What is the evidence that sound travels oj b)5j5wqx3jj./ 7z fksx sj+as a wave?

What is the evidence th4norkbf7.( f dat sound is a form of energy?

Children sometimes play with a homemade “dng -qso5+9ye7o3b s. 4vitv icd:m z2telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly howvbson ic:g5td oqyi3 9 4z-e.7s+mvd2 the sound wave travels from one cup to the other.

When a sound wave passes fyu 8; 7neo rn 8;0bofw5nzxzf-rom air into water, do you expect the frequency or wavelength to cw -b8 o8ufzn0 x5ef;oz7n; rynhange?

What evidence can you give that the speed of sound in air does not dependabd 85+70 ii+q1gyzvt) ppv qi significantly on frezb q5yiidv)+ipq 8vgp t10+a7quency?

The voice of a personsluj::x spn frju9/ 38 who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a rooms8c 528 v,hbce vy8fsi,wuuf: affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the ampu d ue6s-gwo. ae*6 yw6:jkn1olitude of sounds in various frequency ranges. (Anoe*w nk6w-s6e u:y6 do.g1 jau example is a car muffler.)

Why are the frets on a guitarguw4pxoh1u9r*aya.87jqj+ 0 xep 4h x (Fig. 12–30) spaced closer together as you move up ue1 hxah8q+xga9 opp4 xj*47w .rj 0uythe fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hefgg+tg k n5kh 6ls6cz9sn-/n/ar it but cannot see it. When it emerges and you do seeg95k c f6tshsn -gz/kgn6l/n + it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereasc mp4 tjncj-2- beats can be said to be due to “c- j-ct jn2m4pinterference in time.” Explain.

In Fig. 12–16, if the frequency of tfqmx9qg86m*j d)pc8g 2z.zje6m m4hohe speakers were lowered, would the points D and C (where destructiv 29jg4 jfxmh)g o8.z8d c eqmp*6qmmz6e and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hnd 4co a(cmp4(k8a1 eeearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With k8d(pcc( a41eaeo4nm 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 show(qzdekl.s5 p l0is (4hn in Fig. 12–31. Each 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 component frequencies farther apart? Explain.elsp(s . li 5dh(qkz04
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the7/ggs) kc hx.ex ,mv b :colwdx8o3/x. same direction, with the same velocitye/shxmxo. 3), ggo:8 cl 7 bc/.vwxdkx? Explain.

If a wind is blowing, will this alt3-q)e9uai 3; f4go*uizkses h er the frequency of the sound heard by a person at rest with respect to the source4f93o -uq uz3i;k s) a*higsee? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A w6v61wdvs;w,7ly-c 5 hfhsdw monitor is blowing a whistle in w,cwdwvv7yl6f165w-hh sd s;front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the lengthltclteb69-d a s6m+:2bq0+ /u vcfaequ5*s cu of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the a- + ucv:c al5bl9 2b6t mtd*sece06 fqs+uq/uecho 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) juqu/yuh.g-aya, es.um(i5 waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s late m).shaugeuu( .ju y/a y,-5iqr. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wa.el ;.n jxui3a1-f1c nvf3u tdvelengths 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 b(sjxu;be: 8g9 ov :nlon a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33).9:nj v;b: seux8(ol bg How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when eqarn0 6c43j)pka7lrj txr98 striking the water below is hej7ktan a04c)8exrr 63 9p qrjlard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge ston/* 7zyuak xwp- d+kd/f2vipa+e strike the concrete pavement. A moment later two sounds are heard dz+p/d7 *akpu-/ iwfyxv2 k+ afrom 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? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ovey f+fy*rhrv5daqr/1y z n ..j0r one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tr 1. dzr.f+/*a 0yhvy yr5qjfnemperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a s d/r;q4ru-p+su8 b0qe8 j vvqfound 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 *5 ijce4k0el qof a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atyk7* xui/6g lt a certain place, what will be the sound level if only one is explody /k7ug*txil6ed? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from 0yuqx(x gc,fn6sdf v)x84hrdt6 :mg7an airplane with four equally noisy jet engines is experqr vgxnmy6fhc867f xd:d)04 , t(x usgiencing 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 to have a signal-to-noise ratio of 58 dB, whereas foo+ ,8xvsztwg3r a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dxwg+ s,zv83 otB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpu/n 5sttat99 qx4:dypw t of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ovewt:xtsd 5 aypt9 q/9n4r 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 ang/ awwzg49id+ eardrum whose 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 2i 9fy +zxp58uo50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in iy x5o9zup+f 8decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in 6 b /i:-v qkm3puf6njofront of a loudspeak b upi3kvnf:6m/ j-6oqer on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically dete *3msj8roqqu)y h2mjwt+1 9xlct a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sound3j91 +8 wmq2hlrs j)ytuom*xqs whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, tc8- cn w7i/, -lndkhn(a) by what factor will the intensity increase? Increase by a factlni,7ndwkh 8/c- c tn-or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equzlec8zmoh3 8 vq6vzy/)4*o poal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their inteoz6pvzqo8c )hyov3 e *z8l /4mnsities?   

  What would be the sound level qw45cy x1.oxp l*v 3g v)yc a-8r:cjrt(in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating ailj3ra4 g :qv rtc c-vpxo x*5cy.8y1w)r molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a e (ak1f4ssa2w 100-Hz tone that has a 50-dB souk4( aw 1sefsa2nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can deteq3o3h,tk/gwq ct when the sound level is 30 dB? (Seet 3 k/oq,3whqg Fig. 12–6.)

  Your auditory system can accommodate a huge ranj+c.e5h( e 7utzyeh jcj9:be:+b jm5 ege of sound levels. What is the ratio of highest to lowest :je.y5 e hzj +j9btu eej75cb cm(+he: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 fund phs 5g1kkt9g qs/vc2.amental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the strinskgs tgp5.h2 qc/91kvg be placed?    N

  An organ pipe is 112 cm long. What mv6fcvu(lsz 3b5 y 58iare the fundamental and first three audible overtones if the5viz fvu6ls(y3b 8c5m pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect froedee 7wmn-qt 78k7) bom blowing across the top of an empty soda bottle that is 18 cm deep, w8eme77qont)-k eb7d if you 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 piu u4i 6hh , jmjeo9l jn.za8 c:5sy56nxa/.hjjpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHzjy..ijh a h86nn:u/sex9 acl56j j z ,5hjmo4u), 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 Hz as its third harmonico)q1qrba: )a4 d 7fq4lmjunq(. What will be its fundamental frequency if it is fingered at a length of only 60% of its orjn u4)r7:fq am l4)ad qqqo(1biginal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to p*a8s *prj fr;skyb(3b lay E above middle C (330 r8krs*fj3 a*bbsyp ( ;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 pip c wjrzx6r,e,-e that emits middle C (262 Hz) when the temperature is 21 r,x rzec6,wj- $^{\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 ab;vpkz4a xu;1f4fz kbi:l((at 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 ss0l:05qky mushould the hole be that must b :5y0 0slskmque 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 3du2s l8rls u 06 yk9rvb.j0jl616 Hz, but not at any other frequencies in between. (a) Show why this is an open o jldsu2.ryls lb 6 3r098vuk0jr 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. Itjwk.8 5sbgtn f*gjpqf541( pq resonates at two successive harmfg k(8s *t1 gjp.54j nqpfqw5bonics 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 5,m.ppmnuvr9, pr3ngg .- ksv $^{\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 wi.plr - y2)ygytthin the audible range for a 2.14-m-long organ )yg2 yl-ry. tppipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. i 7eblrtyfj90:cz o j:w51klok . .ar(It is open to the outside and is closed lrkoc.5:(9o: ylzetw.i k0 arjf7 b1jat 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 in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eveo-fy*ogjkct4 t5o1bru e+87 hry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fju8f t+ky 1gbr- 54o7ctho*eo ar off in frequency is the other string? ±    Hz

  What is the beat frequenc uuf()zw5sc vw3;z.2xs be+a7 pycd 6by 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 operates at 23.5 kHz, while anoz v1fk+2gm4 lpther (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frefl1m4vz2p k+g quency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning 3 c*kdah3.oot( e (3 40z2rtndrlohja fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vib 3o chnokor(*a. jt34(dahz2d0rl 3etrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned +hfe3lby 5l40/ ji )gwhcdq,l0eg6 btto the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will ie5h +gbtd3e j 0 clwllqbhfg,)/0y64be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes- 1sw fty.ob/ gxa*r)p each try to play middle C (262 Hz), but o) p *g -.sowb/art1xfyne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning vcy,i+bp8:p aforks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possibcp y:a ipv+b,8le frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3tch9;6*4jxzrl xek4d .00 m from one speaker and 3.50 m from the or6zl9*xxkt c ;dj h44ether.
(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 vibrak:i;l; p t (t/j;dm1s bhm4iivting at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one p /kl;bt (;hvdstj: 1miim i;4is 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 andmwmyir 8ub5 q9me0 abe 42nu6+ 2.76 m in air. How many beats per second will be heard? (Asy6e q824rbwm+ mi9ubu0 5 anemsume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fireub/i +/oerktb twffl-, (yw :7 engine’s siren is 1550 Hz when at rest. What frequency do you detect if you ff: wrbik +u(w ,/t7belty-o/ 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 a fire engine whose 6mwvh d l .:/lwn2jc-dsiren emits at 1550 c2n: wwl d -/j6hdl.vmHz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcp: hi*gwpw).c -g5g tne is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freh-ggg)tc: wp5p.w * niquencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one6d*a*r v9bj lv0jw 2wn 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 emi92wn*wb*0 jlva v6 djrt? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz anu8q1 ao rm*bmy s.4q)pjv1r7p d receives them returned from an object moving directly away from it at 25 m/s What is the recei74uar 1qj q p 8mor1.yb)*msvpved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b swn: tq:p6un4at emits an ultrasonic sound wave with frequency 30.0 kH qsuwntn :p4:6z. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubavq1w lwsc i* m(;9wa0f7ju4sw was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the 0fli1s; ausw 7jwmw vq 9*4(wcsame 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. S354(hpvumgjv5k)gfhkpkp ; ,5q- xkj uppose 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 exp(g h;545j3fgvxhk vpkk, )uq-5 pjmpkected 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 jws:ejr8m 4o1 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 wind velocity isw6ca2 t7klkeomr6p;2 12 m/s from the 2r 7l6wa 6kp2cok; emtnorth, 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 il,0)ge zs .ll5ztj4ca f 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 atky 9h3p;oj d9j Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction ofokph; 9d9jy3 j 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 hl)10nts(t htthe thin atmosphere of a planet where the speed of sound is only about 35 m/s (hhnt lt1)st0
(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/kbu;gq97r;q0gsz1v( lhb fs0jtf* 7 os strikes the ocean. Determine the shock wave angle it prj; 1vrozktq70b7 (u fs;f*ggl0s9bh qoduces
(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 l)+ -l+bxpn g6 (hkaro$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sm-wx-psh+ * rxee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear them xwp+-x- hsr* sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward fu5/t knttpi,o4-*t4ys4z s/6ro ustf rom ptt4zf4to* n/t 4ys6is trks , 5uuo-/the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in jm5b+l-mq w;b the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displaysncr el5gs 7va4:ev-: called a sewer pipe symphony. It consists of many ple- lc n7v5svr4 ::gaseastic pipes 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 person makes a sound close to /gurt -mfv751mn(vzythe threshold of human hearing (0 dB). What wi m15-(gmtfv y7r/ nvuzll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dBz + 7 ok2vuf1lms;vr6o sound and an 87-dB sound are heard simultaneously?lv 7mo16 2ku;r+zov sf    dB

  The sound level 12.0 m from a loudspeaker, placed in the k xx5jvy0l-x 4open, is 105 dB. What is the acousticj0-4 x5lxyk vx power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10xqbl /jc 6*tq-00 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at c-txqjq6l/* b15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears. fw0vwe infybwv494*/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 onv *wf ev/w 0biyf449wf 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 systet: uu 50 x4uz rdo5qexi-fs)*lms, 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 a frg-9j/dm(nk 2ri1ul grequency 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 lonxbc/yt9id7,5w jgt01 v:z zthg between fixed points with a fundamental frequency of 440 Hz and a mass per unit length ofd /5ztti w0j gcx:,71tyv9h bz $6.1 \times10^{-4 }$ 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 (yf/x(7zfd bc , j8lhjwater (Fig. 12–35). The water level is allowed to drop slowly. As it does sjfyz8 (cb7(jh,xl/ fdo, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at :g;dkhvzy j v/+r6iqgm4;(y pone 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 the third /v d(rm6h ;z4jiv; g yy+pkg:qharmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonapb(vyl byzyx . plc, m;*h9g,,te 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 qu5b +wi47+ lqnbsd.dcoming from two sources. The sound is loudest at points equid u7i5dd bn.bs++qlq4w istant 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 condunqaeb/-mmh57f4 o ji;7 l9 cfdctor on the stationary tra b/eq ffn;-o4hjmid7 c7m 5l9ain 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 a9wh2e0uplw z5byy ;q/pproaches you is 538 Hz. After it passesuqbhwe y05pz 92wy;l / you, its 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 ew46zcw:/(doz j( *d,ma0no ,sxqbowspeed of cars just by listening to the difference in pitch of the engine noise between approa 6jxawo(:d*4/m o,(eo0 zzqnwscbdw,ching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together,v a ;fkk41az3h, oba8u: vx*lf produce a beat frequency of 11 Hz. The shorter olvkbaz,1f avof; :4ha8u*xk 3ne is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as ya-c-t;;kafg2 t wsv3 it moves past a stationary observer at 10 m/s as shown in Fig. 12–37ytak;v gc3-- s;2wf ta. 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta wu9;p)aa4.f kp0lra fis normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed a. uwf k)9f04laa;rppa long 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 towar -c(ha- fwv,6rint8 abd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detetciaf- nv8ba6w-hr ( ,cted by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.jf gka ukd(24- The pulses are approximately 70.0 ms apart, and each 4gfkakjd- u( 2is 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 the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send i sq(au 0;9wdrm)v e,1sue2lusignals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.as, ueql srm);2id eu0wuv(1 9) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of standir 6+ s8pnc(oqa 5uu-fung waves, 8csfa+q u(np-ouur56 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slend8k3cv )dqb gzj;;ife2er aluminum rod held in the hand near the rod’s midpoint. The rod is stroked ;3i ec8d jb;)kqvz2 fgwith 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 f,y/s ;k ny3eq0e+bt3tt)h xst:*aguhor the human ear at a frequency of about 1000 Hx ,yh3tt/t0e)+hugy;t*sba3q :ke sn z 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 M 1i0ys- hp g/x)gejopxj/ 28noach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the g e2jhjp-18//p )x xoo ny0sigplane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa1v j/bq,r1mahc nt cd,xj5;i66uib w8t 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