What is the evidence that sb( xae4d z*, seth3)gkound travels as a wave?

What is the evidence that sound is a form of r/zrvofr(a(ec s7d 2m cv39qf (8l r;jenergy?

Children sometimes play with a homemade “telephone” by attaching a string to the y;z..a9yaqqlz5n 1vc bottoms of two paper cups. When the string is stretched and a chiyvy9 .l5a; zq1cq n.azld 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 i) 4 ns0pkv1kqtnto water, do you expect the frequency or wavelengtp0 k q)4kvst1nh to change?

What evidence can you give that the speed of sound in airm )1ikkix +zj73okm- lzxu,i * does not depend significantly o ziolmku-x1), 3*ki xk+7jzmi n frequency?

The voice of a person who has 4vl3ruk; o; 4 enc5q(xo kzlz*inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch om nz hra)8no1 k;p7lv9f organ pipes?

Explain how a tube m: 3s(i xarvqzj1uw h(iw;8(ty ight be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example;3i(:rtyhu(wq v1s 8a(wzix j is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetyxwrwgc.5 )zcc-s +-m fy-6bhher as you move up the fingerboar5+ cyyw-6wxhs-bcr) cfg-zm. d toward the bridge?

A noisy truck approaches you from behind a building. Initially yo 7dsh0f o4qsnk)dk*x*dw+ 0 idu hear it but cannot see it. Whe dkdxw+son7**4f s )dqidk0 h0n it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferen5yyc* i1bdf )tce in space,” whereas beats cani5cd)1t *fyyb be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speake3 acq k3cnbxpw69dm0;u q w71 psf:w8ers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer toc;f qd0c qamu8k93wb p w1s we376n:pxgether?

Traditional methods ofehd )do).zicq 0* 9nsp protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts todq *snphec0).d)oz9 i 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. 12–31. Each wave can be thought of as a sup re;30c2mm),fq e uszherposition 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 frq)m s;f03hz2m,ucer eequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thya4+/b4xszuq*j0 ktu e same direction, with the same velocity? Ex 4+z qu4/u asktyj*xb0plain.

If a wind is blowing, will *xrs 7h)q l fbyw+b/6ithis alter the frequency of the sound heard by a person at rest with respect to the source? Ib+i)7wqyr/*fshx l 6bs the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mdc m8 mp6*zlj-6id wd;onitor is blowing a whistle in front of the child on the ground. At whic*6 pdlj dm-c6 ;zwd8mih 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 her sh thl)yn/; s u/ u;zefbb06c2asnm oc1+out reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the letcs0y muan;1 os ;/nbz)ulfe+ b2c/6hngth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his5zbi 8kak amag7*u st2(ym2h- ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly bsu 2ma zti5*h2kyak-a7m 8(gbelow 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ingicm8o w25ow5 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 fosb0* .er2 1 zxjiv vn9;qbdjhe*9dma0ggy day. Without0rz bsv*e.a9hqjm jxb9vd d1 ; *in20e warning, an 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 sqbyi( rb;*m 7jplash it makes when striking the ;ijq 7*b(bym rwater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the h n inja3:fq)+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 1.1ni :+)qfh3jna s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made o4c)esob2sb r /ver one mile of distance by the “5-second rule” for estimatinb2 s eobrs)/c4g the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensiteydig6 .g8)l/km/ q1wymks-e y of a sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ofc ++ox3jh x6dcu0 bv4( azmal7 a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wjfm5.fr ;n - +ymzlhi3s, .gxshen fired simultaneously at a certain place, what will be the sound level if only .z m g3,hjix.lsmnf;-rfs5+y one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain di v9fjdo 8.spx 0)u9lijstance 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 the captain shut down all but ov 89li) x9d j0sfpj.uone engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whe6+ytxa ; bn-tfreas for a CD player it is 95 dB. What is the ratio of intensities of the st ;+ynf6a x-tbignal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversae5c w7(p bp +4i9a;qw1suxmkwtion. Use Table 12–2. Assume the sou qs;wb+pae7i9x c5pwk(m4wu 1nd 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 eardrum whose area is ) y4xfi0elr9/4 l etln$5 \times10^{ -5} m^2$ (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, while4u0 f,xik puf*kq, wg a2;;p/t6 kjcvv the 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 lgw q/ a;xjuf cup,* 0i6fk2,4pkvt;vkoudspeaker 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( g w/ .wntmye446ieehaca7 -z 2.8 m in front of a loudspeaker on the stage.(y.46 - ng7 wemzi/h4twaea ce
(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 sou2u6. 2cgjxe* smmc p) jbnq;8ond level of 2.0 dB. What is the ratio of the amplitudes ofpj2 m*6nsx uqjc 82.oe;cmb g) two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will tvf +vm63as9w ih+ dh5 f/vwug7a+prx 0klxu38he intensity increase? Increxxhv5i06lkp m9vf 8vg+ 3sdhu3w+a7a +rfw/u ase 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 twicecphy 7-*aejw. s ;fcg9 the frequency of the other. What is the ratio of their intc*;syg7.e9 pcafh -wjensities?   

  What would be the sound lev;*qxh2.vp 0s *znbhxkel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating a. *q xxb2z*hnvsp; hk0ir molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1p4xu vhu/eqs.g2z ;3i00-Hz tone that has a 50-dB sound level? (See Fig;qx ve34/gz2pu u .ihs. 12–6.)    dB

What are the lowest and highest frequenciesva0j c svc4zw,6 e065x ar8orf that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) evax06j0r8 , zc4aw5 forv6cs

  Your auditory system can accommodate a huge range of sound level5j8)eqne7e3liuvy9 r.j7rx dkyy b5 ;s. What is the ratio of highest to lowest intensity a;e 8k 5v dnry)rl 7q95b ejyiey7j3xu.t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Theo47syq2zy8l eg3f7gn*7fx p 1 wdnlc9 length of the vibrat2nl qnyxlp779e 7 zog1 4 83wdfc*fsgying 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 long. What are the fundamental and fi j gsmfaxs0sqrbhtca /a*c(+j ) )1yc1 i8(o6trst three audible overtones if the pyc 1gq+s ths asr baj*6iax/0m81((tc coj))fipe 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 oqino -00qy-iwould you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumedq0oyqni-i - 0o 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 hum o*y7s1iqn;x dan hearing (20 Hz *qn7ixs1oy;d 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 frequency of 540 Hz as its third harmonic. What willw4 : 4 (d9p9iimh dwzcm;wzd*p:i ip4cmz9* 4( pz ;wmwdd9hwd be its fundamental 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 tuned to play E abov+okzs4np t)( n c6ayh9e middle C pha)6 tzkysn (+ nc9o4(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe(8c jj fel-jxyg5*t;r that emits middle C (262 Hz) when the tempj5 8;ryj*lgf(x ec-jterature 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 lcb0c bt *t*q)at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thebvhcv9.a;y v.q6: a,os.d*b* hc ntst flute in Example 12–10 should the hole be that must be uncovered to play D above middle 96yh,o;nqba. d.acvtbsvst *:v.hc* 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 cc0qz b2c+ +ngfan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whfbzcg+ +n 02qcy 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 1egw-sm ttz)9*h ,v+dyce3xf5.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330symh d 5z3w9+ -xt*fe,vcgt )e 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 hk9 3adp do,9zstm*p +$^{\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 a 2.14-mol jd lnzh.k+b.y2-v; -long organ pipehlv 2 yzj+b .n-o;.kld at 20 $^{\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 thef,l +mn:ik;3m8madl cv- m2 w2 ddzve+ h.h5ur 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 answer to thehvem,.2 am dnc; ivl28duk:+ d3r mwzf+5m-hl 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 sxqzqkz9xlp cnoju- ;1 3) 81mv when trying to adjust two strings, one of which is sounding 440 Hz. How f9o xq1qjz3z8k; cvpmx 1lun) -ar off in frequency is the other string? ±    Hz

  What is the beat frequency6kl+lteuf(ty6z/0 ;yj )ld)q2fo fx b if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand7wdf+i xp; -kz X) operates at an unknown frequency. If neither whistle can be heard by humans when played separatelkxw ;d+-zfp i7y, 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 sounded with a 350-Hz tuning d lp6a o/d*;g wdx)l5bfork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freqda;o) ddl65b xp/lg*wuency of the string? Explain your reasoning.    Hz

  Two violin strings are tbwo( uf5iq,4ia oqz9;ec/;neuned 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 neuqfo e5 i(; /q9o,4ai;wbczEq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each 1 j1ui*matb-f0 zol bv6o.i0 ntry to play middle C (262 Hz), but one is at 5.0°Ci b1*j zntv.um ob1fioa00l- 6 and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequ+ju7bs -.ff0d3-i7r ejxr sbvue o6b 0ency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togs bue60- f- be3rjxbrsu.dv o+7j0i f7ether, 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 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 ,klemuo1:bpnac6 sp+ rs) q)4 person stands 3.00 m from one speaker and 3.50 m f4s +o k:)mq l1 ,rnpe)pbcasu6rom 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 a piano t*npv rz u/;2avuner hears three beats every 2.0 s when they are played together. ;a*upv rnz/v2(a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.7t v6s7: mp*tqdxcz(9 : eav+eyak-;pv6 m in air. How many beats per second: 7 v9sd; v-*xp6cpy zvaeam(ttq+:ek will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenl6h;km90n43nhve 1vcrtb+tnmul4 0acy of a certain fire engine’s siren is 1550 Hz when at res+0 vu 1kn at9nv;l3h6em0nmhrt 44cblt. What 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 frequency do q wj) ykke6k.1z u7 h.xui+f-vyou detect if a fire engine whose siren emits a.u7fj vi z qykk1ku6+ hexw.-)t 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:y+rh5 fiud2 t source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exac i r:htd2uf+y5tly 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 equip2qj6)uphnt 3)t3cblqtq o :d*ped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 t tlt*6q3jn:o)ub)2hqd 3q cp $^{\circ} $C    Hz

  A bat at rest sends ou kcsdzbar;*5x;abr.6 4ct uo4t ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequeb o4casdr* u4c5k;;.zbrta6xncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sfs19w ,ttq 8f(+i)mqi ah; vvgpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?t(q;a gv 1iw, i8) stfhf+mv9q    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba 8*aig9 e yb6x (td8ky1)an oliwas played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a )g yenk6(8 1it9bo*aildya8x speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood- v o zb+cicp70z ;z1 k12vbmisoio6v:,flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expeczvm oic,6v+o oibk :07bip21z v;sz1 cted 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 ultrasonf/3xrp+i9io xic 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 v9c)13bexe6hido7.pj cx0 owfrequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observ jco eeh o0379wbx1c).d xip6vers 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 at 20y83 c77zs p 3n8vobzbo $^{\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 spe7 (l5ahph0d/ ni smz+led of sound is 310 m/s (a) What is the angle the shock za(/mnd70 5lhilh+s pwave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the ser *o/bawy,gt9t)c zxj 042qq peed of sound is onlywe yc,jo/ t gba*2q4qx0r z9t) about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 850ui)6r. inw+z n0 m/s strikes the ocean. Determine the shock wave angle it p.urn+zn)i6wi roduces
(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 j( 6,h:thfhrv;pk(g x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above( (ny pxjz7jpqd j52o1-fvb2f the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distan jz(1p22(-vo qjdb7yj5pn fxfce 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 sends0j nfnazp7 s-,rv:ha ; 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 minimump0j a;sn:v,hf7a-zr n time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audidftuvp wn/) c ia )n/qy8,i5m.ble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewe: rdwch*gtb s 7pz-k,:r pipe symphony. It consists of many plastic pipes of various lengths, which are open on both enbrpsck7wz *dg -ht::,ds.
(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 kqy;hw po9cm3ev a4r:d26v8r to the threshold of human hearing (0 dB). Whaeh8 ;cp o93v:ad6r4vw2m kryq t will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are kmfz 9tz-8b9s *l0 rmiheard simultaneo sl m z0rmzbk99tf*-8iusly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What w8*xnqcy,v9 ris the acoustic power output (W) of the speaker, assuming it radv9ncrx8wqy*, iates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops *jy s6vk1n:d:l r+ucy by 10 dB at 15 kHz. What is the power output in 1l:vcyny r+ ds6:u*j kwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deli 5(lh6gii a/vices over their ears. Assume that the sound level of a jet airplilig6/ h5 a(ilane 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sysh p-ko, 5; bl8j1xkmibtems, 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 2j93;kv 9qqhe 7cwhf5wxp7oi1$\frac{1}{2}$ 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 3 /06ws,l 0m h:zvig9kuk)be vt2 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per k/sm)z6 9,ltvgw0 bu h0: kveiunit 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 r)8lw1p ,qtpi pfw( .oabove a vertical open tube filled with water (Fig. 12–35). The water level is al(wor,fq.8 pw)litpp 1 lowed 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 thge .f ksng7+r6at is open at one end and also 75 cm long. How much tension should be in the string s +e7r6.gkn gfif it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was 93,e*sry x4t*,cg hmu z+iutaobserved 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 ton ej-anaw(+.sqe 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 othea- a nwsq+.je(r. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz (l mdrjlbo 1o+mu5w 9 z0m4pn0whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequen9nol0 bm+54p0m r w(lz1mju docy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appro hc:lc6e pdrlke5*61zaches you is 538 Hz. After it passes you, its frequen6*z dcllp: krhe 51e6ccy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can e+k,1d2 mz8 nm tz35kzvqr6 z*du u8gzvstimate 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 octave (frequency halved) as it goes by on the stdz mq3 kd8t2m,kzv nv6zz+zrg 5 *1uu8raightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11:h-:ed2zaxtq n *rs-dq ,b wf, Hz. The shorter one is 2.40 m long. How long inab :w:xrd q,d-zf-het* qs ,2s the other?    m

Two loudspeakers are at opposite ends of a railroad car asm5wnl9,g7ija it moves past a stationary observer at 10 m/s as shown in Fig. 12–37ng l5am9,ijw7 . 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 him, at C?

  If the velocity of blood flow in the aorta is normally fq ici+bvyej 2vn :33(about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Asscqb2f+jneiiv3v :3y ( ume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a l63o y go zig(3i:wi4rmoth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detectli(yrzog 33i 6wig :o4ed by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches odbqes i bi:4./v cblq:ct* 9c qm2(-ra 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 nex( : dei9ic.vl2/ q-*o4:rbqc tbcsq bmt chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used toaodbn(2l /rm: l7chk + send signals from one Alpine village to mhod alblc 7+/r2(n:kanother. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stetzq4:i13+rf8 n6npfp -fn zoereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locatioo61r4pf8i3 zp+:nfntq zn f-ens 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 “singinm l49i bda1ge5g rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. Thgil1 m4b5ea 9de rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fr4 ,pd aln*m:gyequency of aboutlmpg 4,ydna: * 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 Mach 2.0. An observer on the ground hears tblu0f2duf 0a vngx76*he sonic boom 1.5 min afu0 2gad70*ux 6ffv nblter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboz v+eok 5uqyg):9los2at 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