What is the evidence that sound travels as a wavc .c1ihljy),d z*te 7je?

What is the evidence t 5tk1rb8 jgh;z* assa9hat sound is a form of energy?

Children sometimes plagelsz k 6 2y/s41gv7uky with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaksusysv /1k g7kez2 4lg6 into one cup, the sound can be heard at the 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 ) j-o)xx9ygp:(c fuqninto water, do you expect the frequency or wavelength qju(o-9xf)n g)p: cyx to change?

What evidence can you give that the g/gom t+0z0x*)z1m;g foz jfespeed of sound in air does not depend significantly on freque1zgtfzeoo 0/fzmg+0;xg*j)m ncy?

The voice of a person who has inhaled helium sounds very high-piip:a f+6nap:y(+eud8e1a ubj tched. Why?

How will the air temperatur-8*2jg8/i balmzyajt lo hw cb0n* .k8e in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce ty4 jxa rn5.5kthe amplitude of sounds in various frequ.tk y4xnja5r5ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. /nk1mfmies y2dx7 d ,m ;0v4sz12–30) spaced closer together as you move up the finger n;k4m7zs/m0 d12s, ymidvfe xboard toward the bridge?

A noisy truck approaches you from behind a bu;w 846 utw(pdb( wljdhilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on j(wb6h 4l(8 uwpdtwd;diffraction.]

Standing waves can be said to x5ccvuo vq 4d/nu 3p( vcf.7j)be due to “interference in space,” whereas beats can be said to be due to “inter(vc d/j54u cqc. pnofv)u7x3 vference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would t)y2jv ,y- )wfzhw8gg yhe points D and C (where destructive and constructive interference occur) move farther apart or closer togevj2w8-h,gf zy) )ywy gther?

Traditional methods of *xg d0 l.zb, na.cg+sfprotecting 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..d c g0zf+*s,agn xlb 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 wavesf7akzo w-29q u.hw7;do a)nzw shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies,owwz w.79u7 z)of ;dqaa-2hnk 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 shqipy+ l: uhj))uy pb77ift if the source and observer move in the same direction, with the same veloc yul7hy))+jpu pqb :7iity? Explain.

If a wind is blowing, will this alter the fre r4yud nuzot88yaq4 03b4 p:xtquency of the sound heard by a person at rest with respect to the source? Is the wavelength or vedn8tao4y3 xpury qtz8u 40b4:locity changed?

Figure 12–32 shows various positions of av,u-;u4 zk5cl1wcq3 +dlognh child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain4;zwq -31 u5clku clvnho, g+d your reasoning.

  A hiker determines the length of a lake byhe5 cp 2/:xsyo2ir8on listening for the echo of her shout reflected by a cliff at 8 / h2o5pcionexs2:yr 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 he; +slixk3mzb v0um3q-ars the echo of l +uvms3;m kx3-0zqbithe sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavee)of u8jcig(x69k5s d6bgy i- lengths 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 foggy nsl;iq j t0g )d(os e;c2w/zz0z:pjq)day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire i zn)0( ;szztqe djqgio;lc/02 jpw:)s s heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makpmo;afs( 8oy + x s-)lqwbwd82es when striking the water below is heard 3.5 s later. How high is the88o 2s-)qo day s+lf;pb( xmww cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the dm j kztq uzy)va14+. j*od1d9wg68yxconcrete pavement. A moment later two sounds are heard from the impact: one travels6oav. jty*ydx)qw +z1d1m89dj 4uzk g 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 dista;,4xa6txl6i+.y) gre: u zdy ebis+r once by the “5-second rule” fxil6 ,z reg; .+uo db) y6as:+rixtye4or estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of aa p: 3hc,sxm/ttg 6x6s sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inten7gmgi 3 n:h;2tw26dv5r hzaivsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers p0jxmr l,3ogmtx/k 88x roduce a sound level of 95 dB when fired simultaneously at a certain place, what will be thomkl8 ,x3mg8tjx/0 rxe sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certa) ;zozys3 kq3lin distance from an airplane with four equally noisy jet engines is experiencing a sound level k3l3 ;osz)yqz bordering on pain, 120 dB. 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 signal-to-noise ratio of 7jrp8(:tfa;8 uwvapp 58 dB, whereas for a CD player it is 95 dB. What is t7;ar:8f wpp(tajp uv8he ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpute:ask)/0qfebz f 5 la: of sound from a person speaking in normal conversation. ):q e0eaf:/b5zslakf Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ar ;r8wq.gqhpt6 w4,qsg jji-,f ea 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 more mode4q7 5n in1.5ovst ybfpst amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.pi.5nosf75t 1bqn y 4v5 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 ofrn4v .aw+ lr im9mcmkc 3,k-0f a loudspeaker on 0vfk+c .3m- imw9mark rcl4,n 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 diff6 2 i2pldcagdf8gap.6erence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Secdfgl.8i2p2 ap66ga dction 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (/l+.b-- i blj4ou+pf*hec sa ha) by what factor will the intensiu+-lc4eaoh+.i/bjhsl *- b pfty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one 7t(hunt , z3pel:bm6 mhas twice the frequency of the other. What is the ratio of their intens,3nme: b ht 7tpzu6m(lities?   

  What would be the sound level (in dB) of a sound wave in air j3(/ur+ dorqlfv. odgyy9c95 that corresponds to a displacement amplitude of vibrating airo95gvq+dyd/ o rcufy(9l r. j3 molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whaylkr.ysscb f;)/r7c* t sound level to seem as loud as a 100-Hz tone that has a 50-dB s)/yclsbfsc7;k. ry r *ound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear cay50n x*4njg6nzuq lh1n detect when the sound leve nz61 4gunl0x y5q*jhnl is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soundv *8mw u.mxe)k,2 eyoq levels. What is the ratio of highest to lowesmy x* )emow.8qek2 vu,t 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 leng3qoax w 3e:u5 teh+q0pth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must teq: eaotup+hx03qw 3 5he string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first s sp.2,e7 )(3;vj alpb f+gobnyzv2xr three audible overtonex2(ap ;lseopvz+v )b r bgn3,72yfs.j s if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blolircozu p7:( /acte ) t)6.muewing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a clos). oeuup)(:atc6le/zi m 7tcr ed 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 spanning the /- wdbn:eoe5 p h7j;dv.n(skk range of human hearing (20 Hz to 20 kHz), what would be the d5 b e:w(k ;dp-sv7nheko.jn/ range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freqt95 .3qiks xlfuency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length offxtl q i.5s3k9 only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long ann jg7g 9)l.sxeu q+l9ud is tuned to play E above middle C (330 Hz). jn).+l7u9gues9qx gl
(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 ope t 7vs5(xhy/tsnra k0a1 *+is;lqg3pgn organ pipe that emits middle C (262 Hz) when the temperature is 2rak *5( tx7sq3an+g 0ts ;p/hs1yligv 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 at m himln+pwz8 az8z)9 320 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Exam- )k. z5bsqhnuple 12–10 should the hole be that must b.k) bzh 5un-sqe 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,z+v0zrqsg :e u u7/w(v and 616 Hz, but not at any other frequencies in between. (a) Show why thi+:u7vqzezs(/ uwvg0rs 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 bjjmn/bhne9;e 9kpzfv cr )5aha1( i,-oth ends. It resonates at two successive harmonics of frequ51 mn; p)9k/j -jz9ahrc,(hfie bnevaencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 ks:3,, wvetrg$^{\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 razs;1yprsuq 5b 32b j,pnge for a 2.14-m-long organ s2pz;, 1pbs 3 qubyjr5pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2knpdk6l rc 9au1-e637)a ycws .5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the re9d6 7ku31cyk) prl 6-ceaasn wlationship 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 sbau7 2vfb0*w y when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequvbbwu2fay 7* 0ency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) po +, (hb* mu:nho.1e) y3wct7lit zagand $C^＃$ (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,h / amqfk;b1. bjf -xnx,0pbc- 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 occursfbcb b/k.f- 1pma 0 n,xq;jhx- when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 z3crig1y3 :yu beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the3y1rzg uc:i3 y vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequ;:uda*+qmap gw( poa+ency, 294 Hz. The tension in one string is then decreased by 2g+p:(aq+adou *pw am ;.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try ;bleht:qxn+mc+fd4, to play middle C (262 Hz), but one is at 5 :dxfmqe,c+t ;+l4nhb .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 6nr)flj9r m1mg44a ldfrequency 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 of A and C? What beat frequencies are possible when A and C are soundednfa g6m )ld4rm19rj4 l 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 stan7 qafnd+ (0 hxmz+na4mds 3.00 m from one speaker and 3.50 m from the o an74md0 q++ (hfxmnzather.
(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 ashb2s)+7tsz.z4:(ut s diqmm piano tuner hears three beats every 2.0 s when they are played tts(qums7 hz)m42bzi+ds: ts. ogether. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m anah tcn83m+pz2 d 2.76 m in air. How many beats per second will be heard? (Assume T = 20 mp 82tnh +c3za$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when ae mz tq61ehe0qy4jf6g8 gc3b4t rest. What frequency do you detect if you mo 6f0byz4qgjg cee638t1eq4h mve 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 ife1boo 2,a0rd.p (fxnug4l se6 a fire engine whose siren emits at 1550 Hz movesg4ol0,(2e opdf .xaerb nus16 at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towc58lj a b:l+rhard you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exj+8:l5hlca bractly 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 smtkt)d h qmv 89bwj8.8ingle frequency horn. When one is at rest and the other is mov9vbk).wqthm 8 m jt8d8ing 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 50.0 kHz and4)h;c+9e4zjw-q3pfuf aep xx receives them returned from an object moving directly awaax 9u4fhq j ; -+)4p3efepxwczy 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 ak9tofho+f)kq -h p07flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hahphok907t- + f)qkofear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba wt2 (l:eqb7 0qgd ss)6aua8 kijas played on a moving flat train car at a frequency of 6)ss0kgit8b lj2ad(: 7qeu aq75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavesszy n(kjmv9.x 1k0dh7 to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of soud(jkyksv 7nh1m x 9z.0nd in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freqp2 hb7.b nuin+uency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the windx: 8e*aaftzvdjf 59y 7 velocity is 12 m/s from the northd* 7t:zxa5fvf j89 eay, 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 objec9exxwt:dvdev6f 7h 72i8re3 kt moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speediwc)rnpx /+v/x3o*0c 8 wdswi of sound is 310 m/s (a) What is the angle the shocrni xc* ) /pcs owvwx+3w/0di8k wave 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 a planet where the speed83.ykhi1 v ny4 ;.brqjtqnpd) rt. h)x of sound is only about 35 m/s q .th.i;rqy1n4 brv.dx 3t8 p)ky)jnh
(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. Determjrau/. :vb++f )jb yievuio1*ine the shock wave angle it producesa*iuv jji).obu:1/yf++vrb e
(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 vusik ,k,96bqp/i c0 p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fy2cx2q2x9hz-p f os; d oxe6.ulying faster than the speed of sound. By the time you hear the sonic boom, the plane has 9u22-6.;2xx z hcsox ydoqefp 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 s+ -y0qkekhv;r1s ldy0 ound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in frkyl0qy +d;1- k 0srvheesh water)?    s

  Approximately how many oct+l-3j y 5hcrgkaves are 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 consistog k:*pu;pl *t4l 3bris of many plastic pipes oou*k g3i r pltp*b4:l;f 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 frl d+)wj( fcjsp;nk4m7e kib; 8om a person makes a sound close to the threshold of human hearing (0 dB) jef 7sn8wm b+p;cjkld);k(4 i. What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are d jp 35 f +18be45dbxndnzxsr:heard simultaneou3d5d+ exr41 pj85bd:n xzsf nbsly?    dB

  The sound level 12.0 m from a loudspeaker, placed in th8gfx59yh 2o b ;xxg,sne open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming9n8g fsyx,x ;gx5 2obh it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output a. :g5, dgsdibvt 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power out:.d,5 ibdvggsput in watts at 15 kHz?    dB

  Workers around jet aircrafvgy0 ki5 6d;qdt typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective gd5i6v0kd; qy 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 pmp5+kz6cr j1gain, $\beta$ 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 viol*/q1r0qys0: aiyvf x tp+cu4lin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed yx-- 0e50yn1p jhk2vkoza9tcpoints with a fundamental frequency of -v502okc 9j-k1htay yx eznp 0440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration abovl5azj0 .d;+jl2 gdizte 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 aga+lgdzj. 5 daliz j0t;2in 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 ibbgzuz2*00 l avu8dz ;s open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (inzzdb* u v g8l2a0z0bu; its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obser/wi/i4z3g vit.ane:aved 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 tone in the 500–1000-Hz range cominh0+a fe(:k)zzv*2kndb ro t5ng from two sources. The sound is loudest at points equidistant from tofzk5nav(t h*kzebd2+)r : n0he 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 whjq(l3 b: 9 lywi, tkz7qnnxb)oe8m7q7istles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz t97 qe ln:w)kx7b (o l,8byiqm7zn3jq beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it osg- ovw+2my3approaches you is 538 Hz. After it passes you, its frequency is measured as sm2y+-3goovw 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis7,d g) c/h5utco .iquitening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway/ dhu.cc),iiqu7t5go . How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency oerwvot4:ug z+ 5xq,;k l7bxz6f 11 Hz. The shorter one is 2.40 m loxxogult zr;: vqk e wz+b46,57ng. How long is the other?    m

Two loudspeakers are at opposite ends of ec+g(h )- gztj y68mkxa 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, at B, and (c) he hears the speahygk ) zt8ex+ g(6j-mckers after they have passed him, at C?

  If the velocity of blood flow in the a tz9hfbxqw.0 28rcmq /orta is normally about 0.32 m/s what beat frequency would you expect if 5.50w zc28qh9/ft.r mb0qx -MHz ultrasound waves were directed along the 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 rg 4wb.kl e8 ,+mzy;6 6g,fu4cicuf zbm/s while the moth is flying toward the bat at speed 5 m/s The ba +f eybcm8gu,4,zzf6.i;r bwguk6 l4ct emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mothruz/ uknl z347. 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 u3/ 4l 7uznkrzbat 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 one Alp 86fbr5 +w4; 0cjrdff;f*qltk y+ikxkine 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 which overtone is close to F shjdfl6 f+xrk+ rwf054q 8ki;fy;*bc kt arp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo l l1o- b wd*fll+j;rnouchx5--istening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the 5-o-*;hw o-dbx f+1jcunlrl llocations of the pressure 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, called “singing rods,” involvedl4k,/rs tv(4d2y 4nd gh-gp 5w7iv+b ezb/zws 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 clear, loud+p wl2z7drv -s kbyz wdi 4(/5d,tb hvn/g44ge, 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 hu9zy bn5pj aw6(cfwli2 ;ua/s)man ear at a frequency of about 1000 Hz is y9b)a/nip65f2 w ucjls(aw; z$I_0$ = $1 \times10^{12 } W / m^2$ 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 atcd55aaz kk,y+ Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whatak, +a ykdc5z5 is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbsn33g)k,z3 wwa;w l gzoat 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