What is the evidence that sound tramjgh ba gnla 40,x;v/-vels as a wave?

What is the evidence that sound is a .pf ,;v kemj))4z0pz rp5 bcd hw3(yogform of energy?

Children sometimes play with a homemade “telephf6.a 2jz ;h ;;skzd(2rheh tinone” 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 the sound w(f;ak;z hnr6th ;z.esj2dh2iave travels from one cup to the other.

When a sound wave passes from air into water, do you expect tpw12jta qv;*ihe frequency or wavelqiv*aw tp1j2; ength to change?

What evidence can you give that the speed o+ib*lbu p xe09f sound in air does not depend significan 0ebx ub9pi+*ltly on frequency?

The voice of a persot+gqdwfs7sr, i l05( tn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch oo ,(cfa ;w k)mrf8lx9ke/c* y2agx ;mlvl n:7sf organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds c .2bpo5nl*o5 tw m8pbjxin.6in various6op nxb.wjto*cmn 82b55 pl. i frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togezp e9kuzivm,9 m-t7 +pjrw 2*rther as you move up thezjm9 k*rtr-zei pv92p,u7+wm fingerboard toward the bridge?

A noisy truck approaches you from behind a building. t05 m0j ctxj58ipfsk.Initially you hear it but cannot see it. When ittsjmicj 58k0t.px0f5 emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfz )5egey:b +68 wsgfyperence in space,” whereas beats can by)wgf5 :e+ b 86zyspgee said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would xb2zcgt cdilc. 6-/, xthe points D and C (where d,-b/26c xi.t xd zlgccestructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplet:nf4cvs+ij 9 who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambci94f sjv +n:tient 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 thoughtarc:o i -sg*k3as; f5h of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component fork -a*5gih 3 s:csfa;requencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift ifxldk 9q8.b7it the source and observer move in the same direction, wit9txlkdq7ib 8.h the same velocity? Explain.

If a wind is blowing, will this alter t*owb5*d dcppm q- lq)8he frequency of the sound heard by a person at rest with respect to the source? Is the wavelength o8cq5 bl) mp-p*wdodq *r velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor g6hpbz: t fchr0skcvt*g:dq2* +/v g2is blowing a whistle in front of the child on the ground. At which positk /g* ghzd26cg st::h vf2p*v0rtc+bqion, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the eceb e*c45rz7qtga w-d2ho of her shout reflected by a cliff at the far end of the lake. She hears the echg2te7rc*5bazdwq-4e o 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 hears the ech(0qtpwr -f+ pwo of the sound reflected from the ocean flotq -wp+0fwr(por 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.    $ \times10^{ 3}$m

  (a) Calculate the wavelqqy1e/csk6pvzo;q* (g g 6aq* a ( 0gea(9ypvpengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is yn bfh.pv.jsp(u74b ( drifting just above a school of tuna on a foggy day. Without warning, anhsujpn4 b(fy7(.. vbp engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a:l*56x: fed8rh-)jx ybzi.p t xg6pfe cliff. The splash it makes when striking the water below is heard 3x e*lf):j6:d 86xp e.fritpgbx5 yh-z.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretews 2ow)bpu 2o1 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 apart. How far away did the 2s 1) ouw2opwbimpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of b;pg1jv; od u8r;dzr 4distance by the “5-second rule” for estig4jd;ro bup; zv; 81rdmating the distance from a lightning 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 levew d(d:bwstl (:l 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 intenxid .k0-)ygn1jae5 u,sef/u9cq zrw* sity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fir+ dx1y6 sv3 rxnp2*dgx- qwpt-ed simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add ins3qx2 yxp *xgd-d6 w-nr+vtp1 tensities, not dB’s.]    dB

  A person standing a certain distance from an3v hrjersad*(;af1g1 airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: (*radr1 hv g1ej3as;fAdd intensities, not dB’s.]    dB

  A cassette player is said to have :dhcxhy.mfk1/ 7 o fy5mr0 pl8a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of t8f1/m 0r7xmkchl5 yyphf. :do he signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power ou wf()j8z734ou*evzy k+p ontwtput of sound from a person speaking in normal conversation. Use Table 12–2. wf(ynz4*jp8o)euw o3 zvk+t7 Assume 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 a wwa gh4;gf9c(d7ueml7--r rtrea 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 modest amplifiers6l btp;hg oo9 )jj)-o B is rated at 40 W j)-s th oo)ojb;gp6l9. (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 in front of//ua)e ,k9sb r9 wccrm7.bq1y w8sxse a lousm s1aubc.b/89 7xcwrs ke)w/9eq, rydspeaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typican wmh7gag-:- xlly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffagn hg7:-x-m wer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is rx3g h*1 itrcr0ev9+db/f s3jtripled, (a) by what factor will the intensity increase? Injhs3/f9v+1 cr 3iebxrr*gt0d crease 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 twicds ujuz: hm:)* 2lbv2ee the frequency of the other. What is the ratio of theirluv):j*em2b zds:h2 u intensities?   

  What would be the sound level (in dB) of a sound wave in air x j9 nntt7t3j6e0rkxo2r3e* t that corresponds to7x tortejx 2 njr*0t3n6tk e93 a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz to kds8ixq2y)/yt*uz cnk04cy0 q eu5 -ene that has a 50-dB sound level? (See Fig. 1)ie5ez*yutk/0cd-82sq 4n u0k yq cxy2–6.)    dB

What are the lowest and highest y)zo9pmcs/+x,l9 g co frequencies that an ear can detect when the sound level is 30 dB? (Ssg) olpm9/cz+cxy ,o9ee Fig. 12–6.)

  Your auditory system can accommodate a huge range of souni5vlt8l *y(zgd levels. What is the ratio of highest to lowev*yzg5l(8 tlist 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 l h)8glirw6t)z.xqj)g+y ik .dength of the vibrating p .+g.l ))q gt) 8zixwkhiy6rjdortion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three au29t; xq-vygoa( sn gr(dible overto; a(vn(-2sg9 rxtyq gones 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 from blowing acx mpbm: omf;c *81jqw4ross the top of an empty soda bottle that is 18 cm deep, if you assumed pj w 1om:qcm8;x4mf*bit was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thsw7jw k0f.lw lb 2zwfdlo( )(,e range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requir,ww ozsldw(b2wj.7 lk 0ff(l)ed? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic.ls7l/6 xqd/ ylw9,p ih What will be its fundamental freque,9hlyxpil/ 67 /slqwdncy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middlewlld d.2 f*+hnrso* 2,h8blfd n5b8cb C (330 Hz)b,8lnhdbr.dsnfld*o2c fb 28 hl+w* 5.
(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 o)+, 5k*nx l2zhoh euthrgan pipe that emits middle C (262 Hz) when the tempera)o2xn+hhh*kt5,ue lzture 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 a hx8 d9 m)l3l7ml1yxwc7kzz:st 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 shphr3g -vaa6u.di 00 viould the hole be that must be uncov3-i guhvd.v0aa0ri p6ered 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, 4401atj,x6tf : ku Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this ist1txuf j6,ka: 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.x)+ bf(a/w p ylqe 1k.1wshmz31fg4kn80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is1we gxhp/13zk( l.) 1wymfn kfbaq4s+
(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 g -iu(gcv2fy*y s:u4. epxp -u$^{\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 audibzj;epta m2y +-le range for a 2.14-m-long organ pipe z+jya2p me -t;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 p y.q::u-h3-(rv amsy/v gvaeis 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 relatv. 3qpyaveh y g:/-sr(a-:vmuionship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when twdf69s, j:mx k6*e:k hc+rzetrying to adjust two strings, one of whichc hx+ e69*dsr:zemtf6 k: kjw, is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 /xh o4m x a4z.so lltrx-f/a x25wu8)aHz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatbx 6vd/n3 yl7g 7zm- may2lp;fes 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 simultaneously, estimate the operating frequency of brand X.y7 v;ylx2-b/6 gfaz3ml7 npmd    kHz

  A guitar string produces 4 beats/s3 6lviydpc-im s2d0 p1 when sounded 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 yplcs -v01yipd 3m6d i2our reasoning.    Hz

  Two violin strings are tuned to the sa* ne*xu:f6gr dme frequency, 294 Hz. The tension in one string is then decreas6 **grudn:fxeed 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 twfl yin.)huu 18o identical flutes each try to play middle C (262 Hz), but one is 1u.) 8 yhulnfiat 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and*/ax+) t 4bzgyoame :v C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. Whatgy /e4+mx o:)tv*aazb are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. Au * clbuxr:y ;*kbu30x person stands 3.00 m from one speaker and 3.50 m fr;:b u uxkxl0*b *3ruycom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 13ss,0dg b4 rzj62 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If4rbsg, 0 6zsjd 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 wavelengtlv vg +9xvg4e,hs 2.64 m and 2.76 m in air. How many beats per seco ,g 9lvve4+vxgnd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engiiy(9 :0d nueajne’s siren is 1550 Hz when at rest. What frequency do you detect if you jei(9a0: uny dmove with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detes9c9hortf: *j ha+i7lct if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 mh 9oc+i*lrhas 9fj7 t:/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freqx bfj6u)-6vo0vtwy d6 uency if a 2000-Hz source is moving toward you at 15 m/s versus you moving t)vbvuo d6w- xj 0y6tf6oward 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 wwfvs1r+5r+( g lgh(rtj;jy (it5j : aiith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns ejgtr:ith(g(f(15lw vj +;s +5iyr j armit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them retpex8 nri)a83tm1 ;yt hurned from an object moving directly awa3epya nt18ir8;mth )xy from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fliesr 3ekvq t09katqq:d; k7, a ,*bodf2lk, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecte bkddr,a :0*aq7;9v efk32tkl q, kqotd wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playbjqybb85aa4m 9 /nc6nbar :p8ed on a moving flat train car at a frequency of 759b8 / mnba a:bp4n6b rac5yj8q Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bl*:iv/t* obge sood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in h*tb: ge*o /sivuman 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(4i vsa g6u9os 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 u :xjf5).ec b 36eebxkwind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, 6e3xcjubx5:) f.e bke
(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 pq8h z octy,j 9x8m2;4e8bpng 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 (hkwp.b 20 0rhspo7rthd . hal*/0b:enenrp :Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpla l.hod7:0h *np2wre/ntr h r p(.0epba0 :kshbne’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 thx2;u yniym n93e thin atmosphere of a planet where the speed of sound is only about 35 m/s 3xy; 92yumnni
(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 8500b 9c)h zrlvkwm ze0b 30;tnhm:j 3ee7(7(gbtg m/s strikes the ocean. Determine the shock wave angle it 0b(mjzgtvk:en9t ; hbb37m3rc0 gwe( z7)helproduces
(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 8 0c;pmtwkr7q$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anxjkeb 0.gk.x 3d 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 a 0e gbx.k.jxk3horizontal 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 downwah))h0t sdw-3c q wobc2rd from the botcc0q) 3d howb2w)-st htom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there int( odvdtxe4 ja(53vv4 the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of manynrfvb/t4w 9g el7dz:( jv5kat3cda,- plastic pipes of various lengths, which are open on both ends. cz 5j9gawn4/l,37rvd kvd -( btfe:at
(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 f l- *,iieoq:kperson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 s kli :iq*o-,feuch mosquitoes?    dB

  What is the resultant sob t:pu-x ,n5 u br,n t 1.q:3cfl50fzdokhkt6wund level when an 82-dB sound and an 87-dB sound are heard simultaneously? lnhcx: bq zkon,: tf0-3r56bfku.w,dt5ut1p   dB

  The sound level 12.0 m from a loudspeaker, placed in the open,oo*o y;nd-u 7.y 0n-dmpoekq1 is 105 dB. What is the acoustic power output (W) of the sp7k01ne.d-y-;pn domy ouqo*o eaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rate 7/-zxntdmcm1tj9a goy9( ittcmm 0:7d at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output i(d7mcjog7 mxt/t 9in0:1t9z m- cyma tn watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protjzma82dysrs0d 5w3 w(ective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet air5w a8 ywdrd 0m3sjs(z2plane engine?    W

  In audio and communicaty vnz.y0y vqcr5(ly*3ions 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 violuez+ioad7 n:c u*g1+ nk2gj9w yi;f7 oin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental2x.wsbdvve ,tf;o*(i)f k;3 wwxfj0u frequency of e ww ;o*di0; vb2sxxfftuj k)3 ,(vf.w440 Hz and a 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 vibration above a vertical open e3zn dob0,1(4yv vcr,ro jk6pog)q. eim1 f(ktube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it q f.c1vbrzvi6o)(ko(mp n e eo,d,rgj0k1y34 does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at(y +q ()28wjoaffe ;+c1nmadjay +xhw one end and also 75 cm long. How much tq( w(fhwa jj2 +fe1x+moadan8y; )y+c ension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsermk .69vzb9,p 5g i:u itttb-:5s viehzved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two so k-.;ch xb/dmo(xv q*durces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m fart /vh(.;bc *x- oqdxdkmher from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. f:)8wcjn,g -th pyjqr0y 2h:oThe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches.cprg2ojn j :h:)8t, 0qyy-fw h What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aft.e-f hbi4p g 0o1hkr0,i95ol; j nendzer it passes you, its frequency is measured as 486 Hz. How fast was the train k1-gz045.eejn 0d fr,io ln;b9hhiop moving (assume constant velocity)?    m/s

  At a race track, you+d0ne+v b rlr sar0j:8 can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (fre0+d jvab +8srn0l:rrequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tu :xlv)wbe 4e,w*u 1vkogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?vuwe,bw )l1e xv u*4k:    m

Two loudspeakers are at opposite ends of a railroad car as it moves5 b k *zs1i9xw(a1ashw.wcd0z past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers a.w*z ssb5i19 h 1 zca(wk0xwdhave identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally abl7iz) 4-quxhu q7tu3iout 0.32 m/s what beat frequency would you expect if 5.50-MHz luz7u i-7h3t4)qiqu x 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 moth at speed 6.5 m/s w34pjf- lko: -hb auub;hile the moth is flying toward the bat at speed 5 m/s The bat emits a sound 4fhluubp;-:3 akob- j 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 pgpf8xcf b7h+3 m7g(/yibugd ;ulses 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 thaby;h3 fu7m7/bpxig8c ( g+d gft the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was nk4ft-vayg -) 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 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 fundame-vk)4 tgfy- nantal 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 i y0f+xtyd-:qcompromised by 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 ydy:qif0-xt +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, slende ji+z-2w0tuuql:qd b4tt4)s*gtw 6 wjr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can b 04wt+ 2iwj:q*- u jqgsdtlbt) 6u4twze made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of azg/p.al a.5n pbouzppg /l a.an5.t 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 gr81pu.*vse2 ngi7kd+h wnmj +jound hears the sonic boom 1.5 min after the plane passeiguvkj .7jmh2eps+8* 1dnn w+ s directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbo g -id*, j8,-)wn)zbtsvtx4 llpgv8meat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h