What is the evidence that /0hm,ag3j(3d0g(mgncv;5 ql shsl f csound travels as a wave?

What is the evidence that sound is a form of enntr:.c yb5 qxz1 :6vah/ zmqq8ergy?

Children sometimes play with a homemadec;mgju k:ck82bjuo p(,v;xf 0 8y0rj d “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.rkyb;(gjpuc0ocx 8d :fmk,;2 0 ujv8 j 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you moxlw8(4dcp x:pao,0expect the frequency or wavelength to (x wpo:x8d0moc4l, pa change?

What evidence can you give that the speedy0 6jclb z4ut /-5kb5n8i ogsq of sound in air does not depend significantly yjocszl0/ 6btgnb-554ukq8ion frequency?

The voice of a person who has inhaled helium soundsm+wl 6bf,xz4-k h nmy* very high-pitched. Why?

How will the air temperature in a c 1kv+o o .p49q((qmicnd fue6room affect the pitch of organ pipes?

Explain how a tube might be used as a filter t-v /zb-7hln8d:fh -ni1mc fob o reduce the amplitude of sounds in various frequency ro c d lnv1nh/fim-78bh-:zbf-anges. (An example is a car muffler.)

Why are the frets on a guitar -q o:tcyv -acwx5ku:7(Fig. 12–30) spaced closer together as you move up the finge kxq:cvc 5-way-:o7 turboard toward the bridge?

A noisy truck approaches you from be8vu ;l2,jt si mdy6hg:hind 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 high-frequency noise. Explain. [t mvl,;isuy2h8 :jg d6Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” w69l;ggegt f2gpq3 6hihereas beats can be said to be due to “interfere; 2tg6f9ih glqg63gpence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the point d9jw(ftd)neu:(im4z s D and C (where destructive and constructive interference occur) move farther apart or clo f t((mz:nd)d4uejw9iser together?

Traditional methods )y/hp;5odmdqhc(4 ml uq) o .cof protecting the 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 noise. Instead, a device is used which detects the noise, inverts it electronically, then q.; ol)uc(hm /dod5phcy4)m qfeeds 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. ki0v)iqj,+ o rEach wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two com k)iji+ ro0q,vponent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source bsuc3 t3y2(f1d ads42 xkgl n:and observer move in the same direction, with thelub c akd( 3t:n1ss4dyf23x2g same velocity? Explain.

If a wind is blowing, will this alter the :wurj0 zk.j kpq)d86 gfrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or vel0)kz 8p.q wurjd gkj6:ocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.qnr;6y o+vj7rkqnr, q0+4dc z 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 hi7 qzyv4kjq +rn;d rc+0noq,6rghest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofla.jix y (ce/t;:y3du her shout reflected by a cliff a.d (y lt:3eyc;ja/xi ut 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 ship just below the waterline. He he4m vygrrfz149 ars 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 124g9vfr1 rm4zy –1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt(v fni6kqwt +1evu/x j/f2taun2 s 3/ehs 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 onu,8zs q.uyvp7q/z wc8 a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before t c7u,z/v8uyz8 qp.qswhe backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cl;fd t)*rn/( v8j kdkmic o2tnx v262h4.o iwyeiff. The splash it makes when striking the water belowot/) 8;2idnto(*hn xf4j6r 2.cwykik m2d evv is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete paveh*b,,ighgb 6d ment. A moment later two sounds are heard from the impact: one travels in the air and the other in thegg,b*,dh6 b ih concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one *+z1jdbf-o 7hmao u6q mile of distance by the “5-second rule” for estimating the di6+fomzaq1d hu-7b *jo stance 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 t)6a h eby;s-( 9kfwpupncz+9/zith,mhe pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level : z0ht8sjg9u3twu(nf xcck(7of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultz*r:x nkwul i0r5vgmf5/( j2ganeously at a certain place, what will be the sound lev2(n gv*/5ir :x jrlfkwgmuz05el if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane witlaexvvj) 8yj i: igs k 94id(f-rc./m1h four equally noisy jet engines is experiencing a sound level borde. /ivg-rysm lj1i9 iva4d ef:cj8(x)kring 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 to have a signal-to-noise ratio of 58 dB, whereas for +2fa)jr,jv sla CD player it is 95 dB. What is al rfjsj 2v+),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 sounxvx24bfqtxa:7)lqia xu8 1o+bl :w ed l4g*0xd from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a1:x0:ft2 xb)elx8ab7 q4wi ox+v l* qgd a4xlu 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 area isnubc b))/a42d-v ok cn $5 \times10^{ -5} m^2$ (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 fv ar)4cb qqnl6/ n;;fat 250 W, while the more modest amplifier B is rated 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 v; c )nrabq;6lqfnf4 /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 ap3ym 9wahh64front of a loudspeaker on the stagaphw6m 3h94 yae.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB.qewhg sif q9+x9s (yx(s:0( /mzch4 gp What is the ratio oif( :p(gq+ s4hqgcsmz09x/( e9xhw ysf the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whlnf0jbvnl)a9n /0gqf(3w;g 0ryxql 6at factor will the intensity iq0; 0glqxgwvar6f 9l nnjb 3nf/)(0ly ncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but onekjph oy*f h2.iq 41h:5 t;dbku has twice the frequency of2qu5oh4dy t 1 bfp.k*khhij; : the other. What is the ratio of their intensities?   

  What would be the sound o4lb1o 0 djzn1e nsh2 xbx:ak3hlg2 4,level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibaxobznx1212j3 ,4l o:ebhh04lskd ngrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seemn 5e jpsuaej+yxe,;va (.b* 8a2-jeh d as loud as a 100-Hz tone that has a 50-dB sounduaeesje *bh-8j a.a+ye(x nd2pj,;v5 level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear)jp g/yru-i+)c( o gz /9y,fl k6n jg5w9jgvoo can detect when the sound level is 30 dB? ng z5o/)ky9 j9p o+lrjvw) jgcu-fy i/g(g,6o(See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sounb1 w-;- tofippd levels. What is the ratio of highest 1b -;pft- powito lowest 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 k36zz4gl acn zv1ooz0)g*c-g 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 string be p3zo l1czvg g kza)g4* no0z6-claced?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible o gb, c14)jphdovertones if g1b4j dpohc),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 tplu+qt4(jt4e gs). i tl )cu: k8)kaayou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clo+)4t g4pli)teq(:j ut8lsck) a tu.aksed 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-tc e*75p7nzhv )e)cn uwube pipes spanning the range of human hearing (25v)c7)e*cwnn7 phu e z0 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequm;xpww5 -t:u bency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered aub-xwt: ; mwp5t 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 abov 9wpr6 ml:wc i9at(xx;e middle Ctmwi9lcxwxr a;:96 ( p (330 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 r2ar7i/g7 usgan open organ pipe that emits middle C (262 Hz) when the temperature igi7r 7gau r2/ss 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 0au77zln; lvet 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 s )ejiu 2x:o0e3 l brxx6ax1req* +xc8xhould the hole be that must3x0xr + 6lx xb*ar euxc)qe2oi1:j x8e be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but qk34+z7hp-vt mmqwd0 not at any other frequencies in between. (a)mpz0qwt-d4kv h 37q+ m Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It ( ca*pcqst))ouzk.s*resonates at two successive harmonick .t ()qsop*ac)sucz* s of 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 c-63 f567kd;fizm d wjtl-ly v$^{\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 prex4rom/199bw/ xbl h7+t rnkwksent within the audible range for a 2.14-m-long organ wrw9+bt hm14/nk/kbxl x97 ropipe 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 is4 ah9hw3deptz,v v5ax*++kzb 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 invpbw ,3zd*zhe+ 9va t4hx+ka5 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 wh8:e swl:qy rm/en trying to adjust two strings, one of which is sounding 440 Hz. How far off ine: qr/ly 8mws: frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) agco).qjytq si 7v79*hnd $C^＃$ (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 operzv n6pq, q6f; ,bakky;uben(2ates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, a,fp, k266zkn;uqbq nev(b;ybut a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 i5vk:6 b9k yth4bpx*yy+q c kn b*gg:/beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strinx5 byk9+yg*t*y cqgb bkkp::i 6h4/ vng? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz(qv,/ xry/+ qj mvbx0s. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? r v (x+jb/qsyq0,vx /m[Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard i mj- ed7srah31 8m0yndf two identical flutes each try to play middle C (262 Hz), but oneh mym-1 78ddrjsae0n3 is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Formihlt 1u* f g/.59zg,ebzk e5rk 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. What are the possible frequencies of A and C? What beat frequencies are possible ,t.f u9hrze5/ ek bm1igz*5gl 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 stands 3.00 m fro va m;c7no*fw/m one speaker and 3.50 m from the o7v;m *oaf c/wnther.
(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 vibratul j-qk 5mp/t,ing at 132 Hz, but a piano tuner hears three beats every 2.0 s when m,/k5uq tlpj-they are 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 wavelengths 2.64 m and 2.76 m in air. How4a (av8 4j)8q6x ctmovojqi1r many beats per second will be heard? (Asj oq8j8qci1 rx tov6(a4)4mvasume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fijfujljfzv2l2w5l2 y5 i -k6z4re engine’s siren is 1550 Hz when at rest. What frequency do flkuijl z2l- y w4 j26jfz255vyou 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 frequency do you deteg+mqdg)jn t,l st9at, 6u;g+vct if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 duv;jqgmtga +6lg,)t +n,st 9m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz s+ptuhqd d1zx c(u//m 6ource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are theq/6 pmt dx+huc z/1(ud 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 v d+ctz89dd sf33( r vmho3-dhqk,rn )equipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 cm (ozh9)dvvn,r +-h8r 3d33dsd tqkf$^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wadlk2m ,o0a pk:ves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is theld k:aomk2p0 , received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wallsav:7e xkpt4 b(dwbu nre. pk9m*67u) at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kH7k*) tsx:u 9r4p6.uknbvabep m(d w7ez. 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 movi:vv akb -v**5gzg*k rjng flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone wh *avk*zg kj5bvv- g:r*ile 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 tpxiq+ i02z; sv) 2.cxpod din )yct):wo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in largey +id ).x)2)opq pxztw s0;cvni2cd: i leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect uutpf,1 k:/y07g nlg btsing 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 jdxc idh mxc9ss0l 7y145xka1 bi)-4y sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who x41hd4 misbya 0dcs)i1 9c-ljkxx7y5 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 i(4ejl;b hp1e gf 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 agim t)zs3z kfad 4k uk8s/, ch)*y7r6nt 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 8z) ya/k6s m,7r4kzn*sh ctdfuk3ig)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 s67i5bhcf1tj. ri9urr ound is only about 35 m/5 cit hr.rbfj 6u197ris
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave ae9lo wkp;lki+(vdq +g4(sz o 3ngle it q4sk+z9 wl klvie3 p(do;(+ogproduces
(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 i+;p fzcxq w:en5h:fr: ie/k .$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground2flgexmlx,: x7fo2d, flying faster than the speed of sound. By the time7 e2x2xdfgxl, fo,:m l you hear 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 sb /(y*fsef**p+c d 8pmwv xzppy4d,h;onar device that sends 20,000-Hz sound pulses downward from the bottom of th; 8ypcmzb*/*hye*(,dp wf sfv+ 4xppde 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 agn1l7 bw+r:yb re there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ca)rd i8ax9iz4 uc.ln:k lled a sewer pipe symphony. It consists of many plastic pipes of variousiud lnk4cr : z).8ix9a 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 rv wfwro5;* olwlf-; 3m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosqu;vrlwfww r;5-of* lo3 itoes?    dB

  What is the resultant soeuyf,t wkrvg8d 6 (*6)s6gtw bozt;z(und level when an 82-dB sound and an 87-dB sound are heard simultaneo*yvgbt)r w,sz6 gt(ef6t 8z;kd u6 o(wusly?    dB

  The sound level 12.0 m from a luruuq*r1/0nz 2ftx, voudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuminuzrt, n0/f1uxur* 2q vg it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropjtf7g 9;jb;lv5tu.8* zbtq prs by 10 dB at 15 kHz. What is the power output in*gj p7 9; . f;vjt8tqltrub5bz watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devic cim++pm/ jl 2fz9ca:res over their ears. Assume that tjz/a2c r+9m plf c+m:ihe 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 airplane engine?    W

  In audio and communications syw8:d hg+ jlcq0p+v:ri stems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to hooqmyr26k7)1 : s t3p bbdsh6z0)f soa 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 vigsirc vteb j84;teceq)/ 7i7/olin is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a majqs/7eevib ic7t r )t84;eg /css 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 ;5ahns enre -na;nb7m; vp7) .bkzve/rl +8wqa vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonates7beeaa5nnp+ v/nbwr;;;e mzklr7q) 8v . n-h 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( ,zkdbg an97d vgjm83.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) ma ngdz7(39g, vd8jkbwith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as b7. by1z3jr(ycv(j*k qyw 0hzone 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 thei+v(wew(2 ffb xhp1 -y 500–1000-Hz range coming from two sources. The sound i2vyhe1+(b xfp(iww f- s 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 farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stkr )scc, es/a.ationary. The conductor on the stationary train hears a 3.0-Hz beat frequencyr ),sce./ska c when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a ste;s8b 6 syhsnt2+uir.nam train whistle as it approaches you is 538 Hz. After it passes you, itsun nb. ;rs6h2styi8+s frequency 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 li,vc;ko::c3 xw g .n0h +ifi 7peews*g;1ssnr ystening 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 (freq3fi.pi;crs0e,vn kxh:+s;*7 so g gnycew :w 1uency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat f3a5*ob6c: 4anm* st; j)a dtyov7azb urequency of 11 Hz. The 47a5soovcby;nab u*j3dm 6z*t: )aa tshorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad ca 0q/dh uoa1pv3r as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakerp0vh q /ou3a1ds, 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 about 0.32 m/s what84x l(xjbknh.q+j;t n beat frequency would you expect if 5.50-MHz ult8( jn hl bk4nq+jt.;xxrasound 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 while the moth is flying tow8v sas ,yvad05ard the bat at speed 5 m/s The bat emits a sound wave of8s5,y avsad 0v 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 its p j9bf 7do0q-i8cy*, 7syahy approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before thed7 9qyyjfs - o,*0yisa p78bhc next chirp is emitted?    m

The “alpenhorn” (Fig. j no-,5 2ldxzc12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popjx5, nclo2-dzular 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 predgr(j )zgd(:vsence of standing waves, which can cause acoustic “dz djg (:(d)vrgead 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 l lwts*fs ss w2ng-e +06+q9bqlong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked withg9t0le-s s l2f6bw w+qqs*+ sn 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 of hearing for the human ear at a frequency of abuf( )ut/bk )*qf 1:yimewc8cso(fybc*it:k81uu sem)w c q/ f)ut 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the0) /cb2yt;k , ul4p dws3pewfe sonic boom 1.5 min after the plane passes directly wydc4tp/2;lu kw ,3 fse)pe 0boverhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 a lr 0:wvj2lyoc +ik:;$^{\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