What is the evidence that sound travelyv t*4 a;itia4s as a wave?

What is the evidence that sound9 sp/ e1do o 8v8(:yfi2ileg jcf(i,gz is a form of energy?

Children sometimes play with a vq;dl.nrkl5 9 homemade “telephone” 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 tqrl;k d v95ln.he other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into -; (+t w 9hidt+fzbulhwater, do you expect the frequency or wavelenitw+ bu-l ;h z9tdf+(hgth to change?

What evidence can you w )*+z)fucqu ogive that the speed of sound in air does not depend significantly on frequencyuf zcu *+w)oq)?

The voice of a person whow-g: k lk9d)8 3j05xf c5rxy,hztc ibu has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ ozm,6dy 86z,3fbdix f pipes?

Explain how a tube might be used as a filt- 0ps7tgc qb(k;j- l f9ypwa:i sx;vm*er to reduce the amplitude of sounds in various frequency ranges. (An example is a car mky -t(;f ;wpvjcqxa*s 0sg m-p7bl :i9uffler.)

Why are the frets on a guitay sgea tp*p01)s)uky, :2p gupr (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridgyke u*yppa,gs pust)12p)0: ge?

A noisy truck approaches you from behind a building. Initially you hear tjrg:9/:pjg 4* zdr eait but cannot se/ d rzj*g:9je: rtpg4ae 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 space,” whereas beats931g aeb6a0m ( cbxk(ottnxs+ can be said to be due to “interference xek31tm 9+o 6xtbnaba c(g0s(in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lot)v4gt st/yg dfo)1- mwered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together? 4tt)1ftv/-o)y s mgdg

Traditional methods of pr p g63:,kdpzwwotecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise leve:dzww 6,g 3pkpls. 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 noise reduce the sound levels reaching the ears?

Consider the two waves s;6p rqjt ii9k,hown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Exj6 i, pq9;rkitplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in thwv/ ;1rrvzomf7l (q7qe same direction, with the same velozr lr7f7(q wq/vmv;o1 city? Explain.

If a wind is blowing, will this alter the frequency of thxeebo3,4 jf7 dl65z6nr nw.od 3xy 1.uijygs7 e sound heard by a person at rest with respect to the source? Is the wavelength or velocity chang3gj wre d.f.uyl ,5j6xo7si 43y1oez7 ndn6x bed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitor/vr:w*axk 7-fx96 l fcrp*wcy is blowing a whistle /*-ww vrkrfyax x:96l 7 cfc*pin front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length o7vp(fs r m,*w w4pq/)wle-ewdf a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the e,p)f e/dmw ( v*-4pw7lswr wqecho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just belol, rn j;hgap(5jkl80*t6zpobw the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2. n *05g; pallp8rz6okh,bjjt(5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelj 5v9bw5f2 u (hnm1iqaengths 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 fogg jqz-d+o esp62 .8ny e-b8 om0cvgye+hy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much tih88dy2y-+e-pne+0 g o jovmzq.bce s6me elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strip,v/: m3jp 0( rgzqxytking the water belowr3:qg xmjy pp(0 /ztv, is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conc h lw+st1)bkt7rete pavement. A moment la7ts1l bhw)k+ tter two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distt .;jr5d 4cx9 :ph0*qa dbhlmcance by the “5-second rule” for estimating the distance from a tchlqa:m4djh9;p50.* r bcx dlightning 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 12 4;wo *q19egk8d4+jeoluhw az 0 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inten c,kpw30bd*pg(g,ik usity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 oi8eka 261 vxwk4ki7kknlj-1 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’slev k1k1i-kaixkj7 nw86k4 2o .]    dB

  A person standing a certain distance from alqfa(v 7f0sf: n 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 :afqff70l (svthe captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wherea 76igrfk70irtznzu*9g)d0 a xs for a CD player it is 95 dB. What is the ratio of i ndgrxi0)*7 z6az7r9 t fuk0gintensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal co )w,9ylawdy,r k9qgxew3bo.4pdep9. nversation. Use Table 12–2. Assume the sound spreads roughly uapeo3 yrdwyw,9 w99 )xl4kq,ped.gb.niformly 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 i0 1y6c pcv/vub.mq1b eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the mg tz0(gh0fp5 . lek)huore modest amplifier B is rated at 40 W. (a) Estimah5 zglkp(e0g0 .)huf tte 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 twn+-,n e tp7cfront of a loudspeaker epn-+7wtc, tn 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 2.0 d1wfde b4e-s v1B. What is thesfb 4 w1ve1d-e ratio 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, (a) by what fact b/s sx*j0p7cmor will the intensity increase? Increase by ax/ 0cj*p smsb7 factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bu3b ,;aggvy q4,w-h hzft one has twice the frequency of the other. What is the ratio ofv qz ; ,gabg,fwhhy-43 their intensities?   

  What would be the sound level (in dB) of a sound wouy,4( 3unt :*h a+hqcf ard* y:7:dxm bky(zqave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3y:urac*ybku :7f a + t(,d zhxnd:*3(qmhoq4y00 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-s-vzb p9/a :csHz tone that has a 50-dB souca9p:-svb/ zs nd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can d asl8oscc; h 1/r8;hksetect when the sound level is 30 dB? (See Fig. 12–6.c8h; klrhssas8 1o c;/)

  Your auditory system can accommodate a h 2die(r+ vph rz0ml)v2uge range of sound levels. What is the ratio +2rpzm2()lie0vdh vr of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length ro*)r8sunm,1 w0pubib 9 ( rnaof the vibrating portion is 32 cm, and inu0(nwr imru osrap *b891)b,t 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 a3txkk zb7.6-)iwl0pu s mrm*l udible overtones if the piper m6zut)-s3k *w7x pmll.ib0k 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 top of a)+t 9. rmdes o.ifzwry2 u3c:dn empty soda bottle that is 18 cm deep, if you asit r w.d.dy)mocfz+:r39 use2sumed 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 witaday( d 3. vviau9*in:h open-tube pipes spanning the range of human hearing (20 Hz to 20a.* 9: i(dau3avyn vdi 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 Hz as1ms a,6pw p 4t 1);hlkdaz wm)nre1z8h its third harmonic. What will be its fundamental frequency if it is )hdnzp)ham 1e w, rl6;wp84s1km t az1fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string iz, f()tshbzvl0 bq 59os 0.73 m long and is tuned to play E above middle C (330 Hz)5btfvz ohl9,)0bsz (q.
(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 Hz) wheg / ty;cbz4ou.g4zb6 mn the temperature is 21/g;.tu4gmbb yz64 zo c $^{\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 203. ru,wtbwlweq)dw+++fx *r2 z.f;+ x kyajwh $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece o*e,1j kkh qod*f the flute in Example 12–10 should the hole be that muoe,d*hkj1q *kst be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz,k8t t5ncsv k30k/x ;gd but not at any other frequencies in between. (vt 5;3t8g c0sn /dxkkka) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates a 3k3gy)qd4 n6q8lzt fbrq8g 7at two successive harmonics of frequencies 275 Hz and 33raqbq3 g6k)qyln 4g7zft 3d880 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 na;lyibo;, /pb6ei 3h$^{\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 au +volrb t t66g99un ju+vlr:1ndible range for a 2.14-m-long organ p1 t:ubvnl9t6rl+ oj 9rn+u6g vipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thg n pw+wggn8)*e outside and is closed at the other end by the eardrum. Estimate the frequen )+ pggnw8w*ngcies (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 tos/p3 g4yi-r(0 j e*ginc vgky( adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the0jykng(csvg 4ei-y(*3p rig / other string? ±    Hz

  What is the beat frequency if middle Cl+iu9 7ppdi;p (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 ook2zfd79jhq*5tya z/( lreh/perates 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 25hfq7 *o (zyte//dlak9zj rhfrequency 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 wii .x f2ryb7v/uth a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fre 27u/iyvbr.fxquency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t l/g+tjw 8.e9/nlntpipem/w v*/ (usl he same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings ( lpv9n/l/. /etgw e/8j+swniutp*lmare played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idensu -3chw h*ee,tical flutes each try to play middle C (262 Hz), but one is a * ,ush-c3heewt 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 frequ0zx /iv +js9/h lm(plpency 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 +9llh/i0s/zpm( jxv pthe 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 sxn8 /+x xzpcrg0za*0jtands 3.00 m from one speaker and 3.50 m fromj z 00gpnrc* x+xz8x/a the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a)m(-e8quy y97.hp x.g57typi e qdophs k3s 9g 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 fdy)3qg q hs9xty 7ygsi pk5m87 p h.oepu-.(9erequency 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 ma/f1 batxvqt53 y+h ms/k 8+jat6h6sdcny beats per second will be heard? (Assume T hqxta+5 bt/h+tdsa6mc /fjy 1v83s6k = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is*8 az8mge,3(6.ctz wf rjli mcn;qf(l 1550 Hz when at restn8a(.rff 3 8lm6zicew,lt*(q;cgj mz. What 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. Whgc1g7 y,rx 0mpat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 0,x7 ygrmpcg 132 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source isc*blvqc4cnl7 . qdhb;vu .,(c moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the sam.n(lbu,hc cvdbc .q* c4q7lv; e? 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 1w4fcdz 8 + d+hxo0sephb;pw +wv0ay0same single frequency horn. When one is at rest and the other is movin; ehb+p8z+yx0wcwv +4foda01 sw d0phg 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 ultrasonic sound waves at 50 ;bej-6d.vkmg.0 kHz and receives them returned from an object moving dir.gvm ;djebk-6 ectly 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 flies, the bat eat7+8k snwes2 u1f)nwli .4el mits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does thue s e2lnwls4 i wf+7ta8k.)1ne bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler d1 8yle k.nvu .7ze9geexperiments, 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 z.nelvg7 8eey9d.1uk rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measured;6 cg/:q zrbc blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tabc6g c ;d/:qrzken 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 f. hgt g3*w4ykultrasonic 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 sous7fzo-v(z :ww nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wilws zwv7f: z(o-l 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 onqn l6ta0r*s 6oxe ;up728xnxz 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 9ncaeok m2ejbsk1e8rtv0 : to(n** 7m 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wavkem* r*be ac7ms:k9o12e(vn to nj80te makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of f:ohuag nw;13 u*q2ry a planet where the speed of sound is fha:g ;*un1w2 oyuq3r only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shgkd1)s:up6anv ;n(t h6o .yg bock wave angle it produces nuytp 6.b;av:(kgh1g s6n ) od
(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 ia)or36widr: x-l +ai$/theta$ 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) nu0cj2l 3wdl exactly 1.5 km above the ground flyincln 3dul) jw02g faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. 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 3gmuuk0gvch9y )wu 5) pulses downward from the bottom of th 3uy0mgv)g 5ukcwh) 9ue 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 pll3 4w3f16vovh, b supu/ vc)there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of man5ih 6m2mxw4m:f 1c 1 yczayr4oy plastic pipes of various lengths, w4wcc4x52r a m:f1hzimm1y 6oyhich are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to uv xbr*a2 +*je 1r tvxlu3j9u;the threshold of human hearing (0 dB). What will be the sound level of 1000j*bu+vxe9u21rxv3at ju*l ; r such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundrqmxb +no5 4j) and an 87-dB sound are hearq+b5mn4xo )rj d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 17:uns,nvo9f8pcjh eut g/ c2um + e *7h5uw)uv05 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally isc,9+fvog7eh7w u/ cmn8ut5 v j )upu2 nh:*uen all directions?    W

  A stereo amplifier is rated + kqyr 534i22kzcikgg njrd(7 at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is theic(r42 z+37jkr2dkgqygk5 n i power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically w(m) cr 4i5/njopgk gp:ear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, )crg4:ppj/g n5o( kimand that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gu8i8 n+bco51r or9 zhfain, $\beta$ 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 frequencff+pfnq5xyu j y : 4*8i:mnnu.+y8uujy 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 fixed points with a fvr9sq: ukp7,y undamental frequency of 440 Hz ak ,7:vruq yp9snd a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration -jxozkjo:h.u/g/2b 4tb 2 q nakou(6r 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.- uo2khubro:jx /ja bt4oq2kz6 (n /.g What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube ,jsrn9f0a -eu that is open at one end and also 75 cm long. How much tension should be in the-fj 0na uer,s9 string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observeqi/u-,17r j.fceq nyh d to resonate 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 toskj m mu3o4w6 bx9:ey2ne 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 6umbe j2: s x9okwm43yand 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 tgj2 ,n-oh j , nict.ev cklr2*6kbg9a:rain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train apto h-er 69 nn a*l2kkji:c2,gbv,.cgjproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 n)bn5g0 .mius Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thebsiung)nm5 .0 train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the difsg7s6 4km 8ali6/.7 beyhcnz hference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightawaya8. s6 kzc n/47yilsmehhb6g7. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The mqxew,/ z1j-jshorter one is 2.40zx, m-q/j ew1j m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroadkj9k,e h y/q51mi olp/ 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 obser ,kpkej/ 1/ol 9iqyh5mver when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what pnyo16 50nkcibeat frequency would you expect if 5.50-MHz ultrasound waves were directed along thnncp k 5io610ye 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 speeth 9 +8avjhl3zd 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of thlhv 9 ajh+z83te 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 approaczl7v0 8c tv :t0,cmwffhes a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before f8l 0vwz tc:fmt,v07cthe next chirp is emitted?    m

The “alpenhorn” (Fig. 12–ew dqzk5c;.p +38) was once used to send 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. 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 whe;cqw.+ dzkp 5ich 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 standtkjn9;g ly 42ding 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 wtg2 j y;49lndkide, 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,” involv)tfic )b;hoe2 /1t kqces a long, 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,” or emit a cleot hqb)cf 2)1/ck it;ear, 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 yv7a y82cncy9 a frequency of about a c7vcyy928yn 1000 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 k2xz h0m rd0q)2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly over mhq )20rz0xkdhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15yab28ba k xe9, $^{\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