What is the evidence that sound plz 0 k6hml 2si09b,latravels as a wave?

What is the evidence that sound is58x1mr kqi 6whwblag6vl65p/fm .drm40q1wu a form of energy?

Children sometimes play with a homemade “telephone” by attac,c:h4a+ *rd 1.ijsro/ enn/q(x av qhghing 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 jra.(s:,c 4io1 vx /hnrqde*+qha ng/(Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect wlshzg;v* 1z0i 0y w*sthe frequency or wavelength to changeyiss zw0w0lg*vh1z ;*?

What evidence can you give that the speed of soundyf9 z w/e,61wgr-fmy*ein 6je-mhi ;o in air does not depend significzwmyjhf,ifeg- iw6/n ryo 1mee6;*-9antly on frequency?

The voice of a person w/krmlh :xq5t ,ho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affec:ly; 9mhg 3 gfj3epap1t the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce 7uh4*fh lk98nr; k2naozm*3 u lxlpy 9the amplitude of sounds in various frequency r4mo92uk; ynhup*9hrzl8n lk3lx *a 7fanges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together .yn gc,6ft-c zas you move up the fingerboard tfcg 6n-z yt.,coward the bridge?

A noisy truck approaches you from behind a building. Initial/;t/u/,xq*.ttkmn-6cn/v kgc akoo hl4hj( p ly you hear it but ca /nu6(t ; q/kj/,op/4ohnkx h ktc.-agcml v*tnnot 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 diffraction.]

Standing waves can be said to be due to “interference in spacd:9cix5z 8m--:cj p+ rkyuviwe,” whereas beats can be said to be due to “interfvu89:p m icx+ c:jw5-rzdiy-kerence in time.” Explain.

In Fig. 12–16, if the f ;),n9) ms ou1xo rwx40gztottrequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move fartox tg9r,zn0t)xmo4s owt; 1)u her apart or closer together?

Traditional methods of protecting the hearing of people who work in ared* j+y4 mz:qewas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more zw* +e:q jmy4dnoise reduce the sound levels reaching the ears?

Consider the two wavesp:6pb ekxod3(7 r4ghe shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frg7pe 6: rph4doxek3b(equencies, 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 shift if the source and observer move in ee1 b)lyk9.)zh b xw3k6q rh3mthe same direction, with theml wyerqx3h)b.6k eb3h )9k1z same velocity? Explain.

If a wind is blowing, will this alter the csyp5d u ozwd3m( p77*frequency of the sound heard by a person at rest wiuoddm7 3*5szp(cy7 wpth respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a c9pz7 s 6;bqralh 0u/ywhild 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 theq/wa96s ;h7l zuyp0br highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lfho2ph(fbt)z35li1 ry k;q+l istening for the echo of her shout reflected by a cliff)z2fqt51h f p3lok b+lh;(iyr at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hea 9v 1ug1d-s*swvkf9 dxrs the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound idgsfds9k9xv- v1u1*wn 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 207zk;,ns6wp tf $^{\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 abofhgr dp,: wwp8-ug;:gys).m dve 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 elas u pm) ghf:wg8.drd:y;pg, w-pses 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. Tq0 win/nn*4 eohe splash it makes when striking the water below is heard 3.5 s later. How high in0eq 4o nw/i*ns the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretela g488b) ,s1kvtpzru pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in 8g81zs ul pbv,rka4) tthe 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 overte3m utds6v* 9 one mile of distance by the “5-second rule” for estimating th6 9utvd e3ts*me 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 pain level of 120 b)zj de6 x ;qqmv;2;lcdB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level ofx+xe15cz5 cbx a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produq5jw9k t*v,bs s6rvu fp1 w2i,a5dwg2ce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is explode,5a ptruk,vsb29vgwq fs25dj w w1 *6id? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fo;1z7w+ak sy: mg-a ifnur equally noisy jet engines is experiencing a sound level bordering on pain, 120 - am ga 7ksn;1y:fwi+zdB. 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 signadsa*/u8bf1dll la7go1pbn. da* )c/a l-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and g/bd 8d) a n .laao ad7*lsluf11pc/*bthe background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fv ta3-*pzqv;a rom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughlytq*a -vpz;av3 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 an 1 *d1t-1jypi lml* rrmeardrum 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 ratkq kx /zc3sy:+wj 12sqed at 250 W, while the more modest amplifier B is ratedc+23x:q/k sw 1qskj zy at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to 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 front of,l9ef5ics1 jk a loudspeakes5e9 1k cli,jfr 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 detect a difference in sound level of 26(+ llh02*qxx p7x,yjr eefau( jxg.b.0 dB. What is the rae eyu7p 2fraxxj j*0x(b,. lg (lxq+h6tio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (ag)jlr1f.+py gtjy7 ) i) by what factor will the intensity increase? Increase by a fg l gjrpy).1f yi)t7j+actor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have pc7tevb;; i.o+a cgu2equal displacement amplitudes, but one has twice the frequency of the other. cgi;+t7; aoc2.p u bevWhat is the ratio of their intensities?   

  What would be the sound levex7o*(bca*o by l (in dB) of a sound wave in air that corresponds to a dcxabooy(** 7bisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what q6lx.h :/bcupcwief/* j87pp sound level to seem as loud as a 100-Hz tone that has cl cf6ux *php q://p wb7j8ie.a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies thatz19lf o,v2q)mkzq4 yz an ear can detect when the sound level is 30 dB? (See Figymfzzk q o ),4qv12zl9. 12–6.)

  Your auditory system can accommodate a huge range kpx p/f98 0gvpl8ns,x of sound levels. What is the ratio of highest to lowest inpxfpvns ,/xk 8p0l8g9tensity 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 fun8ia/ gqk4 pwk(damental 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 mu gp/q(k w4ia8kst the string be placed?    N

  An organ pipe is 112 cm long. What are the fundaw c 1snkwzrzatd9; , rb:joyh4q:55 -rmental and first three audible overtones if the pity;-,rkbh r15dwas4w5 nrjo: 9cz: zqpe 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 blowing across the tt5 x fu(612x*opj /yv)gonvrmop of an empty soda bottle that is 18 cm deep, if you ass(1v5u*j6 t fyo g pv2/x)nroxmumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube piga*4r9n 6dbik.4 hylbpes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ran*r bn694ha.l ibd4 ygkge 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 asf*f5w, -hlr wx its third harmonic. What will be its xw*,h f 5w-flrfundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lo( ieh ug5:u1fnng and is tuned to play E above middle C (330 Hz).5 e(u: n1gfihu
(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 le0. 0lrqhoit1a ngth of an open organ pipe that emits middle C (262 Hz) when the temperature is 2 qial00 1torh.1 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune a:w 6m 0. .lyrpcgcnn4dt 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 should the hole be tt n+ix1 fbb5/that must be uncovered to play D above middleb /+t5 bfitxn1 C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hwkwi,5x x+f7tv+ he w9z, but not at any other frequencies in between. (a) Show why thvwf x 9,wwx7k ih+5+teis is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two r) 1b2 w m qjo/3e-c4fipm:3xuef/ joqsuccessive harmonics of frequencies 275 Hzjuowb3qj mq rc4ixpo13f-/m2e/)f:e 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 ;r jxyc+dl 0x,$^{\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 or6l kc9uu7fn*pno . l5egan pip 5 o.9*7 nu6llnkcefpue 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 c4 u ::;)hw9vbhud8rj 5vcqpz is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standi8vurwphqc u ; :)v:4cz jh59dbng 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 evesq0 -2/ iw nf8wd7fkcnl50ge wry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off eik0c n8-qgf7f2/wdl05w n sw in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzqjd42l.wvm2fd 6up5plsv1 u jy;8z8b ) 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 opentwbp 5q,ftehbn,40. rates at 23.5 kHz, while another (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 qhpenw4. ,b5fb,0t tnwhen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounde (n8 wah7dgy+t (zm fr3e22pzoum6do+d with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain youmf+g2aw3po uz +8rdeo 2hn7( ztymd6(r reasoning.    Hz

  Two violin strings are tuned to the same frequency, rq1u8j kds8o7294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency ho7u8kjq8rs 1deard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two7)k7th va2+v0jlvi fr identical flutes each try to play middle C (262 Hz), but one i+0rfvh7 ti 2)7k jvlvas at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, Ao. g/bcff/co(, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz f/fogc/. oc(b is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible 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 st 0)d mampp;:jhj)pwca: 72xrjands 3.00 m from one speaker and 3.50 m from the otha2mjh x)jwd r:):p;cpmj p 0a7er.
(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 132 Hz, but a pianxu7s khb.bn(0o tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency okxh0n b(. sub7f 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 beats +4:7rfupga;j+r v o0 p(aivba per second will be hea b4:+p; vu0+pa7va(rgfjoiar rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is)07btz d.efeq0gga.t 1550 Hz when at rest. .g0.7ab f qt)gze 0tdeWhat frequency do you 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 detect if a fire engine whose sire zq 6la9qk4fa3n emits at 1550 Hz moves at a speed 9f63lqq za4k aof 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourxw/p ;3 ,obz6rrs.1lu xpxlx5ce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are ,xb1;r/w u lxxpp3l.x6so5 rzthey 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 -cx-gpuv+si; k eo19d frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assumusckdi ep+- 19x o-v;ge T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soundf(qx1 j8oud z h.2yft) waves at 50.0 kHz and receives them returned from an of fot 12u()xhj.8yzqdbject 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 l m yq)kuvlf414 h,a ;nx5mpb;flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hm )lpyvh mf 4nbu;l,axk45;q 1ear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments,wrbzko)8n s ,:gjo /wzet)l :2 a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. rkj )tw8)/,sn2e:wb ozloz:gWhat 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 miqt*+wcq)zdp n b n:n ic)*;n3u0on 4ueasure 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 fo; cu n w * q3u))nnqdcn0:*4zi+pitbnrequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect uen3c8cr4cvfsn *l5 v1 sing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fns 6d ;ulat2uuza1/h( requency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rz hau u;1n6lds/ (a2tuest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its spe41lc b4;bndab0(pn jz ed 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 whereoq6t tf2z( :qt the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of tzt2qt 6: t(fqohe airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wh)(px whkcsmek kk3831ere the speed of sound is os3wh( 3k)mkekk 1xp8cnly 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 f1k+vxys3 u/mthe shock wave angle it produceyf3 sk+m uvx/1s
(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 4x8yjn 53xn+eq -sna v$/theta$ 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 ex46 ( edzzooo)qwn co.si skc*;z5-kb/actly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane b sk csedokz;/nw.ic-z)6z oq54(oo *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 that6ing/e9 ni,4 u.2d0rms6 d5hh impl.0 nrznw r sends 20,000-Hz sound pulses downward from dndu.m5.eh2 r9n,sinr46 0wzipg6/hn mi l0 rthe 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 the human a vlgm* jg( 63p9jat5eiudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a se5 m f5hq;vw7gtwer pipe symphony. It consists of many plw5hvtqm 5gf;7 astic 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 it*)ids q 7kz.1kpcwj xn j*p-8ni;)pa sound close to the threshold of human hearing (0 dB). What will be the sound levej;p)ji.x pd1i zqt* 7kw* icnsnk) p-8l of 1000 such mosquitoes?    dB

  What is the resultant sound level when68h;m3 /j4goqzjojo f an 82-dB sound and an 87-dB sound are heardo4f zjq 3/6;ojho jm8g simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, p:u mbwsf+c g()laced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all (ub+w:fcg m s)directions?    W

  A stereo amplifier is rated at 150 W output at 100qlonqe7(.+ a to6ihvbe/ j n:)0 Hz. The power output drops by 10 dB at 15 kHz. What is th) vobijoae: (qn+/6hn elqt7 .e power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear prom(j,v8w uul.dtective 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 the average human ear has an effective radius of 2.0 cm. What wou.wv ,m (dul8juld 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 gain,/o kjo, eb5a ;kb9n5ul $\beta$ 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 frequency 1fge ..cx.em;9-5 p)npnc nwr g$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points wi-o f1r 0wzv)cxth a fundamental frequency of 440 Hz and a mass per unit )ovfwcx0-zr 1length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tub+rbn(xalo ,srf* c d;+e 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 drd b;s far*+ o,lxc(n+istance 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 x6o2c3bjbv 5za:o9v nfgkqr4l/k k;p.b 1. pqis open at one end and also 75 cm long. How much tension should be in the string ixpcvqzgo l6b4n /9 vjo;qk51abp3. f. b2:kkrf it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res80p0dic jl1z bonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sou0-amhb)u4y pabdq ds,5(ukp 6ph67fojur2 v1rces. The sound is loudest at points equid4-p0rdh 6uoha7pb abpmuq,ys)ku( 16j 2dfv 5 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 conductox3hw5oyf: so q 0lu+u3r on the stationary train hears a 3.0-Hz beat frequenclxwsu+uh 0f3: o53qoyy when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appro7q +)f+t idyb-2qh fcwaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)? cywq hidftf)+q7-2 +b   m/s

  At a race track, you can estimate the speeo +e-/hq rfo2t+h1/gi1 a) gv)ognq mbd of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain ca2 e/btmr1hqo+ -)h g+ifgnq1oaov)/ g r 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 frequencyn6ocqnf wsw.jg79 *i- of 11 Hz. The shorter one is 2.40 m long. How long is the other? 9 s7in6.wg fnw-co*jq    m

Two loudspeakers are at opposite ends of a railroad car as it moves h z.5ocm3 j4rmjt z o3yn68m*spast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have 8 cm4ry3nm*.j5zmh63 js zoo tpassed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 k4yj ;fe8 1y3 52kiwndkw5xlam/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the52f5a jxky4;kl1kn yww di3e8 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 flyi:u;u-1opsxn ing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects1spu;i un:xo- off the moth?    kHz

  A bat emits a series of high frequencyzk tm4jay2sjsbp:,1 7,u isp:-lvk1w sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 1l1 s i:bsk ws, vjj-4:2uky7mzppa,t3.0 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 mm j:rc6f 75(4dfpv qvsend signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. Wvcdvjf m7q fr5m(4 :6phen 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 stand ew8 me/6xpd2nevj4t 1ing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the 4evm t62dx j/1nwpe 8efundamental 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,78e r1 2oe/t. gbg3jdc lb:ddt slender aluminum 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,” obg1t ed/ 38cedr 7.btlgd :2jor emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a fwl)j)yk0zt 3 g-j-szf6y odox/is s) au93, mxrequency of about 1000sw-y )sz3us 6o 9 j g /lzx)txjm)0do3a-fki,y Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer sgtdzs :py/fp jp4*(w;2/qbv on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitjp/g */4wb y2d;:p zfpqs(vstude?    $ \times10^{4 }$ m

  The wake of a speedboaivju aoate/ ,a) wpn27vqr 9n; y6.0ift 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