What is the evidence that sound travels ac)2,h oe 3cd nhpg9lr8s a wave?

What is the evidence that sound is a nl7a+yq enz7 ,form of energy?

Children sometimes play with a homem gx y,u+ftpg/-ade “telephone” by attaching a string to the bottoms of two paper cups. When the stgyu- fx+g/,ptring is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave palwc(ko6 s /5cwsses from air into water, do you expect the frequency or wavels/c6cl(w 5 kwoength to change?

What evidence can you(w p+g8.1krnfh kwc. abs9xycv,b 1ra rm-*-u give that the speed of sound in air does not depend significantlypbk cc8ava rmf -sxr.1(9w*w. 1+ryg,u-b nkh on frequency?

The voice of a person who has inhaled helium sounds very x i 4+rzffn qi,zc4;fv26r/okhigh-pitched. Why?

How will the air temperature in a room affect theupjp8,we)que+q*h juz 2g k4.d2n oz8 pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amuy .2usr 5:jr6no ww0rplitude of sounds in various frequency ranges. rys25.r uwjon: u 0w6r(An example is a car muffler.)

Why are the frets on a gb7y ey r voo6g:mv3i(9uitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridgygvo o(i63emv9 7ry :be?

A noisy truck approaches you from 2ixqadb t3;bs;zc5,b behind a building. Initially you hear it but cannot see it. When it emec;qbiba3 z2dxt ;5sb,rges 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 bt-bsxn y86s78o xgz*m e due to “interference in space,” whereas beats can be said to be due to “interference in timegm s8txs*7-6nz xoy8 b.” Explain.

In Fig. 12–16, if the fre iu9l+m-dmuybqu c +4,quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move famub mdquu +4y i,9+c-lrther apart or closer together?

Traditional methods of protecting the hearing of people who work i*oas*(s- co si m+abf9n areas with very high noise levels have consisted mainly of efforts to bm 9*oab cfo*- s(isas+lock 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 shvz 0j r+szf*s3kf5ad *,xi+eo own 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 thee+* rf vo3fss xz z*ia+0jd,k5 two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sa1zu1x :i1muji1anc4y me direction, with th 11j4 inxu1 uay1mi:zce same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard t;nll:v jv0 xh.ppfc-xw59z:it8g1 a by a person at rest with respect tzxhf1xa l vp ;tl- .:nt9 0vwicp5g8j:o the source? Is the wavelength or velocity changed?

Figure 12–32 shows vpm g:gf xq4;iq)xl7o p 0:ahg/arious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sxa)/gg7lohf0:pp m ;4:iqg qx ound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of he d8y) f0r,- r2a1hfnl;8neoxhj oa/mlr shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of rdmo/l ;fa,fr8)xjha0 e -2o 1hlyn8n the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wl, wy1qgo+a*z zl(c l;aterline. 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 m/s (Table 12–1) and does not vary significantly with depth. ( lo la,y g*zclq+;w1z   $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at :do;kdekwbbnw2vyno 6.;yuu)bns; n :5 h(6l 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 driftinomch8gw :shqkx ,2j1wyj6 :r: g just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anothe g6:y jwh r2:s,8khxqj 1omcw:r 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 tyx 0.br2gzw; ) 0qj* m3ajyoache top of a cliff. The splash it makes when striking the water below is heardw0joz) a2y r y 3g*x0cqamb.;j 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees /gj/vjvatlqp7 bow ra,:* e91 a huge stone strike the concrete pavement. A moment later two sounds are1/wrvt,ve a7 9jp l:jga* qo/b 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 the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by +wmz-y*6 nvtz -h xrn.v7sguy(l h 8/cthe “5-second rule” for estimating the distance from a lightning strike if the temperature is (zszrwnvch/78h+*lyt 6. xnmg- - (yuva) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? 3w* q7m2crf4b shwtt4    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 intensitylpr/a-.uwh 3 1c (f9wca p.a w*kc jybqjd6v:. is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level 5(./fpl : vqsdycms 3jof 95 dB when fired simultaneously at a certain place, what will be dc( l5/pvqfj.3ys sm:the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an air g:g s9 :brek.0ylbht,plane 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 one engine? [lst:khg9 b,br :e.g y0Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 51 ;/.po,cia1 phsg joy8 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noi1 ojpy ps,1 a;oi.cg/hse for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outph36jfvjz7bkd7p np z:0n8 hnx s2t(; gut of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over 7fdz;67 t2 g jb:nzhxh08s 3kpvn(npja 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 eardrqzqgqda. u0l cuc67i7x k 1)o*um whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, b dxq23*zxt:l1k iq/p7 y;+r nmvi v.gwhile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you 3 d+2x: y;kqx/g.imv tqn1pil*7bzrv would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placdr9:h;9 5 z8hrpitcp led 2.8 m in front of a loudspeaker on the ld i;5 zhp:rrt9p c8h9stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.2z 4udkcjp/gt 3 59qc v*yqh)c What is the ratio of the amplitudes of two sounds whose levels differ by this d q3 9*jc5p2vgz ty k4h/)cuqcamount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa rrh5t*fi9zr )ctor will the intensity increase? Increase9r5h rti )rf*z by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenwbfo 0ss(, tgi1y(c km.941lb fl;rmuva :t(mt amplitudes, but one has twice the frequency of the1f.;urscl b4(bmt09a, (mv yf (:sgimk wtl1o other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in aira82mc ck70igb that corresponds to a displacement amplitude of vibrating air mg ciam0cb 7k82olecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level zyt05,cwu b5 v cuh1,ut e6a,oto seem as loud as a 100-Hz tone that has a 50-dB sound level? (Sectcy 0bhzv 56,,5t au ue1wou,e Fig. 12–6.)    dB

What are the lowest an6 qz-m (sbk)ind highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) (s kmqbn)6iz-

  Your auditory system can accommodate a huge raj3 ,cfspp j8 um4k;:/je+h-h8w ogqhinge of sound levels. What is the ratio of highest to lowest intensit8/pjghjfcjiph;+u8: ow4 h3 q-sek ,m y at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length o6jg t3xu3js1uf the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed? j31j tux3us 6g   N

  An organ pipe is 112 cm long. What (lvl8djt vjcx-)./yhmsc* o6)bgsa1 are the fundamental and first three audible overtones ia 81hx vgjv/lyo*(sl)c-s6d.tjm b) cf 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 b7awz)z*ti5zy 5k su 9mlowing across the top of an empty soda bottle that is 18 cm deep, iu 7 zm9y) sw*a55kztzif you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with openswn5q)usqn6wuq: *g) -tube pipes spanning the range of hum: 5qun qwqswu6 n*sg))an hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third haruiinyy;;,ovma58i7.p7 tcp+r mb g4 rmonic. What will be its fundameou;.ma vyp ;ipi,t 8mn 7c+5riy4gbr7ntal 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 5w5 sz-bjsv/ ,9s g7y;ihvqy 23 xptlgE above middle C (330hwl,sy g3js75 t2v;qz/sgy v5ixpb-9 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 (2h qhrk9 vf x0y7r5yx6,62 Hz) when the t 7k5,hfx9vyhr0xyrq 6emperature 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 20i ijh4p7 p h1qio1h m,py,u/j+ $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the hole be thh,z s,(qf*xqsjm+ ie+ at musthiq+*e,, sm(qf zsj+x be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hn i7:b f50uzjiz, but not at any other frequencies in between. (a) Show why this is an open or a 70 jfzn5 :biiuclosed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates1lx2;ug:+e b tkn3; j)ucjcta at two successive harmonics of bcaue xgtj23t;lj+c1;uk) n: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 mzy5 ;jz;.l hk.i h;bp$^{\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-m-long orga3dt9jgj8.xqj(51n pr fsg 1van pi531a8 p9g( xqsj 1dt j.fgjrnvpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximhjyqx)m6;v nnscbuq)z + z *77c+vs0cately 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 relationship of your answer to the information in the graph of Fig. 1n c)+ s7*) cvb07z6qcvj uzx hnys;q+m2–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2p 9g uei9qwhb1 -ms*a3:c6zy f.0 s when trying to adjust two strings, one of which is so*s:yw1 um -3pz9bei6afcqg 9 hunding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat freqiv*wuw*6m6:1 / 7vzz nazipzr gl6tk6uency 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 another9dei+x6(s39x6 a3k j(1 nc rcscznqru (brand X) operates at an unknown frequency. If neither whistle can be heard by hnr(dc nqx336j x9sazuk(c+i9 r c6s 1eumans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when so -u+w3uv ff-2h z,dv(zgw1zcxunded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your re(+,c 3f2xhugfvvz z zw-wu 1-dasoning.    Hz

  Two violin strings are tun;a,*gfn e8p:zuwj/p q ed 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 togethee upg:*nqj;8/ ,apfzwr? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will b2wffyrz qs ( il 4ly8d0o+g:1ve heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.zlg1oqvr8(swy f +0l :4d2fyi 0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; woy)3z xnj d k(uz .ryrf;rc.04hen 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 tofzyr r)o 3(dxzc0;yj.kr.nu4 gether?$f_A$ =    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 oncl z;5zr) jb fa3):8ub mvws*ee speaker and 3.50 m from the 8)wa5sbj zr:lb*mvce u fz3 ;)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 c+ *,ngh ot04iqos5y cvq9mf43tkj0c vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) Io4cig, + cfv0s 0kot3 jncq5*yq4t9h mf 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 2.76 m in air. How many .txh y2v c)nevm8vh.( beats per seco.nhxv2tm ( c8).evhv ynd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certait2 fdf zz9..oxn fire engine’s siren is 1550 Hz when at rest. What fre2d .9.ftfxoz zquency 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 fry (qyjy;2 gn+uequency do you detect if a fire engine whose siren emits at 1q;ynjuyy2+g( 550 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 moving toward you abp5 xxqm6().jlle /ktt 15 m qt(l).xx kep6b/l5jm /s versus you 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 eq6v i i6p3ueyx-uipped 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 iei p-u6vy36xfrequency 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 thyz(i*8 6hm l b3a7 lngrx*78p ivlssv+em returned from an object moving directly away frn6av sg lm7yp(8 i ix8l73z+lbr**vhsom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a2y42wspgs.f d speed 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 ygf4. psdw s22the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played onley+h(9 z0ijg. vxc;x 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 spe zhjx.+ig;v0cyl(e9 x ed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasount(a e/vj-j r/ud waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the (/j/jeut- rav sound source?   Hz

  The Doppler effect using ultrasonic waves of yr3s.g hwr5m qi q-mk:6z9 )difrequency $2.25 \times10^{ 6}$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 the wind velocit/ou 95ci qp;xzy is 12 m/s from the north, what frequency will observers hear who ar/x95c oz;q iupe 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 itazy m ehmew eb./z:-n6i)4:wis 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 iw/t g8p5i hvkt4dq1d7s 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mot7h/1vdp qdgi wt8 4k5tion?    $^{\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 speed of a bbbde9( li;(sound is bl;b(dib( ae9only 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 8500 m/s sze0x6,+fmqi dtrikes the ocean. Determine the shock wave angle it pq+e6zim,0fdx 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 ubn)n0z6 51v uu qo:ed$/theta$ 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 yp4 ,wzx;y;s qqt+ k kp:aes80above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane h q,k ;q0ytp8x;wks4za +yes :pas 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 mcohpd88l ,c(.z3 jqfdownward from the bottom of the boat, and then z8 fo8h dmc(pqc,3 l.jdetects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are th0 v,vbv: h6doew r11gzu8rdn) ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. 4s:a gzw1wez) It consists of many plastic pipes of various lengths, whis:)4w wz1azg ech 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 threshold of 6nd0f vf,(ldp l1e hx/human hearing (0 dB). What will be the sound level of 1000 such mosquitoes0 p/vfed,(nhd 6f1x ll?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB ss rpe6 k4ph;i5ound are heard simultaneouslyr5hiep; sp64k?    dB

  The sound level 12.0 m fr 8etps 9(/cnraom a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) oac 9t8( ersnp/f the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated atasab:es5ey (ll/ vkjjl d;q ;b7nd 344 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is thbvd 4 s;j:eqe5lal;(b jsayd7/3l4nke power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ov ,-8hxpl2qnrkdg od *8er their ears. Assume that the sound level ofnrpgd8 hx*d , o2lk8-q 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 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, tu0;x kg6(e xd0pd2* rbi,qsdnhe 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)tl0 uk .5zz bo.wzrl8 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 cmdb16; ry5 ghlket 8rh6 long between fixed points with a fundamental frequency of 440 Hz and 6br1hehg6k t; y5dr8la 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 vibrafai*) sjpuo e8amqw7gqk3,rn8n9 x 6.tion above a vertical open tube filled with water (Fig8,a39rij ws*m.n )8f xq67kepqougn a. 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 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 strin/hpph b 6n)os fa(,n3jg of mass 2.10 g is near a tube that is 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 harmhnaj)f(3 p so6hpn b/,onic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop va *oj k5 recbaq5bh2m9.*e8m($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz 0 )hy3 utz k;ufnm1z*orange coming from two sources. The sound is loudest at points equidistant from the two sources. To deteu0zzn* tuk );1ymo3fhrmine 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 sound?   Hz

  Two trains emit 424-Hz whistles. One train is ++cbefnki2 lfkr66sard6f 7,stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train ak6ika7 dn6f,f2rslb+ f6+ ercpproaches. What is the speed of the moving train?   m/s

  The frequency of a steam q9 /r,n d . bd/h5h*bgxfknle5train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast l5n* bq,dh/k.nxf9 h/g ber5dwas the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the */gr xp(r))w rwzd,zydifference in pitch of the engine nozr rzxp*r (w)d wg)y,/ise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherdh-a/z1:n .)fkco mzd, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long:n zfzkha-m)ddo/ .1 c is the other?    m

Two loudspeakers are at opposite ends of a railroad cve964*zwv p ch73qkqxygr8w 0ar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heardzceywh873qkvvq 9 4p*6 xr0gw 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 (+ i4zzodaam )d- qc3,cwlui -:-q ,zrulno k5about 0.32 m/s what beat freq-zz:+dr,ld -z o3)i(c knuiwa a5mql,-q 4uocuency 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 mot2+kgne* htaf 0h 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*0ne 2g +fthka of 51.35 kHz. 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 high frequency sound pulsi8cq6 fvl/.p7 uya8;l--jasbj zgio8es as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the e6salcvb8/qp7l8-.y uajiz;-g fio8j cho from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)j3,;;,sc i+:od9zh4l vx elrqf. z rhe was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only r;cxs:l i .9d + eo,qehlhv4rzzj3f,;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 listening can be compromised by the presmab3,ji(wpfsxi9fai+w , 9 1zence of standing waves, which can cause acoustic “dead spots” at the locations of t, bj9ifxwm af+zws 1( ,ip93aihe 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 rods,” involves a long, slender alumiu( t; *kod-ty) s3jfgvmhg(r7num 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 -tukfy(3 )j h t(do7sgv;*grmemit 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 frequen-i0hn * 5dy+qkj nj-yscy of about 1000 Hz idyn+n 5h y-s jk*0qj-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 t*2s /xzm zasa3t( .yh n-a-ecbhe sonic boom 1.5 mi2 c hm(xay/enzzs3bts*--. aan after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 q jg.ae*2p2:tdc: hyh5 $^{\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