What is the evidence that s ha;+do.w iinf:+il+-t c ,bbhound travels as a wave?

What is the evidenceq06 rcm9f2mhx that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a str57 :mm9gawbrzing to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be h mwb9: rzam7g5eard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave pa9u3 zbwr-eia(f3g u7r sses from air into water, do you expect the frequency or wavelength to czf uw-r7 a(3i3brgue9hange?

What evidence can you give that the speed of gu m bmn 2zgd8p0um/q4jm4u/-sound in air does not depend significantly n-m/mu b4 8g 0jdmqpg24/zmu uon frequency?

The voice of a person who has inhaled helium sounds very high-pitched. W nijlrx :qzw -0p/e66vc8kty7 hy?

How will the air temperature in a room affect the pitch of organ p2z1 t+ y,9iv3woev e0ceju ,zg(u+wwdipes?

Explain how a tube might be used ask80kokleq0. v 4a4 goh a filter to reduce the amplitude of sounds in various frequency ranges. (An example ko4l80a 4o.h e0vqkkgis a car muffler.)

Why are the frets on a.bktxw1igx6l p +dd7yo 8k3a3 guitar (Fig. 12–30) spaced closer together as you move up the fingei6d8ydk p +.x 3koa37btgxlw1rboard toward the bridge?

A noisy truck approach4hnkl h7i h3;ies you from behind a building. 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-flh;k 3hhni47i requency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference /rsvwamc1 m(a5 1(uuv in space,” whereas beats cam/uc wa ur(v1s1a(v 5mn be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointss,uao)y v27cp0 1gys 17fqoho D and C (where destruc1ho)us 0o7,yp2a1yc s fqogv7tive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecn.c.8fpmlr h, l ;md8vting the hearing 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 electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more n;hrmp.c8v,ln m f .8ldoise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as -9yzzt8 oxpngvy*w*ble x5h1215mdp a superposition of two sound waves with slightly different frequenci op*1hxl5v-w91*y z5zepxm8yt2dgnbes, 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 shif4ka4 s en,h hq/vc(h-nt if the source and observer move in the same direction, with the same vece/h -vksnahq44h (n, locity? Explain.

If a wind is blowing, willej; m l:r*tq26 m5rxdh this alter the frequency of the sound heard by a person at rest with respect to the sm ld6jrmx2*r5;: teqhource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing3 *tlga.wvv4r)6v w hq. 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 v3lqva *w 4t)vwgh6r .whistle? Explain your reasoning.

  A hiker determines the length of a lake b 9(u,ufspny1by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 b u(fs9uy1n,p s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side ofb,d/fgvl)a ht d27fo qeg2)-t his ship just below the waterline. He hears 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 in seawater is 1560 m/s (Table 12–1) andtavlfge bd,t/-oh 2 d) fqg72) does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air kmu ) 4uhk : :ru8wfj6p(g,lgrat 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 ons0ozi*s.v 3)m9rc( unm4curj a foggy day. Without warning, an engineou9.(4)r mu*c 3ci0j rmnsz sv backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The u m:y;1httv0esplash it makes when striking the water below is heard 3.5 s later. How high is t1h 0ut:mv ;ytehe cliff?    m

  A person, with his ear to the ground, sees a huge stone st15adcrtwsiugk8pw 28:-+ s torike 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. Haw 2+s 5:itsuodcg -8rk1 8tpwow far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second rulnf*4z y:2a vxx5gyh +le” for estimat2g+hnav yxl *z4 fxy5:ing 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 pain level itivz:wg : fzqc(m/(wasl v;82( wl4tof 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 sou9s6qny 5cm rni1wygv0b4 . 2kknd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sou.-dqwpkh i sqe*/,1zb 9(nsr und level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is expl .q kbn9w1heur,/*zqp- ( ssdioded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplaa1ueiyxtv3a8 .h*oz:;2nfr.z cim . d ne 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 down all but one engine? [Hinyac .d he;i o.*mutz z3rx:i1a2 vf.8nt: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBs rgolnof6*9 / enwht j.(3peiq0 x3( xi;p4ng, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ( *jwn9l6n/gfpq0opi4 nxt; 3g.(3xsroie h eeach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a persoai*e e9soxz3 9n speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. 3ex9ieso *za 9$\approx$    $ \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 eards44r2c8d sopy 6x5vwbrum 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 t xm;9:7). vlf/d ceyyqf0vo eihe more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decy ic dve)oflmef:q709;/xv .yibels 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 registy1v4q+m,b sfzfl )8bo6t 4peoered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ztbbqmefs1y ,lp64)o8 + vf 4o
(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 typi5 5c5bplzqx)zu ,ritd -xfga0i.(*p dcally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sot*f(i x -.,ipc 5uqpdrd5)lz gzaxb 50unds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wiljz- vyu + j5/of2 -mou5hckmrfe3 4-tdl the intensity increase? Increa um y-c uztf+-2v35mk4/-odejrhj f5ose by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have huw(3vrtdp s cb- p5e7(l 4ra+equal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of twr r4spl vbautc+ -(p5 de7h(3heir intensities?   

  What would be the sound level va,zisr0,xmob3a6 /n (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air moleculesna,mzra0vio,3 /x6 s b of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 10 2rvl7f4 9*msf scefqn0t;)la0-Hz tone that has a 50-dB sound ltsmrfqfl 2ne9*calf s) ;4v70evel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when theb ey82pkfl 8/j,gps eq8q.dh- sounb/s28.fg,- ekq d jy l8hqpe8pd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge ranch;t kabkwihp27q/ ;n.x1* sm ge of sound levels. What is the ratio of highest to lowest intensity a1xbpi*nkhtw;2s .qc/mahk; 7t
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fu8t x6kc.gcd 6utjkp( )ndamental frequency of 440 Hz. The length of the vibrattj tx8uk6cd)c( .p 6kging portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible fwd)yr, .. o xj)ug/bsovertones if the pipe )xb./)rofyd sg .ujw, 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 yvry/*, c nio zhozj96/ou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed n*i/ ,jozrv69o zyh/c tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanni3 kmvsl b1gxr)1 fzv03ng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?z1gls3r vvf3mk1 0bx) $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wha)5 l 8g0k8odc4 is doxbbyqi4)t will be its fundamental frequency if it is fingered at a len84d) xbk8 iqsby0olic5g4 o )dgth of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E a6- zmf 7wse:0x ydecr7bove middle C (330r6:x 0swz-dm e77y fec 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 op d i4q.):gwtr:n+ebz zen organ pipe that emits middle C (262 Hz) when thenw)ze + 4trbqz :.id:g temperature 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 20 8fhk 1kzhcq1. r3og/s $^{\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 sho 3ie aq.xo2f0h4f5in guld the hole be that must be uncovered to play D above middle C at 294 gxq.5efni2foa403i hHz?    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 reson*7ue,q o)8c2pol pmc oate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe.o pp,l )m2c*o7ec8o uq ----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 tw3v7h7 .oa s,mxgsj.hg-hpf3eo successive harmonics of frequencies 275 Hz and 330 Hz. Wha hjsvho3f77-sa,x gem3p. . hgt 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 )8s:s qsg 1)lmued 3aq tsas.9$^{\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 fob k: 5x4g:zormr a 2.14-m-long organ pipe at mzk:o 4g5:xb r20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is app7 3h7zpam .gg)cxrrf9roximately 2.5 cm long. It is open to the outside and is closed at the other end bygxc3)p9r7mfghz7 ra . the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryinaq0a xla5 k.2fg to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? x ak2q.f05a la±    Hz

  What is the beat frequency if middle rh; kl0k qshgbol fxw+ 44993eC (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, whi j 5hmcjlk32uqax: t9kc20a 7ple 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 when they are p2q ku jkta 30h:527 j9xalpcmclayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when s ay/l2dys 0fi *46mmhnounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What ism062fln4mai y dshy*/ the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 2twoo6w*b1-o y94 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard wwb1*o -y6 wotohen the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eachnyi4y)/f n**)cw kiux try to play middle C (262 Hz), but one wnxiifyn)4 u*y)ck/*is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a f;8.j qgc 2u,ui mv.kdorequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies 8;dui.m qk ,.c u2vjogof 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 03ekrlz5ty+vhc6 t1v n1 hzvk 8w+)z dm from one speaker and 3z8rtn+hzhckvzl)yekvd63t110w5 v + .50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating cbbn +;llgi:zyol ,e34i (j:s at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequen4:+(nis l;bogz3 ,beil l jy:ccy 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 wav 7g(fe(v x/vvf kk3/c-.bqnnqelengths 2.64 m and 2.76 m in air. How many beats per second will 7 / (/xg3cvkkqfq .febnn v-(vbe heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at reiff/yhw9 xx(,wl+/ uci b 9lr/st. What frequency do you detect if you move with a speed of u+wf/9il/,yfr9/liw cxx b(h30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freqijf) 39guo j w7ssdh-va py088uency do you detect if a fire engine whose sireidj wv8jsu )8hg- 37f9 oaysp0n emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freb2l8f*pajxo( quency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s A(l2fp *xj8b aore the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same singlo1g 81oz,pe yret7t,ee frequency horn. When one is at rest and the other is mo ept8te, 1o7o r,zeyg1ving 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 ul 8(j*p.watc olka knk91(ulu/trasonic sound waves at 50.0 kHz and receives them returned from an object movinp(lk (klca9tanju18 /w*k. uog 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 e--bw d8s8(idf qev jq1k; b.z5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freq(wddjbe- .vs bie- q;1kz8q 8fuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedx* 1nq unxb0i 7h7;gej 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 sta*nbhgn1 quixe770;j x tion. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure tounz1*/2qx irt0v9(eby/o +cqc m*hblood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound inr q( m*thuonq9 ecbo/xt/y20*1ic+ v z 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 the sound source?   Hz

  The Doppler effect using i3h ;k r3kl.k(kqtv w2ultrasonic 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 frequen0+95k2lvw mifhpf;c ycy 570 Hz. When the wind velocity is 12 m/s fcw9py2 fh+;ik5 0 lfvmrom the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on lanywz (wi1mlr3.var. 5j d 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 0 cr zeg* gjr5-b:tf/xsound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s je:5 xz0 br/-tgcf *grmotion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speedugbn/(7c xral ;c/ u4f of sound is only aboutfgr cbx/(ucn/;ul 47a 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.6 1wa)ol*nfrt Determine the shock wave angle it w)1for6lan *tproduces
(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 ax +jhllh, d5 +rq:f7 x;0jwel$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and senpm:pj3n 9rupx;* tf i98f wg0e a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance fxjn*wum:i r t9fp8 9 pp30n;gof 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound msbt(az-5/q zpulses downward from the bottom of the boat, and then detects echoes. z/ tqm(5azbs-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? 9wug6gckc65w4fej+5(zc w mf $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer w21q0:a.i,gfep/* ppggahcz pipe symphony. It consists of many plastic pipes of various lengths, w*ew/1 ,.apzhgp:if0apgcq 2 ghich 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 tozq4n) wkav 4s11to x2e the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes1xvaz4 w4 snot)qe21k?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sounf)j;:dc t;fhx0g yfu7 d are heard simul)hjg7x0;dft c;u:f fytaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What9 l gnjn/xr.2j is the acoustic power output (W) of tng.9/2 jrn xljhe speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rat/06tar(t94j g3;rcnr 6x vyd/nkpjkged at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What isvapk6/ 6g k/nc( gtr;jdt9xr430njry the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivif2;od +- yfz5b5rajdrh( 2r-nib7 wb e 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 would be the power intercepted by an unprotected ear at a distance or; njbbrbf25 ifhz7-2(i - +o5awdrdyf 30 m from a jet airplane engine?    W

  In audio and communicationsyxc4+t prw)b; systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fro,iiwt8 v ks )/8j w vq-11th+zgcant+equency 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 1o wm* n/ ki1oy+w*ug6jh7r7srsw64lowp iu; fixed points with a fundamental frequency ofrhujs;iowuk /7w7wg*+ow 11 pl onir6*6 sym4 440 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 vibrbmztq00). 9e6ao+v+i awzj*9dr b hovation above 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 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 forkit aemwvrb+o o9b0z9 q).j6 0hzd *+av?   Hz

  A 75-cm-long guitar string of mass 2.10 2g jeaa79hlbnj/h. (lg is near a tube that is open at one end and also 75 cm long. How much tension should be in the stri9/g(ljblneha a7h j.2ng if 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 resonate as ods9xi 5g+-2 pkz4s mvgne 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 sources sqvnfj9- ,y g*fkhtv)+ j:yr2. The sound is loudest at points equidistant from the two sources. To determine exactly wh2yykgtsrvjhf+n) -,* f9j :vqat 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. O mrk3b7 0lx;zyne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tra; lxy3 kb70zmrin?   m/s

  The frequency of a steam train whisti,udi)fk u1. bs2 ac8uw-ik1 yle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume consta -)1a.u2kyd bc1s,k if8wi uuint velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to sf osop x)3ae79/ u17zr zl;1hovc6fzthe difference in pitch of the engine noise between approaching and receding car)3;r7z 1uss 6xa/ zocl9ofho1ze f7vps. 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, sor/fe o(irsz;,)cisu+ fz 4dz: unding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How lon 4sfrf+)ozd,;/zer: (ziics u g is the other?    m

Two loudspeakers are at opposite ecs m dy ca(9q;h:2dwi1nds 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, in front of the car, (b) he is between the speakers, (;sw ih9:d1m2cc qyda at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood2i-8v xmb pz (((xbrld flow 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 from the red blood cells? Assume 8pv(izm lx( bbr2(-xd 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 ftm9zfg0j yw i2uai26n*t6/3/bb m iyelying 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 thiytf66zg ey wi32/*nb0b/j9ia mt2 ume bat after that wave reflects off the moth?    kHz

  A bat emits a series of hig0 kvh4ls5lha-sf ch97h frequency sound pulses as it approaches a moth. The pulses arec lv04hfh s 5s-k7l9ah 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 from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from ug31d+hqm3tj 9 mg0vu one Alpine village to another. Since lower frequency sounds arg91 gutjm3vh+q3du m 0e 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 li* md4k26wx9.67rue yaebttxu stening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressurea9 uex 7.rt2m 466xkyu e*btdw nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, bb8 /)7 ad7p9ijv 8wg7jfoxqgcalled “singing rods,” involves a long, slender aluminum rqa8fbji8b/dgpg )x j977w 7vood 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 itq rzu,c/ayn /*wg59of hearing for the human ear at a frequency of about 100 wr,*zt cn/a9u5i /gqy0 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 4 i 4zef50fr77sva ac (:xdyuf2.0. An observer on the ground hears the sonic boom 1.5 min aff d 4uf7af5ie7z4cv:asr0y x( ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb4( xw ta m*w8:p9qq/w)podde zoat 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