What is the evidence 5qw/, e mhdyjifx8 o,8that sound travels as a wave?

What is the evidence that sound is a foxx 6eyy6;sl( gu5e-n drm of energy?

Children sometimes play with a homemade “telephone” by attaching a string to t* tlj i2m l2k cl-7ciz8h0by:jhe bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from hl* ill 2mz -k0tic:78c2jj byone cup to the other.

When a sound wave passes from air into water, do you expect thk1 *q lt lbc*wqwgm4vc.6 -*e p:ll0lme frequency or wavelengtl4l .ml:lw-l*gqb cqmkwe*0vp*1 t 6c h to change?

What evidence can you give that the speed of sound in air does not depend sif3n544ypobc tw udzrtkg087* d w+:iupa; vc4gnificant5w poud+i83f7tg4*ctrnz v;cp:kayb u404 wdly on frequency?

The voice of a person who has inhaled 82nn:1h:x0blib7a - wi u qopdhelium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orga/gm. 2hp0ih )njz+hem n pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds i +fidgol(, pcy)0x mt3n v lf(p ,cx +mt0gdyo3i)arious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced cloc3 gz wfz*3fj1 r0illv3:rrt c8ay0e)ser together as you move up the fingerboard toward t1r)ci*l3 r gyff3zz8 te00law r:jc 3vhe bridge?

A noisy truck approaches g6w 0i/x6blx fyou 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-frequency niwxb6 xg 6/lf0oise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” a.drj/oa,ca+ ) o lr7mwhereas beats can be sar)a cormlda o.j+ 7a/,id to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the /2u e8s leox5 6/tz-tfsncq6 s+z,ubz speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer - 6nze85z6 o2teb+/uqs/ ts ,cflxusz together?

Traditional methods offgz90c :a.v(un2r bqil;s rc) protecting 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 t2:lab.;qivzu f s9g ()nc0cr rhe 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 shownlgtzk/yiq 98i(zkson3 x 6t36 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 whi /8 i l i6nzks3yg(6tt9qozk3xch of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source jvb 84ct9rd.r and observer move in the same direction, with the samerrdb9tjv 8 .c4 velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hea4dyp ar i xf7*5fv-w.yw6fyx8rd by a person at rest with respect to the source? Is the wavelength or velocity changd 7 x*6yaripxwv-w 8y.fy5 4ffed?

Figure 12–32 shows various positions of a child d jn+f-*no u1osx, wp6in 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 hd1osu-pwj+*xno n, f6 ighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the z.7rdj lrt sqz*i..p;a5fr:jecho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. E5s.jrr* jqzf7 z.rta.dpl ;:istimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below th xj/43u4u ynjse 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) and does not vary s u4y4 jxus3j/nignificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 2/0pax3*3ddoz holg 3e0 $^{\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 justs;6*y(uqwvpi )x wxr+/:hb v b above a school of tuna on a foggy day. Without warning, an engine bacps+qhr(xbw/ 6 * uxvwi; v:yb)kfire 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 clitwe+a;ch8j irh*,p s:)m xns 0ff. The splash it makes when striking the water below is heard 3.5 s later. How hig0s): jh,+nixr8ae* hm ;w tscph is the cliff?    m

  A person, with his ear to the ground, se jxd45 z vrp+1unee4.nes a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travjpu 5e4rn+e dzv x1n.4els 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 distance by the “dpxx pe .u18*f+-fkvm 5-second rule” for estimating the x.pk+ u*efp-x8 1vdmf 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 ts6/.7r le+yva6 mdzfphe 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 inten:6 cicnsi8ulw 9*ba9wsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sow;- 5m4sc a(qyk +x,mjm7pbchund level of 95 dB when fired simultaneously at a certaaw5;pmx( 4yh bm7c+j-qc smk,in place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a cer((pvqh:5knx y tain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if xkqn( :yp(5vhthe 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, whereas xbwq- y(kkxzk 2x wl,a/ec.:w( l*5la for a CD*5zaxxk ,yew2k(w-qx blak wl.:lc/( player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakingacs:n(- ;ixh ckx*s+h in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere cen h*(i;kxas:+ nh xsc-ctered 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 xil ;25e4 tjocarea 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 mbv1 9t 7g7mpfv zn:4cyodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a pv1 4b7 zcv:tn79myfgloudspeaker 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 dBv5ywv+(h ezw8 a *)qzd when placed 2.8 m in front of a loudsa*hyve+5 dw(wz)zv8qpeaker 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 dB. gzx lcp+d h,kp(*k-, dzv90 rmWhat is the ratio of the amplitudes of two sounds whose levels differ bd l czrv, zd mpgh(+k0x*-k9p,y this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatqkt-k n7x5ogcln cn +.+y)1zj factor will the intensity increaj x 51-l.gnk+q7cktzon+c )ny se? 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 havzdq5m4 kx8 9ns twice the frequency of the other.4xqn 9m5kzdv 8 What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air thoa /; uhxf yx0u,q0o8iat corresponds to a 0y/h0;xuixo8 qf a,uodisplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levelen 9ty )xmlzq(4i7wl. to seem as loud as a 100-Hz tone that has a 509tn4( .me x7)qw lziyl-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecab 9 +w)r)su;tcuit1et when the sound level is 30 dB? (See Fig. 12–b9 etwr a)+uci)t;us16.)

  Your auditory system can awoka9p 6ji 2i6l 3evx*ccommodate a huge range of sound levels. What is the ratio of lo 96v2kiw36x *ejpiahighest 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 flchw2e2 6/idk ; +nygof the vibrating n62w2+y efdck;l i/g hportion 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. ;82n zi v 670v5csu/uu(p4gqvywswtl What are the fundamental and first three audible overtones if the pipe is u7 (i0n24q vls 6vuusc5z /;8yptwvwg
(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 expect1a. fwq*q h7 fol(2cpe from blowing across the top of an empty soda bottle that is 18 cm deep,pl(hfofqq e7w1*2c a. if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orp7u* 6 qiv/qixgh2 2pks ;-doxgan with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r2iqx;2* 6iv-7dupx/q sgpkh oequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wh/383 nep s)cbdo 2tbivat will be its fundamental frequency if it is fingered at a le/3db2s b3)in c8vpt oength of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tun kxq3 icfli,yww 3*8(yed to play E above middle C (330 Hz)kw3q,i y(* lf wic38yx.
(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 thatt9tjklgn8ndt*a 5ia8 gs 3;i;c+j u8m emits middle C (262 Hz) when the temperature is 21 jgnjc;std8tn83+ a;ui5* tila 9 8k gm$^{\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 agje*pv/ teb+6t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should thc j+p pu dp7 8+4a2zosxt9n2mhs6mc:pe hole be that must be uncovered to pm42c h6zp+7ps sj oup c:9dapm2n+ 8txlay 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 2 f;d8pw vd9g-tqa:vm664 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this isv6d9awpgf -m8dqvt :; 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 res8hiw4i o3ir:j bey9,honates at two successive harmonics of frequencies 275 Hz and 330 Hz. W 3,i84hbj:iyehrw io 9hat 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 ea 1od,l3zixh .wakmbn yb-31ew m0-;$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-pg 2z. lnu1l .qdb3ht dxen-r3o1sy 74m-long organ pipe at 20 t xdl-n41s1oey. nr b d7g33.ul2zpqh$^{\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 the q; *neods1ewh+ vlhi.8( zoxkn h259m 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 ise en n dmsx9hz kov+i82wh( o;1.q5*lh the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjude *s 1kze.q,tst two strings, one of which is sounding 44e,d.e1z qtk*s 0 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency ifmw8mo*mc8c t2 middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 2ur/bs 0;2bc)+mtrw o:wm h p/pg7z+ms3.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can o7/ws2 ubrs+ twr0 bmhcz:+;m/m gp)p be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4j frc0,mgo.q 8 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of 08qofmrj, cg .the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sg:n8qm hw i6z-y8 reof2d*-wwame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat f w8 :n26mw8r*h w--yqfiezdgorequency 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 to play mjn6v gc 9age.,t u-fs6iddle C (262 Hz), but one is at 5.0°C and the otheregujfg6a- 6 9vn ,c.ts at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, qmii05g h, sx.fyc7foem /t3 mkj*88uB, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded ekf 0i.xm 8smhutgfyoq5, i c *873/jmtogether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker afc+m k.j,n jqs.l/6m snd 3.50 m from the otj+ l/sj.6 cmn,.kmsq fher.
(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 vdij *h/dks; 5yibrating 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 frequency of the other hdi/d 5; j*sky?   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 andvgp37 maea6mu * 1zn+cb l 2kc2g7cqp. 2.76 m in air. How many beats per second will be heard+mv7p2 3 ebugc*c pkgzln7.m6ac2a 1q? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certsq0m dror1 7,oain fire engine’s siren is 1550 Hz when at rest. What frequencyromrosd01 q ,7 do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose si oz( m8b2 /m(-bf 9nbnx4gkcuiren emuf(inc-bn8gb9m/k( bzo4 2mx its 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 frequency if a 2000-Hz spiasv d9 :qqe*(ys: ,nource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly q:pnvs9 ea( , ds*yiq: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 sin 7ha 6r-- k.nm91tn4xvysrpi egle frequency horn. When one is at rest an7sn.1 ve- i4nk6rmxpy9hrt- ad the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ulxio0kdi ajw j0 ;d*9o6trasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is thodxoi* w ;j0ka0id j96e received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at gpu jz8/yv b7pz dw88 q(8+ltza speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does th7v(q/blt z+yu p8gjz dw8p88 ze bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original k .n,mjdhnz(.e7e so(Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the statioh.m .(ejk ozs7 e,(dnnn at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to -leon);v9gp 6j dn+c pm7i1mcmeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s die+) nod9g;cjcv1plm-p 6 nim 7rectly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves;byj65 1vf :w;msq q )qjxc2x jjto 7+mmdgy(( 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 fretpgxgns 0tp; tz8,j* 6quency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, g8t*j6np0 gtxs,tp z; 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 land if its speed at 20 4jz:rd z5zvz8 $^{\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 sxe pq+; ifcu1-ound is 310 m/s (a) What is the angle the shock wave ma ipue1 cqf-+x;kes 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 plane m:+vnly 7p898zccpca t where the speed of sound is only about cnmc8:8p+zyl9cpv 7a35 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 shoc p5.l8szx(ai d(4thwq(; kctdk wave angle it producehd zca (kis (d4tl (tqwx;.85ps
(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 -rkx3xrzme 9. $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and z9pb -p;w qpp,vuzvphvf:5-)k pul7 4 see a plane exactly 1.5 km above the ground flying faster than the speed of soun; kp5v ulvpbfw-4,pq )pz9-7uvp:pzh d. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a son jb/dvuz6 58o 7ulh. on*ho/izpp1sa:ar device that sends 20,000-Hz sound 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 l1o6d:/z5v ohn zp8ps/o*. i7uh ba jufresh water)?    s

  Approximately how many octc p*uz 7tp0d*yd16 iyqs n08mtaves 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 con5.xagi14 kxq43r iud wsists of many plastic x4xiw.d k4iqa urg315pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0m4j+ox ag:q1,(hfh n uhb4z ;t m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound x(tmh 4 uhh:4n+z, fo;jqg1ablevel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound n6nrddd8 5 z+bare heard simultaneously? 5bzrd8 nd6+dn   dB

  The sound level 12.0 m from a loudspeaker, p :; +lw(oxl1 hfkrgb*xlaced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqh (;f +wxlbr:g ok1xl*ually in all directions?    W

  A stereo amplifier iwbf,l)dx v7)kx hys7(s rated at 150 W output at 1000 Hz. The power output drops by 10 dB f b),hld77 svxx(wy)kat 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thei4u wtp 7r(hq3ir ears. Assume that the sound level of a jet airplane engine3ti r(qw47 phu, 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 of 30 m from a jet airplane engine?    W

  In audio and communications systems, n25ua c;hrabu(ewd/9 + t6f-licyl o8the 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 fr(u5 kbsj* pa-zequency 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 fundament/ qn e:3cz7yy4r.8,n 2rkxhgmv +uakhal frequency of 440 Hz and a v3nkryr ,u2+:zc.na84 ykh7h m gxeq/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 above a vexq6 c9lr nm3sbep:/qeh2qc khi0(.x 0rtical 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 wit:.rqb(isxn0 62lehce cmpq9/xhq 03kh 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 fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is4 dt+q re2-er+.s)iu m3 q;g.o+s qjehuu3xty near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it )jim u-ge 2tsrs t.;qqrod3eyxeu. qu4+ +3+his to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed tyk6hl 8pwfx 61o 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 coming from two sources. z rc8)q:lxf;bc;c9, t 8ndbqv The sound is loudest at po l ): ;,ccqv;dt9bqb8rxfnzc8ints equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationr j0ihioji8 (,ary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approioh i j,(ij8r0aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesr /(kib2 juk9h8 e; l7kuqpl.x you is 538 Hz. After it passes you, its frequency i7kk u l.q9xkiep/8;2rhj lu(bs measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening 2hmdda5.vyl 6;5pdi;j+ uii uto 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 (frequencyal5di6u . +;idy5m;di 2hju vp halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat fre8*kb ni o,x9k by s4fth-sxe29quency of 11 Hz. The shk es,to9 9xsfn48b yk*-bhx2iorter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at oppos ng*2/quude s)gjqo;co01 a7yite ends 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 doun0 e*2 )jq7;cu ggoqy /sa1the 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 no 3ga.0+w* 0*ufc qm 4vscpng7kgd.fjzrmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow anw*7czgma0g*k0p.uvq 4.f+fd jsn gc3d 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 sp.dl7p l zvipuk4g7+(yzsq j35eed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave lvzk3zlp y 7i. g+q5dsjpu74( 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 hp:uz)m n6s , 1iis4jvsound pulses as it approaches 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 soj,m is4zs i1pvn):6uh that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usw1r moi5p /kynx d/c6b27cou: ed to send signals from one Alpine village to another. Since lower frequency sounds are less susc 5c d7w rymno/k:2xc61u/i opbeptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stad ryi))s o22pdc/+uwc nding 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 wi y2c/rid2d)c) o+wupsde, 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,” involve9(kjx y*d-l6em15u gsu nmz8js 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 practicey5kz 6j ej9nudlxsgumm- *(18, 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 threshol7u(.igzs6mhn )sz +d gd of hearing for the human ear at a frequency of ab.6(g+zs s)ihdunm 7zgout 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 2.0. An observer on the ground o7c*ub z+s .hrhears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s al7rb cz.+s* houtitude?    $ \times10^{4 }$ m

  The wake of a speedboa b qugi y/-64om:7lgm9cwev*dlv2f6t t 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