full lq4xs h2bq-snn ge ,,-o8ndq9woop ($\frac{1}{2}\lambda$) 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 pur 1)qipqjltrm*,bm 8-y e tone in the 500–1000-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 is the frequency of the soundyp qj- qmr,it lb)1*8m?   Hz

  Two trains emit 424-Hz whistlesu8fve2d2js3 bg3 om ) o32ca(:xa clvzo;8wly. One train is stationary. The conductor on the stationary wyg2cf;e3dv3aajbo2:38ov)ls ul 2cz( o 8xmtrain 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)+1aphunf y7t 28qctu whistle as it approaches you is 538 Hz. After it hc qn7t18 )utyu f2+appasses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you hg7bdta s2p6 0vr-h2g 9/zcklf a n*d*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 f/dgz- ag9c vl*th7*260a nfkrhp 2sbdull octave (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 11 f.*g3 zj zb0wco* vw:rHz. The shorter one i*gw:r c*.z3wb o0jvz fs 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pasa)ae m*:38f 6t dqp m8jeh10afzvx8hz t 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 hafmam 1 *va)zxz8j0q eh 838:dtf6epthe 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 him, at C?

  If the velocity of blood flow in the aorta is normally about)z)4a+6b1cnpf9h jiqui ;/m zqj hy9 l 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavesuna)/jzcpb j1 qihf ) ym4ihq96;l+z9 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/y09avuft*8re9fmt +*dn t/.m6ydg up s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kytn/8 u t6m+epdy*g0fa r9u *dt.9 mvfHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of higxo*7ed,qn9u/ig lx ;gh frequency 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 awa9xgld7xqe,iu o g n/*;y can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Ap60a* m7wg nmf*ujs 7plpine 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. T mj70spa guwm6*n 7*pfhe 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 s*; miid 5m eck0io8s1vtereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room eomk c15vi;m8 i*ds 0i5.0 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,e,u 4-m tgl*ao called “singing rods,” 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 clelomt*4ae, -gu ar, 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 freque-lc z2hfnb;mj fuw cr/;vxfh j1q 97wp4)-c3uncy of abo jj1xuhpm )lvnfb-;;792qcc zwuh-f /4r3fcwut 1000 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 M ocp.cnu5 qd0f1hu:;w ach 2.0. An observer on the ground hears the sonic boom 1.5 min aftcuw5d: .o q;npuf h01cer the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ze y8ytz)v02 b;q/gcuek g)m; 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