What is the evidence that sound travels rz) 5i;z * 2kmmc.kasnas a wave?

What is the evidence that sound is a form /2phe(m (xtyn of energy?

Children sometimes plai uyjvv7bhi r7 7hstlv4k3/;1 y with a homemade “telephone” by attaching a string to the bottoms of twovy3;7u74 l/r71tbhk hs jvvi i paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequei+tsc-0y/tt,vdx 95(m8 nciob(h i mh0+rj o hncy or wavtd 0bxhm+ti, r 9(cvci(+n-8 h j5oom i/0thyselength to change?

What evidence can you give that the speed of ,ij5(34 h :oqwa/ur:zawcjo p sound in air does not depend significantly on frequenpi5jw:w3aaj,zooq:( h/ 4c urcy?

The voice of a person who has inhaled helium sounds very high-pitched. Wcq:.g +rs):pfbzge n 0d(e:b-wd-jcthy?

How will the air temperature in a room affect the pkux60+ka. e ucitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds. y b g7ajci.1qd3ie+v in various frequency ranges. (An example ii1y.. jceg3iq dab7+v s a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mov* h7b9 pk5h8dhd2 nzdjw4 fpx/e up *2d fjh/hbz 7dx95p4p dkhnw8 the fingerboard toward the bridge?

A noisy truck approaches yo1s8j6sn a g:0nhx g*lju from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sos lhg6 j:jn x*snga810und 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 p7tt(-n+mwt0b rb 1q hto “interference in space,” whereas beats can be said to be due to “interference in q 1-t(hbn7prtbm0t+w time.” Explain.

In Fig. 12–16, if the frequency(4fls;hck.iyo epbz:r1u+ 6h of the speakers were lowered, would the points D and C (where i yckofbs1z4e:; +ru6hp l.(hdestructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas pjbt i ye3)+/cwith very high noise levels have consisted mainly of efforts to block or red pc/3+iy)tebjuce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sua* h-a) 2c pnimwl0t6zm yfi;3perposition 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 frequencies farther apary- h26iw am;3cn am0i)pl*zftt? Explain.
(12-31)
(12-18)

Is there a Doppler shift if thc4btu x u.+k/ie source and observer move in the same direction, with the u+x.bkut i/ c4same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard byqzulc2v /h 2h9/af;hn pe3h(l a person at rest with respelqz 3lpe/(; fhh2h acun /v9h2ct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motionciezsg:*)zw 3 on a swing. A monitor is blowing a whistle in front of:si e*zcz)w 3g the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length )h k.l6ls r :ntk0z4uaof a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shou4 0nkuk :l6r.lsta) hzting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hearsr a:xhi6fzyfpb ilm75 :i*+e0 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 spyl0f b7p *iixa zi h:5e+6:mfreed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengthc5f il+azxe-wpi 1nyu ; ;hb 6oz)mr-+s 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 boafi kw; pr*scl8o100g kt is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (ai f0rlko;*p0k8g1 cs w) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a) 5xsirri2+w vzqb, ,:wzzgj) cliff. The splash it makes when striking the water be siz rq wzxvgr:,2ji)w+,5)bzlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone stpn-m9l0oa7v 6.q cmw+wjp 6o orike 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 apart. How far away did the impact occur?o 9pm7qc6 ovwwao+m6 pjl0n.- See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one m1y 7-rvih6nopd: o u7wile of distance by the “5-second rule” for estimatin 77 1-ivhro6wypod:u ng 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 su*urnxz/fsi-( h76l e ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whox f :be3y*8nwrse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ats j s /c;c8 5jphv02c*vy3ltgv o(5akj a certain place, wha0y5cao5h2sk;sp j ljjtg/(vcvv 38 *ct will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airpl cky :y tg:5.//;jazk)k vsjp :cl4pzjane with four equally noisy jet engines is experiencin ysz j:pgk:5pyj//c)4c:.zktvak; lj g a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said/ uslpwd2(b. z k0e8nfjo6m2s to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiessuds fepj b /.22(lknm680zwo of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fj 7x)4z8bh9 ikdi3ow1 b()j9qz, compmhaca7rom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cenb)9oc x 9hm1c7akz8ib jqip m37(zwjdha) o,4tered 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(aqwfzhws0(2n(td e4 zp gx0 . 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 t0u 0x cz 9(vbnemhsi((he more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point mn(ev9s (c0z(x0u bh i3.5 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 g9is+efg9ey7 front of a loudspeaker ig9+ef gs 7y9eon 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 detectxarc jlu 0*/ssa6 lp3;rubpf5ugzy+ ::fm (h- a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffes -p(:ysuzra0a b6uxf*;j lpmg3cf5:u + hlr/r by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will t:1- r3dn y, cpbf6swzlhe intensitylsd:-z f1 y6,rwbc 3np increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have 8s1klpjd uft 4a,4 q,zequal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of l,p,dk4ftjs84u 1qaz their intensities?   

  What would be the sound level (in dB) ofs.mo);bc mcp( erif 1, a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.1 f;1( mmbci.,cop r)es3 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem mr4wwbqmp -8m1m( x: nas loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1w:(4rxqw -nbmmpm 8 m12–6.)    dB

What are the lowest and4. ,6 wmjqboao highest frequencies that an ear can detect when the sound levejobo m,6.wq a4l is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sep,+ ipyaj.;/lcmaa+ic xu*yap/ e8*v53 pmqound levels. What is the ratio of highest to lowest ipa 3 c,pjv+exm / y*+a8m uecay ;5ipqa/*p.lintensity 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. Tt c ( t8bhf,jtu0+wy a80jcra,he length of the vib+ 8c uhj0fbtw(cra a t,t,y80jrating portion 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 cmg: ;hv ra;hzd+ long. What are the fundamental and first three audible overtones if the pipe is ;v+ agr:hhd; z
(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 frequenc32jjt o(fzo)qd1 fz4 9l bqlk,y would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if yft)lz,o2lqzdj( 1 9 q4fobkj3 ou assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes m 2wy-cah7i ft+c nkyq9da:5c+*tqn 5spanning the range of human hearing (20 Hz+i75n: at2q-*y +kcn5cf9 a tqymw cdh 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 frequency of 540 jituh::h zn 92Hz as its third harmonic. What will be its fundamet ni z:juh:2h9ntal frequency 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 middle C/apn*vyindz/ 29zxb n9. gh0d (330*npdyz //gnxhban.2z 90d v9i Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle /p3pskmp jxqt2,, -eh C (262 Hz) when the temperat,-tmq/xkp, es3hp2p j ure 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 2e3 k+fj/tev+j0 $^{\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 egq2; 3j:qxnf that must be uncovered to play Dqej f3gx q;2:n 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, 44ibqvwuo 0(i(+yht 6j7+ ed2 6gd3dpmp0 Hz, and 616 Hz, but not at an di 6( ge(++h6y 3pm0b ouijd7qp2tdwvy other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1ti/ gaan,kk rp;ol33d ;wsg6.o: znk).80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 6p:3l/gnk; t3r ; kwos .,kindaga)oz 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 wd9;o+ zco ibb3/ a.qa$^{\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 withinc5 q6l5vegqcag*l6 3n the audible range for a 2.14-m-long organ pipe at 3c 56q5ql6 elgn*ca vg20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxvcx57guq eur7o+p , 25s/ hczsimately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audib 5c/ugz,q7r+u h5oesvx c p72sle range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one be s4m-j .ohbk1;khlrl5at every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far ofm;5r - 1so. klbh4kljhf in frequency is the other string? ±    Hz

  What is the beat frequency 1ci vje2r-,87/b qn.e yfwd kjocqq;)if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle 8 ,csd; :lqls5jv+cgc operates at 23.5 kHz, while another (brand X) operates at an unknown frs+llj, s8g :ccqcv;5dequency. 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.    kHz

  A guitar string produces 4/7 je y. lnxhczzz/d 7rcf :2 elhml9jsj49)4f beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning4scf. ljj4 9h)dl f/rm zj:7che9x yznl7/z2e fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 jeq-tv 92 ru4da6r n;aHz. 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? [Hint: Recall Eq. 4v;ternd2jr -qa 9a6u11–13.]    Hz

  How many beats will be heard if two identical flutes eack ,s7nfute/ 4cu5ok -mh try to play middle C (262 Hz), but one is at 5.0°C and the ms fecn5- okt7/ 4uu,kother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequet ew2*x81fap0jikqwb g157k ency 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 frequencieskxw25aqk0wf8j*pg7b 1 1e e ti 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. 0nzb4jrz-s3::r (szaqi.fx na qo0 c1 A person stands 3.00 m from one speaker and 3jfa1z3 oq0 b-czr ::xsqn0ri .az(sn 4.50 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 19ebl/cyz 2y ttcb :.z:32 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the zylc9cbt: e:2yb./tz 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 2.7ctt(n*iz zs5x0gfz)wh i, . wg3k8ry*6 m in air. How many beats per second will be heard? (Assumeh, ztxyisn5.zz*(8gw k rw)ifctg *30 T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is fi c+;3aqac6z2et (lc1550 Hz when at rest. What frequency do you detect tcfe;z l 36a qi2+(cacif 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 detect if ap* pi9ycen ;1px;;mf s fire engine whose siren emits at 1550 Hz moves at a sp;pnpcy 1fs;; m*ei9xpeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shifw 8;6w:w tlnqjil6 .lwt in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exac 6lq.w ijl6 wtl:w8;nwtly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. W0j w,4von-qusrl8o( x 9j /eefhen one is at rest and the other is moving toward the first at 15 m/s t r9n/ju04j -sfqo ,e8xev (lowhe driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ( er5,s adfi4 6hki0 udjb+r2xreturned hj 6+ ik( u,afisrerd4xb5 02dfrom an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat ep ho* wqc.j6ewi5p :u4mits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat h5puje*:4o phwq iw c6.ear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiment *2j(vke *d grcrjmd40s, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba playedegj*4 jr*dkc 2rv 0dm( 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 blood-flow speeds. Sup (ve0f9n zbym;pose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/;zbe m fy9v0n(s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequen5h)ovqx vg 3 oxu3/v/hmvx,.i .,czdrcy $2.25 \times10^{ 6}$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 emits9ju5 p1tlegm n7 5r,fc sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers he9 g57 m1r, jfpcnlute5ar 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 its spef7x zaqeym )8lj0 .vd8ed 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 4xixe.yzdu8 ww6h b44 speed of sound is 310 m/s (a) What is the abzyw44h ew6x4ux.i8d ngle 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 spec7+ol7(:6z2 i4;h mczhrwjr- jrb cw bed of sound is oi2w767rhb:b+zr 4m o c- jhlwj(c;rcznly 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 strikes the ocean. Determine the shock wc 30wwuja:u c8qsv.:1 8nbw kkt0s:tfave angle it prod :wkvw 1kw0cu. f0j3::tnsc abt8s8quuces
(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 -k njnsen/-2uf (1zq$/theta$ 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 a/p2j 0m vh;fddbove the ground flying faster than the spe;pjh2v0f/ mdded of sound. By the time 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 sonar device that sends 20,000-Hz sound pulszr rbck.1u010 or :stj*yo.knes downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designet:k0rkzro * o1.0n.bj ruys1c d to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octa:jml*6w sl)tg y 1vo 0firy;o5ves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s7gusz6 zr 3zd8r gc+q9oq sy-4ymphony. It consists of many plastic pipes of various lengths, which are open on both ends. z8 -oug46zzqg rsrdcs79+ qy 3
(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 persy0f9l2 *l .e5sgxk1hj9l v ha;r6mfi oon makes a sound close to the threshold of human hearing (0 dB). What will be the sound levlxok 0se6fj 1 *alh9my.gh25f ivl;r 9el of 1000 such mosquitoes?    dB

  What is the resultant sound level w* i 4lua,gc0lmhen an 82-dB sound and an 87-dB sound are heardu0lac i*mgl ,4 simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, ic6wo 2abn s(3 k7qce6ps 105 dB. What is the acoustic(23qpcnsc 7 ebwa66ko power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpu+gab4l :kwr+;r zxf.xt drops by 1 4.+x;ax kbfrgw lzr:+0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ear:pml2mel8 q(ms. Assu (mq2lmep:m8l me 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 airplane engine?    W

  In audio and communications systems, the gwx 0tbl /ig*:dain, $\beta$ 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 *c,t.p9vi. j307vmfxk y qqmxis 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 point*x7en :knm2gu s with a fundamental frequency of 440 Hz and a mass per uniteuknn 7:2g*xm 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 tu1yu -wb-nj0k gkfr)c51 sb2xfbe filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the ts-fny- b0 xk)b 1fjw kcrgu512ube 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 strila12k j+3meew a3q2f zng of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce res+j w3lzeme3f2 a kq21aonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonat myia*ug8lz0p(du 65le 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 froar ccj1qzq:o2d,p m*4m two sources. The sound is loud cr*p, qm aqcjozd:124est 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 whistry.vjed;o8 ( w3toi1 ules. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachiv1(o; .rtoyw j3ued 8es. What is the speed of the moving train?   m/s

  The frequency of a steam gxrtnvww93x (n,a ;(3 jyy1jo train whistle as it approaches you is 538 Hz. After it passes you, i jwvgrtx((no91 3nx ywjy ;3a,ts 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 o8cmj oh0q c+*z7v(kt of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound oj(c0q 8ozo7*m kh+vt cf 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, 6x 4t c2od/x*oydsj8w produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Hoj8o4d/2xw6y xos c* dtw long is the other?    m

Two loudspeakers are at opposite ends of a railroa rned,qfaj3s *)7mv f-8l 5,behfbu/gd 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 the beat frequency hefsbqa b /ve7fn,u8f*,g )-h jld5r3e mard 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 th;fna,ni4(s1b4b su 6c6k fw fze aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speub sn(wbizcf 44ff 6,aks;n16 ed 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 toward o(fy2-qykk7b o 3aj3 *oh6 dn gu)-fxythe bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of k3-k ofbfjxn7y6(yg*oq3o hy2a )u- d the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soun5v +po-rj y1mld pulses 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 ymp1vj+ -l r5oby the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to senl(- vgf + hj/mbuf0kh9xpg (r0d 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 musica0v m rgpx-+k /(uf h(gfj0hbl9l 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 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 steq rdv4c;v-u5 np n34xchla:q2reo listening can be compromised 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 2.8 m high. Calculate the fundamental q a4n- 4d:qc 2hvc;punr53lvxfrequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, .lflxh486mw l called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, themw4 8.xlhllf 6 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 hearinix ckt ez.d),ex0tp.jjp sfw+n;c: 24g for the human ear at a frequency of about 1ixjzf;.wt4 cnp 0 kc:p,.sejd2 +ex)t000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bo/ivx ;4;:icsx 9 sdsyeom 1.5 min after the plane passes directly overhead. What is t/s:e s s;x4yi9vdx ;iche plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is l9hyo rxepya-. i)u. v(6ye(a 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