What is the evidence that sdk7,lyr)b4;k2 *grs pz 6xrnj ound travels as a wave?

What is the evidence that sound is saym qfq +y9gkv7*/ah* (yg2ja form of energy?

Children sometimes play with a homemade “tel9kp 6mem5y.fk+/cpo ahys.m.ephone” 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). Explain6ops+. 5 9keky pm mh/fa.yc.m 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 frequnglgwy6dx(n 8 ktm o39t)6i 4cency or waveleng 86dt6g4ygn)ck( nmo ti39xl wth to change?

What evidence can you give that the speed of sound i9 +eovxuv0k;whmwm 39 + zi8sbn air does not depend significantly on frequencv+98w9ih0boez wkx+ 3msuvm; y?

The voice of a person who has inhaled helium sounds very 2l3 0h+ /kfq gyr35v- b pdvz7*kevcfqhigh-pitched. Why?

How will the air temperature 8i1(5nl)rx z bkjh6by in a room affect the pitch of organ pipes?

Explain how a tube might be used as a8j*5lnt ; ejq1 r upf,gjcr we1y)d8;e filter to reduce the amplitude of sounds i )8tj 1l51npfe*c;w u r;8je,dqje gyrn various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move u:y7/ dv.p xmppp the fingerboard towarxdy/ pm7.:p pvd the bridge?

A noisy truck approaches you from behind a buipj( 0iav 2(ziylding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffy0i2 (ai (zpvjraction.]

Standing waves can be said to be dp , 9tsz y+kr4:mt)yjbue to “interference in space,” whereas beats can be said to be due to “int:9k)4zy y jp,mb+rstterference in time.” Explain.

In Fig. 12–16, if thec*xbsr kps5b1g(rvnk(,* o (fg7 lpp7 frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or clok7lcg 75(bg(1nf* k bpxo vpssp*rr,( ser together?

Traditional methods of protecting the hearing of people who work htk2sk,+ pb 7xin areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wtpxbs 2k7+ k,horn 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 thymf8 fv* tx01k;f1 wyeought of as a superposition of two sound waves with slightly different frequencies*k weyft1mxvy;1f0 8f, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shif44kgqk z04jlc3c m bxqk 9ksyvue /6k erz9);6t if the source and observer move in the same direction, with the same velo/z 6 ;jk k394r4k4scl u bqkexqzkcg )ym0ve69city? Explain.

If a wind is blowingj/ z7d +gwzrl37jf; ud, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavele r7+zfug3/lj dw;7j dzngth or velocity changed?

Figure 12–32 shows varioiz hpaa,0no-(;un3obc 3jy 3 mus positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on bho n-ci;0znp(m3y ao3u3 ,ja 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 of a la*qjhto9f y2 t;v+dpda,pu;o* ke 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 shouting. Esti ,pptvqj2*y;a dh ou; 9ofdt*+mate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears tta(.-(w.od(rolthg qg j m)7 zhe echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with dept.zo t gt(l7)hjo(.(-darwmq gh.    $ \times10^{ 3}$m

  (a) Calculate the wa yyhj4zy5 0xidhmmbi /,5hf6 1velengths 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 on a foggyh1 l 14e/qcq tqyty*d( day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before theetyt c lqqh1 ydq/*1(4 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 strikin7l5k;znl w a3h2enx d9g the water below is heard 3.5 s la;7wxdnhzl5e 93 a k2lnter. How high is the cliff?    m

  A person, with his ear0 10hge vooj88 u jwftmqc6j/* to the ground, sees a huge stone strike 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. Hj0tve80o8fq*6/mw j1oujg h c ow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one milpwofq-gzz, hdb-1+y rka 9, p2me)n -ce of distance by the “5-second rule” forkhgp q--mw9 edzb ozn ar2p)cy+,, -f1 estimating 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 sound at the paiyf) kt;bz1/zb 1 sfca t8s5hj)n level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sounxp-b745o) bdy f7dej vd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whe(jza.sa r t;y 8xg);bfn fired simultaneously at a certain place, what will be the sound level if only one is explodedrabt.j s8yx;;)fa z (g? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance x3ptiym(q b-vnb(k81from an airplane with four 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 dib13p( btxk vyqn-(8 mown all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rd8r d z l61vo1eetzn bsk476n4p3i 9 8o9adricatio of 58 dB, whereas for a CD player it is 95 dB. What is the ratce d46 1pvisnzotnko91z8e7l4 d d6 a b8rir39io 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 sp- i)6e h)ve * nswzm9qvkb;l5eeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on-v vnel i) z56eseqhwm9)k*b; 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 stri 1k- g-gyepq-og-j6wp;agc*k .if 9dvkes an 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, whilec *q7r jfeb7c, the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conne j7e7, fb*cqcrcted 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 frtb:t59 :kkf rk a+xvd2ont of a loudspea b:krtx2 tkv+59dk: faker 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 typi ;n.ldxmz;ae3gs hm84cally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounnsm z4x8; .eh3gl;a mdds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave7m 8enqi dw8a5 is tripled, (a) by what factor will the intensity in w nq85midae78crease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the frey (8/1)zsrinfi-fq kp9srg l 1quency of the other. What is the ratio of thei-1lzsrgnyk1fi qri/()8 s f9pr intensities?   

  What would be the sound level (in dB) of a sound wave sdfqg/ +iok: 0in air that corresponds to a displacement ampliti +f: ko/gsd0qude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud asarotd7offpp5s,26w6 a g;n2 l a 100-Hz tone that has a 50-dB sound level? (See Fig. f 6d6p 2ofraalp5osg,27tw ;n12–6.)    dB

What are the lowest and highest frequencin8 vz ke+2wo.1rwgb5qerxa+7es that an ear can detect when the sound level is 30 dBwbe+ rz8eqonvw.2rk5 71+ gxa ? (See Fig. 12–6.)

  Your auditory system wg q738 pisay9can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensw8qg7 9apys3i ity 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 funtvn g 6 ,5x;wo,gmhvad ld3+(odamental 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 mvwg6lhmv+,x(d 5 dgo ,o;tn a3ust the string be placed?    N

  An organ pipe is 112 cm longj9q 0cx1zvkt 5 yw kh5d+yux-,. What are the fundamental and first three audible overtonej5h-9 zq0wtk5+d y xyu ,1cvkxs if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowi7(bfssov/gn, wp1 jn.ng across the top of an empty s /n(b njw1ss,gfo7p v.oda 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 op*r6viu twu8xzg kg -s+a zb6x:*ps14ven-tube pipes spanning the range of human hearing (20 Hz tvw **iug+a v 41 6pxgtx:8s6rksuz -bzo 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 Hx(py:vck 3vz3cj9f x-z as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only z9pkcxx(vv-c :y j33f60% of its original length?   Hz

  An unfingered guitar string is 0.73 oojrca sv63,3 m long and is tuned to play E above middle C o,c6r3j vaos3(330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Ho i ;*kz--6uxmap ov7tnyk2: vz) when the temp6 7otz -;iy:u-vvk*mnxk po a2erature 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 2r: k g9sjz)nv 76ah*nf0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutec 2uc.jo8t hy6 in Example 12–10 should the hole be that must be uncovered to play D above middle C ay2 oc8c6uh.tjt 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, joe8n+7fc40tg z8* /cumhcv;2e z ob i440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open4izghucj zt oc o207een ;+*c8v b8/mf or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both e7 zrpg31p enw1k7n8 ixnds. It resonates at two successive harmonics of frequenc73 w prn11zpknxi87geies 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 l9 )smb)uoy fv,+azb( $^{\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 withpemeb;si/ c8j )v6 vbza9v u)1in the audible range for a 2.14-m-long organ pipbp6as8 ;vzeumv)ce/9 b)vji1e at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal i 8 3f ;4aflldaw(8konps approximately 2.5 cm long. It is open to the outside and is closed at the other end by the enlok4;lfwpd8afa 8(3ardrum. 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 every 2.0 s when trying to arps8 v5 i2+sg1eg ;dlf,am w9cdjust two strings, one of which is sounding 440 Hz. How far off in frequency is the owe+p,rg189 ;isf lcdavg52 s mther string? ±    Hz

  What is the beat frequexd(7i/h3jhzke/*e h 0a3 sggtncy 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 another (bras. fo o:c)zh,ue/*wh o**qriind X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrilo* och.,) i:q*w/rzfu *soehil whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork andbqc7f jbw dk) v/sh)3+ 9 beats/s when sounded with a 355-Hz tuning fork. What is bwsch 7/)v kf) 3+dbjqthe vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2* e9n0-d7ilgkinn0 dz94 Hz. The tension in one sldziekgd *70inn 0n-9 tring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be he4sv03qy)us5 e-mcl.pu tmn-a ard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at 25.-m vnp4um-3ltaeqs u)0ys. 5c 0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a:f1h2vjy0w fzy i2:yw )a 1yoand 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 f woyfhazv12ai 0) yw y1f:jy:2requency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speiesuh: 0r p.2aaker and 3.50 0ih psr:2eu a.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 sx nip k973o6x) uapu*-c am8lbupposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s wh ika*76pau -x)uc3n98xmopblen they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many 5uhsngo 0qs,3gp va3:beats per second will be heard? (Assumev 5gso:p, 3u03nsgaqh T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency off ujeu g:h +mnxl2n/1 r-k0eu0 a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move 1 uj m00+kn-x:/h neg2ueflruwith a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. bdu who 20iw.7What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves 0.27w boiw dhuat 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 source is moving toward you a b/yq;d 7qz2hct 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exacth;qc d7qb/y2z ly 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 frg(2ma* t7nlb9dkoecw;4j cc 6equency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears k7cjgcncoe4( * db;ma 9l6 tw2a 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 r/2 ; v(wxx)hb7 tunujxeceives them returned from an object moving directlyj uv x2tx7/xw;) nu(hb 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 fliesja tzv0sji/4 w11lbk 0tt3b5f, the bat emits an ultrasonic sound wave with frequezw/a 1bt451tk il0s0jf jtb3 vncy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played;qg1h /sa +ew(f5ojuk on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at /;+e(f1oq j asuhk5gw 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 ultrasouwh la/5l033werg :fksnd 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 arter3fs g3wrl hewa /k0l5:ies at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency ;; dioub9uk 1t:0b4qs3rdg j) ydg:km2fv 4wl $2.25 \times10^{ 6}$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. Wm+ cjgzqpo z.+-+4bdhhen the wind velocity is 12 m/s from the north, wh+hqz.pjcb +- o +dz4mgat 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 x-w:w1gp4-yp /mcsyt a y4os-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 is 310 xtsg u8l,,d5 lm/s (a) What is the angle the shock wave makes with the direction of the airplane’s motix, gs8d,ltlu5 on?    $^{\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 pla -)i q6du6s4a1h(ntx onve t;dnet where the speed of sound is only about 3q4sondntxea16 hiv 6ud;(t- )5 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 oceal5m ls+ysz,d (n. Determine the shock wave angle it prody m(,dsl+szl5 uces
(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 ms 9*ey(xfnu38 nm +js$/theta$ 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 7 ;r(ln kh4zdaar 873jrm6yyu the ground flying faster than the 4z urr7lydk;a 6m78(rahjn 3yspeed 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 son*ddyvqf9 a 5d6:gov5oar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects yvdovdg *qafd65:o 95 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 the human audible range? prw5. u 87kjfq$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipek)z0h35j+kxnh j pr2) +d bmcn symphony. It consists of many plastic pipes of various lengths, which hk+dm z 5nrxc) bn0j+)p2kj3hare 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 personx2p,g-tzn 1q s makes a sound close to the threshold of human-1s,gxzq p 2tn hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound ac6 -o w6z*vd6hyh erq+ykv5u 0nd an 87-dB sound are heard simultaneous6zhh*u -y kvewv5+6r0o6y c dqly?    dB

  The sound level 12.0 m from a loudspeaker, ae 6nm,f;ym3cplaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it 6m,na me ;3fcyradiates equally in all directions?    W

  A stereo amplifier is rated at 8wxegkju8s falqvt *-dc6 qs02a. 2h 19jqzv*150 W output at 1000 Hz. The power output drops by 10 dB at 8.w* *zxqgqk9 6v1- sq8a 20jflua vdecsj2th15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicyn )lm4kz 8 owug.*m(fally wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that 8 f .nk4lm)* zw(ugmoythe 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 syste39 bu( fxmsr8oms, 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 tochry62gm/or/ b h lp6i1bt6o9 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 lohcb0*c rgq)i+ ng between fixed points with a fundamental frequency of 440 Hz and a mass per unit length ogi+0 rccbh )q*f $6.1 \times10^{-4 }$ 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 pvy p2g/ssl+ci 5/w a:a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance lvc/gs:5wippasy + /2 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 ih s*lj*5 t0hy; i+0spo 3mjm4 go/xwups near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) i oh xgtl04* *;sspw+35ym/u0jm jhpowith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loopboc ;tbo 2v./v ($\frac{1}{2}\lambda$) 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 tow7app ..abrk )ne in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther 7aw bar.).p pkfrom one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationejo-eg 938+ajl b) i5x e/nfymary. The conductor on the stationary traim+-eb3) 589 ag fnioeljj/yexn 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 steaj(6 emsk*rsvn6q m)s 2m train whistle as it approaches you is 538 Hz. After it passes you, its *ms nrem6jsqvk6s)( 2 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 juhps n7trea 1e b9(q9(hst by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency ha(e1pr7bs ha(9n eh9t qlved) 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 11 Hz. Tfjx w 525 qyv3,kq;m81mo jkxohe shorter one is 2.40 m longxo5x 2kw3 fm;5 ovj8k,m qjy1q. How long is the other?    m

Two loudspeakers are at opposite en n 84bj7fgzi;qds of a railroad 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 heard by the observer when (a) he listens from the position A, ingqij47bzn; 8f 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 is normally about 0cb1c d i9l6*qtnb)d.v .32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reb.6dt)vqd91 lni *ccb flected 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 toward w4n/t2py0ue tlhlw 1r 1x4eu2the bat at speed 5 m/s xu2e wwhtyl4/nu21pr 14t0leThe bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. hd5 defn b9( v,b(*g-ti1, kaxd:ylcrThe 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 f*(91 t di-vndgfa(, yb dxk:,elhcbr5rom one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vi5,qrmlj :br ck98jr4kllage to another.jkrlm 8qk5r:c9jr, b4 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.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of w) fliy)g68 -t)ckcqxstanding 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)-ccxtyfig kw)l8)6 q, 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 loq i8rzs18w yz-ng, slender alumin8i q8ry-ws z1zum 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,
(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 ol6 ,s(.aqt 0.6oimnpdy/ hmh kf hearing for the human ear at a frequency of about 6m sylh./ ndaitpm, . k(qho601000 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 ;carjd8m +/c dobserver on the ground hears the sonic boom 1.5 min after the plane passes directly oved j/8 cr+cadm;rhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is ih l+b;)vkg(n15 $^{\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