What is the evidence that soun 0gayi// y2uind travels as a wave?

What is the evidence +ftqy z4ys*f-that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string c3t :sj*)p5a ltomnw03sy :bz 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). Expw0 zn c)sotlm3as:tbp5 y:3* jlain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into waxyokz;7e u/ 8hw(f+u l-mou t9ter, do you expect the frequency or wavelength t; 7uoo ehfw8zykmxlu/ (+-9uto change?

What evidence can you give that the speed of sound in air does not depend sigyup,7hj2kw ( gnificantly on freque(pu j 7hkyw2g,ncy?

The voice of a person who has inhaled helium sounds very high-pitched. 1 8fustzj 4 rpn )9s77*ndhm2v.elpweWhy?

How will the air temperature in a room affect the pitch of org )xz:hihlh:jq1 -/m kran pipes?

Explain how a tube might be used as a filter to reduce the +mlz04tcv9;l qw5d gsamplitude of sounds in various frequency ranges. sw0 lcd;4+m5v9 qlgzt(An example is a car muffler.)

Why are the frets on a guitar (F/an nhhkat: ;* co:xa8ig. 12–30) spaced closer together as you move up the fingerbh :a*;xkn8at : /onachoard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear i1lh(3kh*w6e rrstv 7lt but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” —s*t6 rlr (e37h1k hvwl 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,” whereas beats u 62kwf8 iq((1j.aryr q us3izuuuc:2can be said to be due to “interference in time.” Explasiuu.: a8(fq ru3 2r(qi 2wujc1ku6yzin.

In Fig. 12–16, if the frequency of the speakers were lowered,z-h3 *jxp, bi0)catyc4u+ dzq would the points D and C (where destructive and constructive interference occur) move farther apar h* cc)pdyz+ubtia3, 40x qzj-t or closer together?

Traditional methods of protecting the h8emr e4oo u oyx9wj bhv f0*i(j888e3(6mpingearing 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 electronic 9 3e0(m8 o(oji ofw8i8x8brh*gyn6 jmpe4veually, 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 k,av/c /:q7wj*gvpb cFig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18* v/ kc,:vq/apjw cgb7. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obser ak8y4n +k8few*mtm8r 1k(ig3av 9hmfver move in the same direction, with the same velocity? Expa8hf +3t e9k(m w1v4 armnk*m8i8gfkylain.

If a wind is blowing, will this alter the frequency of the sound heard byflhakj(f5-b a 91h2mm a person at rest with respect to the source? Is the wavelength jh -am9 2lfahkfb(51mor velocity changed?

Figure 12–32 shows various poslkg;hes2p1l0mq9 7hz-r a4qpitions of a child in motion on a swing. 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 highest frequency for the sound of the whistle? Explai 4 sla9q -pk;rhz0he2q1lmg p7n your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shout xudegimo,1; 1p st4l4albp*/ reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aftel 1,dto;/mpe4i bp1*a 4lg uxsr shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He heodd:v6is jj qv/rn 5,;ars the echo of the sound reflected from the ocean q6,ijd s5;nvrv/d:oj floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2,kykm p 3 61o 7xt2qkx4jjkcj:0 $^{\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 abovqf0/ /n jau2 :ppo.sive 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 hju n/qvi/20 :fs pp.oaeard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes-ulqydx:kk 69nr -j* y when striking the water below is heard 3.5 s q6ynkk 9-- dljy:x* urlater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike t vg 62 klltanp7.of*r5he 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*r7opg2 nt56lvl k.a f away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erdht5(e0 m2sy7rf90u lapatl5v8pwmstj /p.5ror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatu.p5ut 2a ymmt (rjtp5v/h sw07l 580sa epfd9lre is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofqupj/msgbe;fi :o7 ec00,t *d a sound 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 whose intensity is orvp* k dog8 a94g ,.xckbn5c-$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sim;v9j5/j5sytl q+ zwxsultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensit zy5w+;s jtvxq /5s9ljies, not dB’s.]    dB

  A person standing a certain distance from an airplane with four ,5+ aff t3z9d)vnko6yn* w +y sulpnj-equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intn+sn *5+)vda-pf yn, wo9 3lkujyf zt6ensities, not dB’s.]    dB

  A cassette player is said to have a signalj 5p;sk1 vwkfsk)ix,--to-noise ratio of 58 dB, whereas for a CD play-k fsi jk k1vwxsp),;5er it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normaerpv ;4;y0b sls3q/ucl conversation. Use Table 12–2.; c;vql/y3sp40e b rus Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes ankz2m /1iw 0jmaz(aum- 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 250 W, while t17g/g;ws9yu1 jcn u daoma 0y)he more modest amplifier B is rated at 40 W. (a) g0 / 1ug9o71 adwm)us;najyycEstimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in ry6n 1bw mp(i2 ,5j2bczzv;qg front of a loudspeaker on thr2mvyzwjp5b n; (iz1b qc2g6,e stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in soun*61 ivzir1q:6k b4otq1nmssfd level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffz:4kr*s tqm 11fiqsb6v n o16ier by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inuzuj; od8(jk: tensi;dj u (jo:kuz8ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, 5 mxiw4,a o;nbb(wxy6d.. 3-hmzqzrb but one has twice the frequency of the other. What is3 . 5om,y-x;q dzai6x mwbn4(.hwrbb z the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thatlf0sw1)3 ncki i8 ck:s corresponds to a displacement amplitude of vibrating ) lcis:ks8 nki03wfc1air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level told;( y 0hllmvi*7 w7pl1j 1nxs seem as loud as a 100-Hz tone that has a 50-dB sound level? (v l*0 jshpxl(17n 1lmd ilwy7;See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an eakm8apkz -*8 - b.wwzbfub.-vkr can detect when the sound level is 30 dB? (See zpwbw u--k8 b.kmv.zb8k-*a f Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the ug) l:g vbha/7ratio of highest /7) a:uglhvgbto 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 fundameeq0 ;n) fxr ne drgd0;yl2.jq pu54zq/ntal frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has qfe/;yu; qx qld jdz rn)r.240gne0p5a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible o dk ox3 jr499k5;aojlnvertones if the pipe is x4 od ja;9jknor39l5k
(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 exp isb60 9;9qm* jejgpeject from blowing across the top of an empty sod*j je09 6;jspmgeiqb9a bottle that is 18 cm deep, 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 pipe organ with open-twd7yfb y+my;. ube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipeby7y ;ydw.+fm s required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string j y45,up rf32vqc:ein2 saow9 has a frequency of 540 Hz as its third harmonic. What will befapvri o25eq:c j49nswu y32 , its fundamental 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 tun 69du6u b(nhjtlfc-h6ed to play E above middle C (330 Hz -l6h(j dbcn6hf9u tu6).
(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 ov +tl z*vf0:vrf an open organ pipe that emits middle C (262 Hz) when the temp0vl:+v*z vf rterature 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 ats- ln8ou yh.b5 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 rhq+ uqa:t *e igbrp6f: iw-+1Example 12–10 should the hole be that must be uncovered to play D above middle Cqtw1 b6:ir q hr -u:e+fai*pg+ 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 +q:g;lfm-ny ed unz/,616 Hz, but not at anyyfz n;e,+ndg -ql/ mu: 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 1.80 m l (qb*,iwo k;wlong is open at both ends. It resonates at two successive harmonics of frequencies 275 Hbww,q *il( ;koz 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 n fi i2s()g4oi$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgp l)y2kngb0 8ban pi p8yl0bk2bng)pe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the oul5 yz gl;)kjy1tside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the sty )l g1yjk5l;zanding 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 every 2.0 s when trying to adjust two strings ot- t5bvj1ny 06mehja1h*a n+, one of which is sounding 440 Hz. How far off in frequency is1nebjjm1 t*+nhoa yv 5-0ah t6 the other string? ±    Hz

  What is the beat frequency if middle oiz5 yumed*-4C (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 another (brand X) oplnur,9lg+l b s a(:ncc 2tz/j tic80j3erates 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 simul398czaij:ruls ( c,ngt0 /+cjlb nl t2taneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunic m9pw : st-rbcfr/8z78m a1tqng fork and 9 beats/s when sounded with a 355-Hz tuning for:78 m 9rtcwbqr f/ca1tspm-8 zk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tujn3klqo. bd8zh c5;dki.3 o) lned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat 3;dhnkqlc8d ..5oj izkl3 )bo frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical1b blxrsy5g7 /my pu 6oo,(-k3vh,pcr flutes each try to play middle C (262 Hz), but one is at 5.0°C ay rgy(l-7 bso/oxuc6 1v,h pb35,rp mknd the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B ha 3qko i7*jty a l8erhu-f4ic34s 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 possa4cf7u3 o*ti-l4qk i8jhry3 e ible 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 ap8i90d h,jvlejart. A person stands 3.00 m from one speaker and 3.50 m fro de9h8l jjvi,0m 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 dh/oqq (3f6b ir +msi9132 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 /hsq +9bii3rqf d 6om(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 xo 7cz-)z:; dllzsy2dand 2.76 m in air. How many beats per second will be heard? c)7zllxdzz;o d y2s -:(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ok2.,ak : jjttn+uw 1hlf a certain fire engine’s siren is 1550 Hz when at rest. What frequency do nwjk2 1,:h .tkuj+ta lyou 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 d,q26oa eb y at,zd.5oietect if a fire engine whose siren emits at 1550 Hz moves at a speed ofo qb.,iy25,e o a6dtza 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 202swz ugqd /m.000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? d0s/2.wug q zmAre 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 vszpmh e09y1 s m,xl/s;u0q3ufrequency horn. When one is at rest and the other is mo mzs 0xvly 0,9/qmp s;eu3ush1ving 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 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonii4cmst1bmhodae-)d5q v q .e x 9,y-0vc sound waves at 50.0 kHz and receives them returned from a9dq oymv05chxiqd.v,m-b s 4e) -at1en 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 flieszz puxlh.370 v, the bat emits an ultrasonic sound wave with frequency 30.0 kHl7. uvpzxh 0z3z. 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 lh; -nxyr(;yrhw 8rp-moving flat train car at a frequency of 75 Hz, and a second identical tuba played the sa(nlr;-xwr-hr hy p8y;me 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 ultrasounvgkqu,h) fj-.d waves to 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 large leg arteries at 2 cm/s directly away from th-fjh kqv,.ug )e sound source?   Hz

  The Doppler effect using ultrasonic waves of di(87rt0*unbt our8wfrequency $2.25 \times10^{ 6}$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 f84v38 7iu/ pack3h/fthz r q1kvrkhy8requency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear avtkf hyri u8kh /78zc4/h 3v8q 1r3pkwho 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 movioh8i c /wgq/j(ng on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is4 sl) gp3i)pes 310 m/s (a) What is the angle the shock wave)s3 4elippgs) 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 t c)w0l xia;ux(hin atmosphere of a planet where the speed of sound is(x ua );0icxwl only 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 wave anglerc43/c5d ) .rnzmlgfe ilcr4grm.5 e)3dn/c fzt produces
(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 m hkmna1 6af(fv92da2eig2b,$/theta$ 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 grooc h)n6-zu 9txea:7mcund flying faster than the speed 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. Detex6zn-c t:oeu97 hcm)armine
(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 sen*bwd -w3jgds la,3i39n9hea nds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what i *i-sb h 3an 3edwn99lajg,w3ds the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the hum3h4u( pkmok6gan audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display callec 98yl qicz rf3q0v4k45pr5 fdd a sewer pipe symphony. It consists of many plastic pipes of various lengths, wh5c3 d4kc iq85zr4fp rv y90fqlich 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 the threshold cr g2epk/(ui74hr yv.x ipq9.of human hearing (0 dB)vgekq/x.p 2r( 4i .ihcu7yp9r . What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sgm9e usv04 ahav -c.-iound and an 87-dB sound are heard simuli-h0v 9m4 ga-cav u.setaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wh9o* -a,j qdbbxg ri o-u-/ra+eat is the acoustic power output (W) oroq-b g re-b, *adua/9x+- ijof the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output z*hz ql-)6nrzat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the po-z 6r znhz)*qlwer output in watts at 15 kHz?    dB

  Workers around jet aircraft ty)h:awntb*t) c pically wear protective devices over their ears. Assume that the sound level of a jet :ahc )tt)*wbn 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 gag *fqbevph)/b;6 bq b(in, $\beta$ 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 violi dp81cl7*uml0a :ncqwn is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fij /5ce-wn( m fggei(7ieu-g*lxed points with a fundamental frequency of 44in *jg- im7eg(5l-cg ef(/weu0 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vert/ttjl-dp l7j 7 cgef.3(cdz2y ical 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 wa/ jj pzl7 lf2dy.3gt(7c -ctdeter 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 ygv m)pckni0q) 8-g0 wopen at one end and also 75 cm long. How much tension should be in the string if it is0 8yvw-np)qi mc) gk0g to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f0 -;0v,ps mrku2w*hmnhkokmd0(f.ql.mt ux 0 ull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone v(6pzr.kh(gg5+ b gwdhp(hi7in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To dete+g d k(g7rp( wghh .6pvb(5hizrmine 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.,cmwc n;*7vsq2*-yav2 ky 5zd,r vely The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches.ys*,2e 5v2k*cmdzl c vrq7aw y-y,v;n What is the speed of the moving train?   m/s

  The frequency of a steam train whistlssj4 q5m5t.w s5 -urjx;odrrjb4 7;q te as it approaches you is 538 Hz. After it passes yjt5tb;j qoss;d7 x q45.rw m4j5r-rusou, 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 speed of cars just by lis2wn*a l)z vyg2tening to the difference in pitch of the engine noise between approaching anlnvz)g2wa* y2d 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, produce a beat frequency of 115fv)g jml9xd/k hc+-u Hz. The shorter one is 2.40 m l +)x9u -hl5kvj/ mgcfdong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta5;)r5j2p;cnm5a ljzqbvi/gxz 1 y.abtionary 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 rabl;m55z.yz ;2q/jj5pbv1xg c )nia 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 f8g y0a6k pbh m.tkjot(:vn)k(low in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected froptth (ajbn60()gv: o8 kkm k.ym 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 toward the biet sk;q51hy: at at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wavet1;sq5 ikh:ey detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series 5uicz)vos7 bvi:/ yi. of high frequency sound 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 by the bat so that the echo 5y)vi ovb7sci/ zu:.i from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usjgdv9 ;b-dao; ed to send signals from one Alpine village to another. Sindga jo; -;db9vce 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.) Model as an open tube.

  Room acoustics for stereo listening c1qj7v-e f- yjmh0(m ceuw 8nz/an be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodeeujmq-(cz h 7-wfm yv n/081jes. 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, slender alumie 2f i4zp10cyli fet;9num rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,ifz4yp2e 1f ctie;0 l9
(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 threshop:fwq3bjb1 gmep0/.m yd;/j sld of hearing for the human ear at a frequency of about 1000 :g.mpdjp3wbb;fjys me/ 1/ q 0Hz 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 soni2s r0a2(eg23 hockbruc boom 1.5 min after the plane passes directly overhead. What isb r 0kr2(2goa2husce 3 the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat iowj *ipll gb e/x r8v85.c3t5vs 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