What is the evidence th,dnw)gfnpvm7jf c0 at:o+(8x at sound travels as a wave?

What is the evidence that sound i2stk 55wk)pvk hsrg 7-s a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to 62sp1s ura.mbthe botts1.rpas26u bmoms 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 the sound wave travels from one cup to the other.

When a sound wave passes from air into /ok1usibg j:. water, do you expect the frequency or wavelength to cb.:/uj 1go skihange?

What evidence can you give that the speed of sound in air doesh4 fp8 fee7zz2 not depend significantly on fr p2e zfz8fh7e4equency?

The voice of a person w,0 ycksoln-r -ho has inhaled helium sounds very high-pitched. Why?

How will the air temperaturejk (p(duc1vs1qym qm )1* pl/o in a room affect the pitch of organ pipes?

Explain how a tube might be usem2ojnp o0ni0xms6(+i3sax5a hulc8 :d as a filter to reduce the amplitude of sounds in various frequency ranges. (: p nio0n2lcjm 5ia8hsmx+0x6o au3s(An example is a car muffler.)

Why are the frets on a guitar (F sr. r j:3) +*slalsusrjd,5hfig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?rrrsaf.s)u 3*jd:lsls 5+,h j

A noisy truck approaches you from behind a building. I+wj ) o;3+vkim mo0lhwnitially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mmjwm )iv+olho 3w0k ;+ore of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,”z7mr55i q5tz m whereas beats can be said to be due to “interference 5 m57irmqtz5z in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poindgkr4c*z/g. tu: xyk 6ts D and C (where:z g6y.c 4gtx /dkk*ru destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in are 3ct4stsecr jivo(:n0m 05 /gsas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more ntieo0 s jst5g(nc 3 cm4/s:rv0oise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave cauls0uxid/4.qhj..a r s7 (jsqn be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two (0 aqdjjhslr.u /74 s..xu iqscomponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the ph;d r9qylm *u-5 a;nd r-um7asame direction, with the same velocity5 mr-;;a hudm 9dl-yn7 a*urqp? Explain.

If a wind is blowing, will this alter the frequency of the sound he0 bqa6b9v4 w7w; nlrznard by a person at rest with respect to the source? Is the wavelenn wvlr ;nbqzbw67a94 0gth or velocity changed?

Figure 12–32 shows various positions of a child i g48aphuz,g, zn 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 sound of the whistle? Explaiz,,4hpugg za8n your reasoning.

  A hiker determines the length of a lake by listening for tdkr* gmtzi8 ovimm f,))9 ,q2rhe echo of her shout reflected by a,*i ,d)q2rr8k)fmz9motmvg i cliff at the far end of 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 pesa ;fz(0g m5ship just below the waterline. 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 spp(5;mz f0gesa eed 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 in air at 20wbyds 7n1x+w* $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy dv 0nfsgr hs/(2ay. Without warning, an engine backfire occurs on another boat rsf/ 2(sgnh0v1.0 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 3v3hcda/*wk v9u/dvv the water belo/ avv h*v3ud3c/ dvkw9w is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hug/92;ei ju v ue7kz2ipwe stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s a e2;iu9/ejzpki wv2u 7part. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made .beta;o zh nca22o-l-over one mile of distance by the “5-second rule” for estimating the distance from a lightninge;tnc a.2o-z b-2ho al strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level oo-0-n1oyzwucpra *xb2 d83kuf 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 k5az 3 gtq*wwtzt41 p/ f-9mfjwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a syy jgcp,1p :8iz v:86d /hzpmml+gc8wound level of 95 dB when fired simultaneously at a certain place, wm 1dm/::lgzp gycz8 yivc+6hp88pjw,hat will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jej12h2j el 2k.goeg1k mb4j)lg t 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? [Hint: Add 41 j 2j1m egjk2gh2bkl og)el.intensities, not dB’s.]    dB

  A cassette player is s uz*ylz3 o6 h+go-zm;raid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities orz6zo+ og l ;zu3mhy*-f the signal 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 convers6kx1e6f ghu22dxn ow: ation. Use Table 12–2. Assum6h fk1dnu 2:2gxwxo6 ee the sound 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 ck*b ;(c2ksw ylu+li(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, while the more modes 3 i,k7h c+a3avf eqtwltkk9)-t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you ww 3itlke,t7fa k9vc3a khq+- )ould 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 ree)ep lj: vr9e7gistered 130 dB when placed 2.8 m in front of a loudspeaker on the7 9e )jel:rvpe 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 lebvi-f+dh rotogsyf 4 a,8 7+4pvel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose level4 4fv , bpg7s-+ior t8y+fahods differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilj2jw4tk)ev4me83 xlc l the intensity vkle m3 te)jwj42x4 8cincrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frequeb3 zj*-fq*e kbxmphq+;kyd;yets *)* ncy of the other. What is the ratj*fh)pb**sq3 +k eyd -*e; t;zxymkbq io of their intensities?   

  What would be the sound level (in dB)ro78 wdv(f g;h of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules o78fwodgv (; hrf 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level b 6 8zl9u 883uv3lljq5fjmwrfto seem as loud as a 100-Hz tone that has a 50-dB rmfzv9jj8f3ul35q u86wl bl8 sound level? (See Fig. 12–6.)    dB

What are the lowest and highub4k r- yqoqq7p84k1p est frequencies that an ear can detect when the sound level is 30 popqy8u417 q-krbk q4 dB? (See Fig. 12–6.)

  Your auditory system can accommod*dg7 - b*yh::oslifen ate a huge range of sound levels. What is the ratio of highest to lowest intensity at gh::- fo* *sedn iy7lb
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamwww2.h rivrt,k;65 ,3ctdrqs u 6g1faental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the s.63ah rvww tgrf;q scu6r52tw,d1 ,kitring be placed?    N

  An organ pipe is 112 cm long. What are the fuo26 xzs :6c vppg9lt+kndamental and first three audible oc6t ps6ok 9z2vlx g+p:vertones 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 exp n; a*wcx.h2ohm6zjn2ah*(lf ect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? ;*az(6jn*n.2acoh mlf xhh w2    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 rangez4 fh3)gu9e4v8w,tyng7vs k h of human hearing (20 Hz to 20 kHz), what would be the range of the v3gwn4ehz8h u4 9)g7y ,stkvflengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar stringf3nm jz5eg g/1j0 kj2d has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a len/nmk520dej gj3jg f 1zgth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 6gfov0a3c o (f/l,)tpj /jcd nm long and is tuned to play E above middle C (3 gp jd/,ov(joafntcf) 0c3/6l30 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 emczfl0r59pn0; /d fvjwits middle C (262 Hz) when the temperature iczf0n5 wf9 ;d0p jvlr/s 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 ;btk2nr) /pm x20 $^{\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 ry l ulb)cmbp;3zp:6 2that must be uncovere p):zy bc 6blp;l3umr2d 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 ca pwumj; j2maoj13f3 d 673whadn resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Sh2udw wjaa1o 7;36mm hfpdj33 jow why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ; o:eh5xtfvr1ends. It resonates at two successive harmonics otv:e x1; 5fhrof 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 -oa4mpxz3/ qfv;.nw-f: byb4k xe m9b$^{\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 cp:rrlu9p 5 oag8 ph.432vqie8vi.kq for a 2.14-m-long organ pip8.ivokah u3i9e5 rq.2:p8 pv4grl q pce 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 1qn4/fmp xq) gvy::qy kqv75eia 3p1 hand is closed at the other end by the eardrum.:eiq/n )7q mf5k vvagqp1: q4h3yxy1p 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. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s wheneoe79e, sv.e2 2isa8tt6ab de trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o7eee8,ei6. 22oaae9st st bd vther string? ±    Hz

  What is the beat frequency if middle C (262 Hn0y3k9 cb n1jaz) 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, 1bm*gj1(pgfg70baz* ) g4vdh jivzm (while another (brand X) operates at an unknown frequency. If neitherdz jp4bbm7vgg1hj()0zam v(i1ggf ** whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beat4/i:mvq+ eg- vfreohxr;3k 2ss/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tu /qh4 r;k:eg2v xv+i f-rmso3ening fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The t6 sv1lc *kgsgo- nsm iqe)sxe7( h3yn3ha9;3zension in one string is then decreasedg)7333l-ahee z*nh s1i (yss;xkg9m qcn6 s ov by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C(7cyguy 5+jjf hkrfbq9 act( ;82r;ot (262 Hz), but one is at 5.0°C and ty( t q;kc h7f ur98r;t2+yjj(agfocb 5he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency kjpxjk8-wc u- 0og52l of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possowjg kkjc8px -u5 l0-2ible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person oe-d 8t9jb 5knstands 3.00 m from one speaker and 3.50 m from the othernt 5doj98eb -k.
(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 tuner c2fzr/bh:yx0g3 fq ;o hears three beats every 2.0 s when they areqoy/h0 zgrc :xb2ff;3 played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wlt(*5qxrk k g2 a+ fsul8r+9xeavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume Ttr *2ql(kf5 rsx8k + l+u9eaxg = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirenuxp;2kkrwbsw lp-2++ lo:*s81zl qki is 1550 Hz when at restu1op2 lxk:kqp+-*l; l2rwb zwsi8k +s . 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 freq uqij1ql8g 6 4/oj2gyg7mk9 acp*p;fxuency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed oj jc2g4 yp8i/fx mq9 76g*lg1qopuk ;af 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency 8j,p3aifh dl5; raba5fj4rc:d*(n gy if a 2000-Hz source is moving toward you at 15 m/s versus you movind ;r, gf*a55d3ij8ar:4hb(nyfapcjl g toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the sameqyt7qfqj i-m-:4,yiv 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 7t :fyq4vmyqi-,q- jiT = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasorwl8xb8zja.rk 66 f1onic sound waves at 50.0 kHz and receives them returned from an object movia8k6j 8 zbolfr w.x1r6ng directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a wwd+h4xrn (nrc- an +k+lp/4 rspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency (ra /nn-h4rlnr4dw++wp +xck 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 was played on a mo l 1uqlo-*;hn pec:l8uving 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 81lp*:uc e;-hln uloqthe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to m ywz /u9u9f99qo+f/ ci.7fgxnyioi r/easure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed ofnw7 i u9qcz 9o/ go/fr.f9iyxy +ifu/9 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 sound source?   Hz

  The Doppler effect using ultrasonic waves of freq,fl 4 mm1lmp6mmdd5m7uency $2.25 \times10^{ 6}$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 itn nqqve4+srugj* kha.h;wd (t .42 +wind velocity is 12 m/st ;nga4jn2 h. 4r(duh+kq.w eit*q+s v from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on landoa;vl60jfo n ; kim2;d 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 ths: j1t 2jnm7wte speed of sound is 310 m/s (a) What is the a1sm 7jtw:tn 2jngle the shock wave 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 speed of sounuraasu 2;7d4hq z;) ycd is only about 3hz27) 4dryqauua;sc ; 5 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 the71btk plge(n2r0tfou /de 9lf f,+s+x ocean. Determine the shock wave angle fksl0puf/feote9n 2 7r lt,d1b+( gx +it produces
(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 d, ieew(.y ote9(g2 no$/theta$ 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 kmpaxz- jo9oab*0:iv1p tl wrp+7ly t1( above the ground flying faster than the speed of sound. By the time you hearpvazrjy7x:*il( l+1 b 9twp1to-ao0p the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward kdtc5kv c+ukf82)vw )from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed td)kcu8k52)cft v wk v+o work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many ocaaf83 rjd5m :ntaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displa0qwc nh*4:i:zy3tkvpy36d j9g 2ku n gy called a sewer pipe symphony. It consists of many plastic pipes of varig3iu 0n3y pjcz y kdqk42:9nvtwgh:*6ous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of humctza w76;p*ydkvb6- man 6 -wd tacb z6vm7;*pykhearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sounh h53tbexsyip5j1 gh b .91kx8d and an 87-dB sound are heard simultaneous15ibxhh e9 xbg3j.y kh pt85s1ly?    dB

  The sound level 12.0 m from a loudspeaker, placed int; gwr x1)67,fmtxpdn the open, is 105 dB. What is the act1r6dmp7xwfn t x,)g; oustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rateh ;17pjg; 7h5 kfi) wdupftu)id at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 k if )tw 51i7 h;pd)u;phjgu7kfHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. A 6/fjfg,j xlex-rs3n+ssume that the sound level of a jet airplane engine, at a distafg/ 6n +lj,sex-fx3rj nce 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 communicatio-lm- q8.y rsmjns 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 txbc5fm vr55owua +) pbne5:.g o a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betweenj+ *md ei8e*y;) jgrzf fixed points with a fundamental frequency of 440 Hz and a mij *r jz8degy;m )e*+fass 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 vibration above a vertaqmht .(o5q p7ical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water ha. t7poqmq(5 level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at onlji.l0.l r ln3v k1dl7e end and also 75 cm long. How much tension n.li3.j llld07 v1 lrkshould be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonapk c48l3btr*m 0mqu) zte 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 tone in the 500–1000-Hz range coming from two soutuc1;ngw;euh*t c/i ft2 6nm3 rces. The sound is loudest at points equidistant from the two sources. To determinec;1h3*n;6u twg m2/ut fctine 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 stationak 1x xtlvn4rp78xb m,:ry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movrb,x :4m 1ltkxn8 vx7ping train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftesnzo3yog: l n8x(,lq+r it passes you, its frequency,sno:lqx g8l n( 3o+zy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to 0g9p 4eva:v7 r+ju7kb) bxj owj.6penthe difference in pitch of the engine nonr o)pej.va7 0vg6eb4w x:j97kpb+juise 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 togethe pl3j/vdq:i a5r, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is/v:ijl dp 35aq the other?    m

Two loudspeakers are at opposite ends of a railroad car as itqmw1 d .hxq5r r9huojd( 5r+4o 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 heard by the observer when (a) he listens from the position A, in 19hj dxoq5 u(q5rdm.h+4 rwro 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 flon)oa /+/aihtfnnvj31w in the aorta is normally about 0.32 m/s what beat frequency wouljaf/1)h3na/+tni nov d 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 98ffw,,ju.a6 fck/rym br7 xpvnbt33 moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 f9cn by3pk3jvta /,8 ,f muxrf6br. w7m/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 off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. iuc f2hku t )xc(4-;lxThe pulses are approximately 70.0 ms apart, and each is about 3.0 ms u-cx)t4(u c x2k ;hifllong. 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 oo)vz phl pxfn q)*e7s+5z/ 0stnce 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 one of the overtones is resonating. The most populznstsp f0lxe7v/))o 5z*+h qpar 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 presence of stanaqky u/m y n7c.*mz45gding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living 5cua4* yny m/q.mzkg7room 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,” jp75kfc; h0 qpinvolves a long, slender aluminum rod held in thp7q;kph c 50jfe hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 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 ouvl -r7keqxr o262 1c:1r gyepf hearing for the human ear at a frequency of about 1000 16xykcpr2eol-:2rrgeq7vu1 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. 5fa 9i0wi 329-eghy1u ku.ze m,id bnkAn observer on the ground hears the sonic boom 1 wgu, i1ai35h9 .9uz-iyefnm0 debk2k .5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is mmd8b0i:uege6y *fp qds t;9515 $^{\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