What is the evidence that sound traveh/ +) ij2cfe6.xwkfp vls as a wave?

What is the evidence that sound is a form of ener2yjk,qy *y(a ggy?

Children sometimes play with a homndhj4eakk0d or3/hp 3- 5w z3hemade “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 sound can be heard at the other cup (Fig. 12–29). Explain clearly how th0h-rzk wdj3 3ha4ndpkeh o53 /e sound wave travels from one cup to the other.

When a sound wave passes nhfsrs5/c7oklk -8xbzahz /43(nw1 e from air into water, do you expect the frequency or wavelengt/zk/-sa3c k( ws4fbx18 n z7lrnhheo 5h to change?

What evidence can you give that the speed of sound in air does not depend sibgsuofu/8 - c8doojpuv(/ 8a1gnificantla1o s-fu8 (g8co8p uovduj/b/y on frequency?

The voice of a person who has inhaled helium sou kg y2;v f;+lfhra2j8dnds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes?a7njw 91e qtg,

Explain how a tube might be used as a filter to reduce the ampg7l6 ntxo4q0 qlitude of sounds in various frequency ranges. (An example is a lq60xog 7qnt4 car muffler.)

Why are the frets on a guit10eqks;5- n z2 nwyeq kkel9m)ar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bri5k; senmeeq1 9w ny)0l-zq2 kkdge?

A noisy truck approaches you from behind a buildj4 g,wg(hhb2 c8jf+k fing. Initially you hear it but cannot see it. When it emergehc+,gf(h 2gjf 4 wk8bjs 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 “interference ycup.iydksd0q:o yq;+2rt)n q1:1je in space,” whereas beats can be said to be due in0yk+ 2d;s .djpytoyr::qu ec )qq11to “interference in time.” Explain.

In Fig. 12–16, if the qe.av + ugqis*7.6 te, ygafwoe51xp 3sl57itfrequency of the speakers were lowered, would the points D and C (where destructive and cons1g3. etlqi s7 v,t6gxy pwe 57f5 .+*aisqoaeutructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work ax. dc4ztud 2y0 :mlmnw*0;tz in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relativel2 *a; czd04nm :0txu.ydz tmwly 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 sgp . z 5l6cikshk/uw86uperposition of two sound waves with slightly diffw. 66/ 5pi zcuksgl8hkerent frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the sam sb+p);a.amyz 28u dfve direction, with thf)2msy.va8 b;d +zpu ae same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard b.d i v89ynnqig*dy+2 ,ngki4dy a person at rest with respect to th,2 dgkny.v*n4gyq9+ dii8n d ie source? Is the wavelength or velocity changed?

Figure 12–32 shows vav v,m (ss7ba+s-qky9qrious positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. A ss( +yvq,bv-7 sa9mkqt which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fhh ;y-)vj gr1eor the echo of her shout reflected by a cliff at the far end ov) -rgjhyhe ;1f the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hern5si :paz13xz b w,2oars 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) andoz w3b1,xn 5sra :2pzi does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ne) o7m;s ch *hosbp31+ )pfxcair 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 a* ymv1:a+,s mhc blup9bove a school of tuna on a foggy day. Without warning, an engine backfire occurs ohu: m+as1l* y 9mpvb,cn 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 splash it makes when striking th gf)up0nt;4yi 2ze)y he water below is heard yng40; h)f2i)ez yutp3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike ttc k8uo*jh2 0*hk5cnohe concrete pavement. A moment later two sounds are heard from the imh8u hjc o2k5 *kn0*otcpact: 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 the 0fjoa-oh*r 3u2nh 0 vb“5-second rule” for estimating the distance fr0b * nfu2a- o0o3rhvjhom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensitbwirr:9mz)as,;. m/ /dsx xzyx +cca;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 of a sound whose intensity ism/hm 4m rbs19zbu 2c6f $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wh7bjeei 4m -vxkj(1b :gen fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s -( jkemg1jebb :4ixv7.]    dB

  A person standing a certain distance from an airp + m0zl.j:forolane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Who+.:o 0mjz lfrat sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-o0+vj o,e0-x)soo azbto-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noe)o0ozxo 0 vajs+-b,o ise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spe2 jxci.4k 5w k n9q scywiy2;da,fn01aaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a .ic x2kaifw q1y4nywk2 95;jdsnc, a0sphere 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 are yb-qqq 0.ow7wa 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, while5agk1/: zvnx e7y co6o the more modest amplifier B is rated at 4/o1e zx57 :c6vgknaoy0 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m ip( r ve7ll9dq;n front of a loudspeaker onl7rl(v ;edp 9q the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound leve9npt.ve;7vn: t(s meg ycz:-el of 2.0 dB. What is the ratio of th(:;z: .n ge vycmttvn 7-s9eepe 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) by what factor will the int)oqivnap5e( oss g.:7. ;ucyxzzap0( ensity increase? Inc. quso0zezag7(ac opny5.i v(s) x:p; rease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one kjvnvrm 1 t90wx j.i1*has twice the frequency of the other. What is the rat*jjv1ni.0x9r wmt1vk io of their intensities?   

  What would be the sound levb j0,par (qjfs82me;t vqe:5s el (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibj5sm; rsb,vee :af0tj 82qq(p rating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz toldoruo :/ d/t l8.d:dwne that has a 50-dB sound level? (See Fig8drd::o /.tdold /wlu . 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the sount.m+ m ik m2l ral+;2xad2fvrl2 5p4ojd level is 30 dB? (52 ;ol l.vd2a+ lt+am42imprfmkx 2j rSee Fig. 12–6.)

  Your auditory system can 9h iehh3 5 ram,.xtjyk59mr p8accommodate a huge range of sound levels. What is the ratio of highest to 8,593h.empajy95 hmkr trxi hlowest 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 Hz. The xewd98e, 3 hbclength of the vibrating portion is 32,w 3x8bdce9eh 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 fundamenf kh h0w,t4aka2m;, xgtal and first three audible overton,k0wx,2hag t 4;mhfkaes 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 fcort5nyfa,0 *rom blowing across the top of an empty soda bottle that is 18 cm d* o,5c0tf ynareep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spa(l3 u n6eu.:imeqhx +e- rcqt6nning the range of human hearing (20 Hz to 20 kHz), what would be t nix m(6 .-lu+eqq6t urc:ehe3he 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 v;y9jq 3j(xsfits third harmonic. What will be its fundamental frequency if it is fingere9jv ;jxsfqy3 (d at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p0k b swo8eby(px517fh m g;w/play E above middle C (x0k(y;pm hweofs/ p57 g w1b8b330 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 gwxlz466sgil 1z,s n48ik i9 hpipe that emits middle C (262 Hz) when the tempi64g,1 n9kl8xzw gh 4ss6lz iierature 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 v gd;u;1(xzat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should thbyezea *y *z::q8g4t 0o/5j7 puuydhfe hole be that must be uncovered to play D above middlz4yogjyy h::eeqd87 **ft05zupu/a be 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 pipe2 k5 9 niuxbq(mqlc9x+ can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequx2qlu5mc i99( qb+xknencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long 4.alpjd azd67x:4 tvl is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hzz4l xa7.tpal dv46d:j . 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 . om/rqfg 5bk;4s xmh:3co i3s$^{\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 /gg; xzwbj 1y4u me8r+audible range for a 2.14-m-long organ pipe ;1xwyg4g+zbm u8ej /r 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 the outside and c/+z:mda mgj4e1y j1g 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 1zgmc / +ye4ja1mg:jd in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two srz kxn2z-d6q9trings, one of which is sounding 440 Hz. How far ofnq kzz6d 9-2xrf in frequency is the other string? ±    Hz

  What is the beat frequgme8qwn.7tlmqis6. p8 ,y e0uency 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 23qxb4 s b;+1apw zw;fk-x 25d8kx;esvv.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played p ; 2x4 vqwfsvxd5+ keazb;x ;1sw8k-bsimultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunij ;)uno;5a vjtu7gvprc +4d,s2r 5dpong fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whjd4;2 aujp7 ovp;vu scot+5)g,dr5rnat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensi6*rbgs8rh:v5c3gsxy on in one string is then decreased by 2.0%. What will be the beat frequency heard y: 6g3 *brxhsc8gvrs 5when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if f8ypb j;1nt:h two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at ;1y fb8pth jn:25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44g6 9mg,.lvyd8glv2nq cas) 6 b1 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 a6 y6gqbdg2. ms, 8v cag9)llvnre 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 a. wzv84ien 6c5w1i a73tto ykapart. A person stands 3.00 m from one speaker and 3.50 m from the other53 17nciktavwy tw zi4a.e86o.
(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 piae8p4+par8rn l*24 v-nmp sj(t espla +no tuner hears three beats every 2.0 s when they are played together. (a) If one is vi (e 8-n4n +tmplj eassap8rvp4*2l+prbrating 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 wavelength-*5+ afipeh2pt,a pb ie-ny4ms 2.64 m and 2.76 m in air. How many beats per secondmephapitn5-2*fp4y -b +i,a e will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550,b3 9ypjc;d2p nrbti - Hz when at rest. What frequency do you detect if you move with a speed of 30 m/spi2,t jrybb93n -;dpc
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freqh2 .n-l*wz/g gzw.d* vssnl i)uency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed s zzhg l*wv*-lw).sd n.2/ngiof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frehgxmyif)9 ,s6quency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are6f9s hixy g,m) the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the savk:kxux2 k- +n9y2f mtme 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 frequen-kuvmt2kx +y2k9 nxf: cy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic s nir1d1)i*1w)hxm)kq n-qx ek4z 4gadound waves at 50.0 kHz and receives them returned from an object moving directly away from id)1*ixq1e4n-kam h1k qw nxg)) 4zdrit at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of rhutv) j)mb;93yg he )5 m/s As it flies, the bat emits an ultrasonic sound wave w9gh) bhv je)m; ryt)3uith frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba tz,8bm.h)oq j was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone wh)bzojqh8 t .,mile 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 measc2q5j ) s :wypv*z-vbxure 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 artejzbp*v ):x-vw qcy5 s2ries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrask vqp93gacc.7hcf62i onic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12rgb 5c 23glxc1w( ij,mr/ u666icew oy m/s from the north, what frequrwb j/mxge6g5 yr1o (li2i cw3c6,cu6ency 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 mou bnuo)j0 2fb)ving on land if its 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 1r i2v0 l nxeb)f3b,efis 310 m/s (a) What is the angle the shock wave makes with b)f0xf vrn , 1biee32lthe 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 speed of souncx*4q*p pxn )i5u-uqyi+xo y5d is only oxyxpix4pqu5 q-*u)* 5y+n i cabout 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 wavebm sgctjz* r 1s6u)f+ q-he3s; angle it producet h sjufb36;*s-zcmgqr +e)1s s
(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 q by 2*v 6)a8)0ziusibea 9run$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overheor-s9wce2 uo ,bw+qafdvy:8;ad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled awc-wqb8,df uaeoo:vs29 r y +; 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-H(4rk(* zv qd(zd a;mtrz sound pulses downward from the bottom of the boat, *(dd 4(rz(kaqzrt vm; 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 water)?    s

  Approximately how many octaves are there in qj wdng2zwwq .vgl8go +kj-3c*9m:1a the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. /2rz:pm4 ko),:4vtb s1 yovk bygd 5vrIt consists of many plastic pipes of various lengths, which are open o5rpy v:zt s44y1v ,d :bogkb2rm ov/k)n 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 e-)cqx wh /avp ;txnwr29:4 wca sound close to the threshold of human hearing (0 dB). What / 2ww)phx- c:qa twcxe; 9r4nvwill be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 8c9cwju6lusdw -we7 322-dB sound and an 87-dB sound are heard simultaneously? 9lww 3w -d6 ecc7uj2su   dB

  The sound level 12.0 m from a lo977cgedk6sznk v-yry 7st0.judspeaker, placed in the open, is 105 dB. What is the asjv- 6t9n77r gyc0dk ks 7yz.ecoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150i8 z: yi;gqa6o W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wha 6zioyqi;a:8g t is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. rj 1ilg5e*7kn.ichj1ocg * k1(ilr8slylh*, Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and thathhjg cslje7 c*1ikyrr5,. n io1gi1l*k* 8l(l 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 communications7c*wjs a5wa1k systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a freaxlbw. mx(0w 0quency 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 qame y l.3g6b*c:o/)utx,cev between fixed points with a fundamental frequency of 440 Hz and a mass per unitx/c: tl aco,e*g6v) q3ubyem. 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 intoxk-ceix xkw )3cio .n18mi4r( vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to reso3mwxk 1)x(c8-.rx ciiien4ko nate 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 strwo*c02 gxygv()9- yhwl ovpt4 ing 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 thir vo )9*xg0p-(hlcgyyt4 w2ovwd harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full ll4* g5ex)nk+gl. rwoqoop ($\frac{1}{2}\lambda$) 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 500–1tkrlfd3 7 **2)asb:fgq .qshx000-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 poi2:h ba7s*d.xt*kq)3q g srl ffnt 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles e iqy 4ri.+:03ztb.kcjgng7d. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when:3tn q.jb i.yz04cgde 7rkg i+ the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.e;bb2tm x z+zn 1l71dhoe.a7n After it passes you, its frequency is measured as 486 Hz. How fast was the train movinen1mx.1l d 72 +anhoz;zb bet7g (assume constant velocity)?    m/s

  At a race track, you can estimate the speed ope84 ,nzm e/aof 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 straightaway. How 4m8on,ep/ez a fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency o+gv 2/me4yai m;tol4tf 11 Hz. The shorter one is 2.40 m long. How 2yt4tmae; 4i lo mv/g+long is the other?    m

Two loudspeakers are at opposite ends o)rgwmv, h j-,kf a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identick-gv w)j m,hr,al 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*+s xqqi :a88vleyio) aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directe)a* yli8+ieoxvs8:q q d along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whimlaj; c8lz 3c1le 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 detected by the bat after that wave reflects ofc mja; l1l8z3cf the moth?    kHz

  A bat emits a seriesmgb. wvr:- c.w of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eachv.. :bw-rgm wc is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once us89 mbju(hp zq.ed 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 sucubzq.8hj 9( mph a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised v af,)jt09poj5j6fi 7ij lxf4by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculatei,jj4v9i5 x6j7f ftp0fo)alj 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 abvkuabh.1a -1 luminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practab -u 1ba.1vkhice, 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 huq3dm h+oyso2 nim:o4z) ec+x,man ear at a frequency of aboutx o oe q34: nm2zd+oc+hmis),y 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 the sof1 uitjy k5;n6q(l1rk nic boom 1.5 min after the6jfnr1uytq k51 ikl;( plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is: xa/4iktigy3 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