What is the evidence that sound travels x)ffs-: x ntk+lgg:q+ as a wave?

What is the evidence that sound is a form od8)9ng*kbv -xx)r ausos2+ ylma1)xa f energy?

Children sometimes play with a homemaj8c*tye46 /7csy 2 am ukgf+y2obqme( de “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). Explai(s 7ty+42a eqf ymu* yk8gcjeo26m/cbn clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, d:v8m;l rcxe ;ao you expect the frequency or wavelength to chan 8x:a;lcrev m;ge?

What evidence can you give that the speed of sound in air does not depend sign daj)qa2fo 02s +xp 6o(hrjgw;ificanf2j2hgq)(d wraop sj6a ;ox0 +tly on frequency?

The voice of a person who has inhaled heli, n,de-w,omeig+xc b3um sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ,t ig/f49 ryz kqyl7+c7w gd:norgan pipes?

Explain how a tube might be used as a filter to reduce the amplitude l(ycq+wa70 8jwkdj0 z of sounds in vark(7za8ly+w 0jw q dj0cious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1n)wru 4y( 3s ipv, kkmu)zcu(62–30) spaced closer together as you move up the fingerboard towa,)v 6iu(zywpu4urkn3s (ck m)rd the bridge?

A noisy truck approaches you from behin-4q(*crnli lia l8my*(a er+cd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the highqal( cri emcy*-(*4aln irl+8-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfe36/ j2a3(utvt6m jmpch6we. x7q zwgirence in space,” whereas beats can be said to be due to “int qi/t gut. 6mz6a6wje(33x7jcvmph2w erference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers p-medo,ku2n (8 qw*zn were lowered, would the points D and C (where destructive and constuodem-n, z2 kn(8*qw pructive interference occur) move farther apart or closer together?

Traditional methods of protecting the9v))rm/ruru g hearing of people 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 ambient gr v/))muu9rr 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 thoughtwbk-r gw,h:nk v i4m3. 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,irg:- w kwbmk4.hnv3), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thw(.x 0 wkq sg+erqp k)gcc0ul ib.q,6(e source and observer move in the same direction, with the same velocity? Explai0.q (q, u0iq+e6kb(lwrgscpkgx c .)wn.

If a wind is blowing, will this alter the freque0e )23;lfh 1a9agm 8lckig mkxncy of the sound heard by a person at ;fmc30m i2 1)algge9 xkla kh8rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swin7 pk1i. a/x 2:8 ,apijpqyhhtpg. 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 hjh .pik:ap ,8 12pq 7ah/ptxyiighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout 8d ik.tl)lri3vc3t c/reflected by a cliff at the far end of thekt3 ivc8icr3d).l/l t 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 thc yzsa r.gj71q:cs1lickj5v; v ,s6 r.e 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 speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significag1;. s 1 cvsqiralj .,jz5s6:vcky7r cntly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waxv ix/ 1/j-zbfvelengths 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 drifting just above a school of tuna l:+xu. /j/y 7 r/n;ybw/z4radad jr imon a foggy day. Without warning, an engine backfire occurs on /ib/ /dm/n4ry7zradlu ;.:ajrjy + wxanother 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 ul1gy,2j lm4 s51qp vx( wu,setop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the clifsmg1,,v j u51(e pqllsw4xy2u f?    m

  A person, with his ear to the ground, sees a huge stone stri t sx(14ur owzwar+o8:ke 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:zwwur+r o8xao4(t1 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:4n0dwum/ tue distance by the “5-second rule” for estimating the distance from a lightd/w mn0:e4tu uning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the paik(lehhq a w7+,n 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 b qskrzr/jsml,byd+vh3jp, 2 :8 7yr ,whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sbi sk8 v,1vo4kimultaneously at a certain place, what will be tv,o4vbkk s18ihe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an air,e ontlcv 9ly08uq 2;hq7 (xvcplane with four equally noisy jet engines is experiencing a sound level borderu 07yclev ,n 9qvo2lx(8ch q;ting on pain, 120 dB. What 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 to4 jf y992zg5hzd- ehg2s;7po: c tirwb have a signal-to-noise ratio of 58 dB, whereas for a CD playerp: -zb5i sfjd2c ;4 y7z9hhort 2gw9eg it is 95 dB. What is the ratio of intensities of 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 nornz c)o ehq:*v /l*xh,emal conversation. Use Table 12–2. exvce )zl,hq/h :n*o* 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 wh+qme, gzqypr ,;*jly lu/19fjose 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 modest amp ldr y/7uk;kdlow4( y:lifier B is rated yoydk wl;4/: k(r7udl at 40 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 plgj 97w.x u9wygaced 2.8 m in front of a loudspeaker on.97gxgwu9j yw 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 differel( wggtfk4)+j nce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See )lkjfgw (4+tg Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inte1ssa hkw(3cqh5k).g xnsity sq3 wxk5a(sg c1 hk)h.increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but zwxdmw :lb -qq 4zp9 0x(en.k9one has twice the frequency of the other. What is the ratio of tbzkpx:q m0qx(w 99en.wd 4z-lheir intensities?   

  What would be the sound level (in dB) of a sound wave in air that corr521kcnf +u* q :evskaeesponds to a displacement amplitude of vibrating air mol+uk5skc 2a n 1eve*f:qecules 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 tox3,1 wjpzz6qey oxoblf +9 ;6bne that has a 50-dBbx39b;pxj6oz oz e,fy w1+6lq sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an e.qb d5vdmx)fsa1( yus c: +4u)foeba:ar can detect when the sound level is 30 dB? (See Fig. 12–6.) q(fv:) u+b5d.u scex:y1ofamad) 4bs

  Your auditory system can accommodate a huge rangyg46x )il f0mge of sound levels. What is the ratio of highest to lowest il0 mgyxg )46ifntensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of t8kf oy0ft ;0ihhe vibrating portion h;foft00k 8yiis 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 arergiamma (1) 1j the fundamental and first three audible overtones if the pip1m(jig a)1ma re 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 a,2m dbn+9xfgzgeyu0 5cross the top of an empty soda bottle that is 18 cm deep, if you assume9ubgng0f ze2 +,mxy5dd it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of hu rbuwqg,ui+ )w.zq)2kfts4 p9 man hearing (20 Hz to 20 kHz), what would be the range of the lengt,i wuqfp zqw4gu t)) b.k2+r9shs of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string ha2k p1nf;shkhvs0.k1z s a frequency of 540 Hz as its third harmonic. What will be its fundamental frequenksf1v; phz k2 0h1nk.scy if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar sth-ta fmbr9m/-ring is 0.73 m long and is tuned to play E above middle C (330 Hz). mb/at- f9hm -r
(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 thzwlu 7w18:rnfat emits middle C (262 Hz) when the z8 7wnrl:1fwutemperature 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 2mmog vhw; r gr8 )uv2xh/ m6do;i2lg/;0 $^{\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 thxut+- c(led k8yghj;.at must be uncovered to play D above middle C at-ug (hd;yxtj8.e lck+ 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 resona ml0kvf/5czwfqx4u-nu)3 7 d33 lsrjb l kcq*6te at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why 5s /clqfrbv xm6k3f )w jzl *c-ul70k3qnu43dthis 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,,e+-dt jzljr wjo,d . m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz d,rzd+jw. joj,e-, tl 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 wuze ,)sq2j *s$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.1 ke5tww 1;4awq4-m-long organ piet;kq 15 w4wawpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm -b0.grzgej8g.,c qwp oim i,+long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in0gg- 8gzeiomwi ,b.,r c.+j pq 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 a.+gk9u: o;rdhr0khch djust two strings, one of which is sounding 440 Hz. How h.d;hk: +r9k hguc0orfar off in frequency is the other string? ±    Hz

  What is the beat frequency if middle rjukw j:b.6v ph3bt( 3C (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 2*(q/- 12d dzvsfm vvk*)olt jv3.5 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 frequenc2f jz/1 * *dv(d-tmslkv) vvqoy 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35e:i gn7k. rev85u/y pg0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringrnp/ i85v.g :uyege7k? Explain your reasoning.    Hz

  Two violin strings are tuned to the4 buey3cmq b8q*,7oyj same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toge8o jy3e4u,7qcyb*bqm ther? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each tryn3f5fb41tvs)bmksta1 udsbt 1-t48 u*s: e it to play middle C (262 Hz), but one is at 5.0°C and the other :nt-b m)3dsuit*b5a8 fe41v f1s4tt stbk 1usat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frev,mubin 6s 2-jquency of 441 Hz; when A and B are sounded together, a beat frequency of 3i6umv2,ns-j b Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.8z0 1szvt 7i,bvkf l7vnd (jc250 m apart. A person stands 3.00 m from one speaker and 3(l0 s7vzvd,5 bz ckin2v1tj7 f.50 m from 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 + beb8g1 -6kvclsv1;j z6jdp vg l3jg/132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vij8d c +gp/g1 vjeb3l;bz6j vs1 vg-l6kbrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. H1k-rzbs dy4- fu6 j+vrow many beats per second will be heard? (Assume Tr4rk-61yjsd v -ubfz + = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenc1);ox luw (rjv*7 novdy of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a s)r*n1jvou (o w7dx;lv peed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do8p(tknb3nam b s88mm w/ 9 giekt64du+l:w8rz you detect if a fire engine whose siren emits at 1550 Hz moves at a speed ofwp3nlmra8k wm9b+ g :tzd4kbu/886 timesn8 ( 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving . .biokb3+zjyi u0)yu toward you at 15 m/s versus you moving towko y 30uyzuj.bi).ib+ard 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 wiaaez6 vy;5 v;mth the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 2;m6ye zv5;aav 0 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz p 6t2lz.ownd3/ e,g0f r-mth nand receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequzn twt,r0. f 6ed3hpno/-glm 2ency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of:zc1zzp-f r:y 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0r pzz zy1-:cf: kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was p gqp5xn7+.*p8h g ndtllayed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached thg. qtn*87 l+h5ngppxd e station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloobi3nwdi5y wp.k :ey/x4r fb* 6d-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed 4dp.er y/65xiyinkw:fbbw3* of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using5rz7x(q(ngs+9 nt2ixw hqj *ks*dt6l ultrasonic 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 winda :/8aq pwn(-pfr2 bts velocity is 12 m/s from ttp-srap: bn(fw q /28ahe 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 land if ccat) x:)o2cch/p1 rj 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 sswn nvj1:+x 0i)b.u,:a cm7f b3/ni ;xh etxyvound is 310 m/s (a) What is the ani1 .:xtm +: vs7vxyejxn0wb3 /ab ch;i ,u)fnngle 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 sound xbhlhofy14xus4l2) 6 te/h(i is ohhoe)ibh 1ll /ts 4x 42x(fy6unly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s striked gucf aq1n: ,sg5fj.mtid2t83w 6 hh6s the ocean. Determine the shock wave angle it producehsti f, fgdj25w:8.t6mdh q1 a36gnucs
(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 f w9o vp9sr6 l(e*j37xcsd:ee$/theta$ 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 exactlyszw1 a 6e6mjl*zmq0u0 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sq0m za 6su06ml*j1wezonic 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 ded0ax 1 pn3tt3ovice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is to3a n tp0x13d200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are therenjg)(xd:ibl+6vyfsu y 3he6) in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaydl cnct0.o9m bzt).q1 called a sewer pipe symphony. It consists of many plastic dob0z. 9nc.tql1m c)tpipes of various 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 perso jay2uqg i o j(:/-dm.yz6(mxx( y8svon makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? ysiomxd z8 g2a yyj/: m(j( u(.voqx6-   dB

  What is the resultant sound level when an 82-dB sound and an ss-1h rgjq8cm8,v*xi 87-dB sound are heard si c,jsghs1r8v* x-mi8 qmultaneously?    dB

  The sound level 12.0 m from a lodkwbs, frnmsw- n3u,0it 5l83udspeaker, placed in the open, is 105 dB. What is the acoustic power outp,si3fnm5ns0 klw8wb dut,3r -ut (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W x/p/1umm ; lqr3pgisdo:sg0*output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power outp om gd3s0r*1pumg;:pi/ /qxlsut in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earzr)xv( r ,zj;;zuoj4 os. 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,zo()zxrjo r; u4;zvj distance of 30 m from a jet airplane engine?    W

  In audio and communiu;zh8 d w jn7d0e+ ;spj(f ,4zirzwap*cations 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 qwaiqrco 7kvz,4;)3b 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 c/cw +p/d v(hdom long between fixed points with a fundamental frequencypowv+ d(dc//h of 440 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 tube filled with water9 qu/ivtw085g6ha h dm)jh0bo (Fig. 12–35). The water level is allowed to drop slot0ohi6 /bqhhagdu m09vwj )58 wly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that 7mhscs6(vgvp .* lw /*fklj.dis 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 vl7*(6j.vs k w /dhp.flgsm *cthe third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f)/tzu pbdr(qj, +dfe3 ull 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 500–100wnxns92ni s elhxx3 s8rlh8)nsj -+. 00-Hz range coming from two sources. The sound is loudest 2nrxex 3wjsx.li9nl ns8h+ sn0sh8-)at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor f96+f1 nhp.uu s 8tlcyon the stationalt 6ufs y+p h91.nu8fcry train hears a 3.0-Hz beat frequency when 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. Aftqps n1-xgev myl-0t8o dlv99/er it passes you, its frequency1q nxe8yop9gv 0v-lm9dtl s/- 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 *-xk 9m dja6l-b b(blvcars just by listening to the difference in pitch of the engine noise between approaching and reb*l(lxdb a6j9-b -kmvceding 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 together, produce a beat frequency vbuo 5*y0xcy8 of 11 Hz. The shorter one is 2 8v50yyo *cbux.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railrolyn e,g4xfh05tt1 u0) f9mafpad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is th,p0hf ufxmtfe0y)l 514 9nta ge 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 bloaud ;qavx9*t.0 4ee74fww4 ubcvk m b-od flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the w.94 * qxbe4;t04vdmvabwcf ua -euk7flow 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/qnhp nfe,2 70bs while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency enh2bqp, f0 7nof 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 appn0s-tv;7 o a)dc3t3 lrhsk ms-roaches 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 bst0tav hc3;s 3dom l r-7s)kn-at so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was ofmxcjlmes0353 +qlb t2x7rl (nce 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 overmlbmsfelj2l rx353x+c (tq07tones 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 listen1:pp- lxk+ wiqrw(7av ing can be compromised by the presence of standing waves, whicalwq 7:v1kx+pw(ri -p h 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. 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 longssmz:g(a) +7dn 6kju-ahqvu 0, slender aluminum r-(q vg6akzsudsm 7jna u0:h+ )od held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or 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 thresx,zfvom3 n;(uer* 0n +i/a ytqhold of hearing for the human ear at a frequency of about0( /e mvuo q3;nfayrn*t ,+zxi 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.d7w+0 uzktrm, An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wh zrtd0 +u,mkw7at is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 28yrkjb6ya .e;qodv +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